Chapter_2 _Degrees of Freedom

Chapter 2 Literature of American RomanticismA Brief IntroductionThe American Romantic period is considered one of the most important periods, the first literary Renaissance, in the history of American literature. It stretches from the end of the eighteenth century through the outbreak of the Civil War. It started with the publication of Washington Irving's The Sketch Book and ended with Whitman's Leaves of Grass.American romantic literature is best explained by referring to certain stirring events of American national history. Historically, it was the time of western expansion. The western boundary had reached to the Pacific by 1860; the number of states had increased from the original thirteen at the time of independence to twenty-one by the middle of the 19th century; its total population increased from four million people in 1790 to thirty million in 1860. Economically, the whole nation was experiencing an industrial transformation, which affected American people's lives. The growth of industrialization helped restructure economic life. The sudden influx of immigration gave a big push to the booming industry. Politically, democracy and political equality became the ideals of new nation, and the two-party system came into being. Literarily and culturally, the new nation needed to express its own experiences: their early Puritan settlements, their confrontations with the Indians, their frontiersmen's life, and the wild west. Besides, the ever-increasing numbers of newspapers, magazines, journals and books reviews provided a great market. All these produced a strong sense of optimism for American romanticism.This surging romanticism also had support abroad. In Europe, the Romantic Movement which had flourished earlier in the century both in England and Europe added incentive to the growth of Romanticists in America. The American writers who traveled to Europe and kept in touch with European Romanticism were greatly influenced. Washington Irving was the most important. The greatest benefit for Irving during his travels in Europe was his contact with Sir Walter Scott, one of the most important British writers of his period. Scott introduced Irving to the Tales of German Romances, upon which Irving wrote some of his best-known short stories. In addition, Scott's border tales and Waverley romances inspired such Americans as James Fenimore Cooper. The Gothic tradition and the cult of solitude and gloom came through interest in the works of writers like Mr. Radcliffe, E. T. A. Hoffman, James Thomson and the “graveyard” poets. Robert Burns and Byron both inspired and spurred the American imagination for lyrics and passion and despair. The impact of Wordsworth and Coleridge's Lyrical Ballads added, to some extent, to the nation's singing strength.American Romanticism was modeled on English and European works but exhibited from the very outset distinct features of its own. For instance, the American national experience of “pioneering” into the west proved to be a rich fount of material for American write rs to draw upon. Then, there is American Puritanism as a cultural heritage to consider. American moral values were essentially Puritan, and its influence over American Romanticism was conspicuously noticeable. American romantic authors tended more to moralize than their English and European brothers, and many American romantic writers intended to edify more than they entertained. Another thing merits attention with American Romanticism--the “newness” of America as a nation. The ideals of individualism and political equality, and the dream that America was to be a new Garden of Eden for man were distinctly American.As a result of the immerse influence of European Romanticism and the American writers' efforts in popularizing it, American Romanticism grew rapidly, bringing into American literature a swelling tide of newness, freedom, and individuality. Basically, Romanticism is often described as “emotion rather than reason, the heart opposed to the head,” as “imagination contrasted with reason and the sense of fact,” and as “a sense of mystery of the universe and the perception of its beauty.” They most highly value is originality and emotional sincerity.American Romanticism can be divided into two periods. The first period or the early National Period stretches from 1800 to 1830. During this period some American writers began to attract notice abroad. Although English literature was still influential, and was admired and followed, American writers began to use their own scene, their own culture, and their own history as the material in their writings. In this period, the important writers were Washington Irving, James Fenimore Cooper and William Cullen Bryant, who are seen as a trio, the first truly successful American writers. Irving's Sketch Book (1819-1820) is the first work by American writer to win financial success on both sides of the Atlantic Ocean.The second period stretches from 1830 to 1865, which has been called by some scholars the “American Renaissance”. Ralph Waldo Emerson's The American Scholar(1837) proved to be a declaration of American literature, in which he announced that: “Our day of dependence, our long apprenticeship to the learning of other lands, draws a close.” And he told his countrymen that: “We will walk on our own feet; we will work with our own hands; we will speak our own minds” Writers in this period can be divided into three groups: Transcendentalists, “brooding” Romantics and the Brahmins (literally, a member of the very highest caste of Hindu society). Although all of them share the general Romantic ideas, they each have their own special emphasis. Ralph Waldo Emerson and Henry David Thoreau were the spokesmen of transcendentalism. Edgar Allen Poe, Nathaniel Hawthorne and Herman Melville are called “broodings” or dissenters. T hey were filled with a deep awareness of the human capacity for evil. They stressed the presence of evil in the universe and rejected the philosophy of transcendentalism. Henry Wordsworth Longfellow, Oliver Wendell Holmes, and James Russell Lowell are the three Brahmins, the members of the genteel school. They were, to some degree, New England aristocrats, socially important men for whom literature was an accomplishment as well as a vocation. It should be pointed out that John Whittier and Emily Dickinson fall outside the classification.With Ralph Waldo Emerson's Nature published in 1836, Romanticism came to its climax, Transcendentalism, or New England Transcendentalism.The actual term was coined by opponents of the movement, but accepted by its members, one of whom was Ralph Waldo Emerson, who published Transcendentalism in 1841. The group also included social reformers. Some of the famous members include Bronson, Alcott, Thoreau and Hawthorne.Transcendentalism was a movement among young intellectuals in Boston in the 1830's. They formed themselves into an informal club: the Transcendentalist Club. They edited a journal—The Dial, to voice their opinions. Transcendentalism was, in essence, romantic idealism on Puritan thoughts. It was a system of thought that originated from three sources. First, it is from William Ellery Channing's Unitarianism. Channing (1780 - 1842) represented a thoughtful revolt against orthodox Puritanism. Unitarianism believed God was one being, and gave each congregation free control of its own affairs and its own independent authority. It laid the foundation for the central doctrines of transcendentalism. Secondly, the idealistic philosophers' influence from England,France and Germany, such as Wordsworth Longfellow, Coleridge, Carlyle Kant, Hegel, Schelling, Goethe, Richter, and Herder, exerted enormous impact on American transcendentalists. Thirdly, the ancients: the Greek philosophers, especially Plato, the Neoplatonists, the Christian mystics from the Middle Ages to Swedenborg, the Hindu wisdom of the age-old V edas, and Chinese classics. As a result, New England Transcendentalism blended native American tradition with foreign influence.Basically religious, transcendentalism emphasized the importance of the individual conscience, and the value of intuition in matters of moral guidance and inspiration.James Russell Lowell (1819-1891)James Russell Lowell was an American Romantic poet, critic, editor, and diplomat. He is associated with the Fireside Poets, a group of New England writers who were among the first American poets who rivaled the popularity of British poets. These poets usually used conventional forms and meters in their poetry, making them suitable for families entertaining at their fireside. Lowell graduated from Harvard College in 1838, despite his reputation as a troublemaker, and went on to earn a law degree from Harvard Law School. He published his first collection of poetry in 1841 and married Maria White in 1844. He and his wife had several children, though only one survived past childhood. The couple soon became involved in the movement to abolish slavery, with Lowell using poetry to express his anti-slavery views and taking a job in Philadelphia, Pennsylvania as the editor of an abolitionist newspaper. After moving back to Cambridge, Lowell was one of the founders of a journal called The Pioneer, which lasted only three issues. He gained notoriety in 1848 with the publication of A Fable for Critics, a book-length poem satirizing contemporary critics and poets. The same year, he published The Biglow Papers, which increased his fame. He would publish several other poetry collections and essay collections throughout his literary career.Maria White died in 1853, and Lowell accepted a professorship of languages at Harvard in 1854. He traveled to Europe before officially assuming his role in 1856; he continued to teach there for twenty years. He married his second wife, Frances Dunlap, shortly thereafter in 1857. That year Lowell also became editor of The Atlantic Monthly. It was not until 20 years later that Lowell received his first political appointment: the ambassadorship to Spain and, later, to England. He spent his last years in Cambridge, in the same estate where he was born, where he also died in 1891.Lowell believed that the poet played an important role as a prophet and critic of society. He used poetry for reform, particularly in abolitionism. However, Lowell's commitment to the anti-slavery cause wavered over the years, as did his opinion on African-Americans. Lowell attempted to emulate the true Yankee accent in the dialogue of his characters, particularly in The Biglow Papers. This depiction of the dialect, as well as Lowell's many satires, were an inspiration to writers like Mark Twain and H. L. Mencken.Henry W adswoth Longfellow (1807-1882)Henry Wadsworth Longfellow was an American poet and educator whose works include Paul Revere's Ride, The Song of Hiawatha, and Evangeline. He was also the first American to translate Dante Alighieri's The Divine Comedy and was one of the five Fireside Poets.Longfellow was born in Portland, Maine, then part of Massachusetts, and studied at Bowdoin College. After spending time in Europe he became a professor at Bowdoin and, later, at HarvardCollege. His first major poetry collections were Voices of the Night (1839) and Ballads and Other Poems (1841). Longfellow retired from teaching in 1854 to focus on his writing, living the remainder of his life in Cambridge, Massachusetts, in a former headquarters of George Washington. His first wife, Mary Potter, died in 1835 after a miscarriage. His second wife, Frances Appleton, died in 1861 after sustaining burns from her dress catching fire. After her death, Longfellow had difficulty writing poetry for a time and focused on his translation. He died in 1882.Longfellow predominantly wrote lyric poems which are known for their musicality and which often presented stories of mythology and legend. He became the most popular American poet of his day and also had success overseas. He has been criticized, however, for imitating European styles and writing specifically for the masses.A Psalm of LifeTell me not in mournful numbers,Life is but an empty dream!For the soul is dead that slumbers,And things are not what they seem.Life is real! Life is earnest!And the grave is not its goal;Dust thou are, to dust thou returnest,Was not spoken of the soul.Not enjoyment, and not sorrow,Is our destined end or way;But to act, that each tomorrowFind us farther than today.Art is long, and Time is fleeting,And our hearts, though stout and brave,Still, like muffled drums, are beatingFuneral marches to the grave.In the world's broad field of battle,In the bivouac of Life,Be not like dumb, driven cattle!Be a hero in the strife!Trust no Future, howe'er pleasant!Let the dead Past bury its dead!Act, - act in the living Present!Heart within, and God o'erhead!Lives of great men all remind usWe can make our lives sublime,And, departing, leave behind usFootprints on the sand of time;Footprints, that perhaps another,Sailing o'er life's solemn main,A forlorn and shipwrecked brother,Seeing, shall take heart again.Let us then be up and doing,With a heart for any fate;Still achieving, still pursuing,Learn to labor and to wait.Notes:1.This poem was published in “V oices of the Night”. In nine quartrains of alternately rimedtrochaic tetrameters, this popular didactic piece stresses the importance of a full and sincere acitivity in making the most of life‟s brief span, rather than succumbing to moods of vain regret or dejection. The poem established the familiar Longfellow‟s pattern of clear, felicitous expression of common ideas, melodioally encouraging memorization.2.numbers: meters, rhythms3.For the soul/ not what they seem: the temporary body of human being dies, but the soulnenver dies. When wer a re doning things of no miportance, we say the soul slumbers. “The soul is dead…” the poet means that when we are hopeless.4.Dust thou art, to dust returnest: see Holy Bible, The Old Testament, Genesis, chap.2 sec. 7.“And the Lord God formed man of the dust of the ground, and breathed into his nostril the breath of life; and man became a living soul”.5.Art is lo ng, and time is fleeting: Chaucer‟s “ The Parliament of Fowls”, line 1. “ the life soshort, the craft so long to learn.”6.funeral marches: some pieces of music played in a funeral service.7.sands of time: moments in time (as measured by sand in an hour-glass).8.main: the sea (poetic diction).9.take heart: to gain courage.W alt Whitman (1819-1892)Born on May 31, 1819, Walt Whitman was the second son of Walter Whitman, a housebuilder, and Louisa V an V elsor. The family, which consisted of nine children, lived in Brooklyn and Long Island in the 1820s and 1830s.At the age of twelve, Whitman began to learn the printer's trade, and fell in love with the written word. Largely self-taught, he read voraciously, becoming acquainted with the works of Homer, Dante, Shakespeare, and the Bible.Whitman worked as a printer in New Y ork City until a devastating fire in the printing district demolished the industry. In 1836, at the age of 17, he began his career as teacher in the one-room school houses of Long Island. He continued to teach until 1841, when he turned to journalism as a full-time career.He founded a weekly newspaper, Long-Islander, and later edited a number of Brooklyn and New Y ork papers. In 1848, Whitman left the Brooklyn Daily Eagle to become editor of the New Orleans Crescent. It was in New Orleans that he experienced at first hand the viciousness of slavery in the slave markets of that city. On his return to Brooklyn in the fall of 1848, he founded a “free soil” newspaper, the Brooklyn Freeman, and continued to develop the unique style of poetry that later so astonished Ralph Waldo Emerson.In 1855, Whitman took out a copyright on the first edition of Leaves of Grass, which consisted of twelve untitled poems and a preface. He published the volume himself, and sent a copy to Emerson in July of 1855. Whitman released a second edition of the book in 1856, containing thirty-three poems, a letter from Emerson praising the first edition, and a long open letter by Whitman in response. During his subsequent career, Whitman continued to refine the volume, publishing several more editions of the book.At the outbreak of the Civil War, Whitman vowed to live a “purged” and “cleansed” life. He wrote freelance journalism and visited the wounded at New Y ork-area hospitals. He then traveled to Washington, D.C. in December 1862 to care for his brother who had been wounded in the war. Overcome by the suffering of the many wounded in Washington, Whitman decided to stay and work in the hospitals and stayed in the city for eleven years. He took a job as a clerk for the Department of the Interior, which ended when the Secretary of the Interior, James Harlan, discovered that Whitman was the author of Leaves of Grass, which Harlan found offensive. Harlan fired the poet.Whitman struggled to support himself through most of his life. In Washington, he lived on a clerk's salary and modest royalties, and spent any excess money, including gifts from friends, to buy supplies for the patients he nursed. He had also been sending money to his widowed mother and an invalid brother. From time to time writers both in the states and in England sent him “purses” of money so that he could get by.In the early 1870s, Whitman settled in Camden, NJ, where he had come to visit his dying mother at his brother's house. However, after suffering a stroke, Whitman found it impossible to return to Washington. He stayed with his brother until the 1882 publication of Leaves of Grass gave Whitman enough money to buy a home in Camden.In the simple two-story clapboard house, Whitman spent his declining years working on additions and revisions to a new edition of the book and preparing his final volume of poems and prose, Good-Bye, My Fancy (1891). After his death on March 26, 1892, Whitman was buried in a tomb he designed and had built on a lot in Harleigh Cemetery.Whitman‟s poetry is democ ratic in both its subject matter and its language. As the great lists that make up a large part of Whitman‟s poetry show, anything—and anyone—is fair game for a poem. Whitman is concerned with cataloguing the new America he sees growing around him. Just as America is far different politically and practically from its European counterparts, so too must American poetry distinguish itself from previous models. Thus we see Whitman breaking new ground in both subject matter and diction.In a way, though, Whitman is not so unique. His preference for the quotidian links him with both Dante, who was the first to write poetry in a vernacular language, and with Wordsworth, who famously stated that poetry should aim to speak in the “language of ordinary men.” Unlike Wordsworth, however, Whitman does not romanticize the proletariat or the peasant. Instead he takes as his model himself. The stated mission of his poetry was, in his words, to make “anattempt to put a Person, a human being (myself, in the latter half of the 19th century, in America) freely, fully, and truly on record.” A truly democratic poetry, for Whitman, is one that, using a common language, is able to cross the gap between the self and another individual, to effect a sympathetic exchange of experiences.This leads to a distinct blurring of the boundaries between the self and the world and between public and private. Whitman prefers spaces and situations—like journeys, the out-of-doors, cities—t hat allow for ambiguity in these respects. Thus we see poems like “Song of the Open Road“ and “Crossing Brooklyn Ferry,” where the poet claims to be able to enter into the heads of others. Exploration becomes not just a trope but a mode of existence.For Whitman, spiritual communion depends on physical contact, or at least proximity. The body is the vessel that enables the soul to experience the world. Therefore the body is something to be worshipped and given a certain primacy. Eroticism, particularly homoeroticism, figures significantly in Whitman‟s poetry. This is something that g ot him in no small amount of trouble during his lifetime. The erotic interchange of his poetry, though, is meant to symbolize the intense but always incomplete connection between individuals. Having sex is the closest two people can come to being one merged individual, but the boundaries of the body always prevent a complete union. The affection Whitman shows for the bodies of others, both men and women, comes out of his appreciation for the linkage between the body and the soul and the communion that can c ome through physical contact. He also has great respect for the reproductive and generative powers of the body, which mirror the intellect‟s generation of poetry.The Civil War dimini shed Whitman‟s faith in democratic sympathy. While the cause of the war nominally furthered brotherhood and equality, the war itself was a quagmire of killing. Reconstruction, which began to fail almost immediately after it was begun, further disappointed Whitman. His later poetry, which displays a marked insecurity about the place of poetry and the place of emotion in general (see in particular “When Lilacs Last in the Dooryard Bloom‟d“), is darker and more isolated.Whitman‟s style remains consistent throughout, however. The poetic structures he employs are unconventional but reflect his democratic ideals. Lists are a way for him to bring together a wide variety of items without imposing a hierarchy on them. Perception, rather than analysis, is the basis for this kind of poetry, which uses few metaphors or other kinds of symbolic language. Anecdotes are another favored device. By transmitting a story, often one he has gotten from another individual, Whitman hopes to give his readers a sympathetic experience, which will allow them to incorporate the anecdote into their own history. The kind of language Whitman uses sometimes supports and sometimes seems to contradict his philosophy. He often uses obscure, foreign, or invented words. This, however, is not meant to be intellectually elitist but is instead meant to signify Whitman‟s status as a unique individual. Democracy does not necessarily mean sameness. The difficulty of some of his language also mirrors the necessary imperfection of connections between individuals: no matter how hard we try, we can never completely understand each other. Whitman largely avoids rhyme schemes and other traditional poetic devices. He does, however, use meter in masterful and innovative ways, often to mimic natural speech. In these ways, he is able to demonstrate that he has mastered traditional poetry but is no longer subservient to it, just as democracy has ended the subservience of the individual.Whitman‟s po etry reflects the vitality and growth of the early United States. During the nineteenth century, America expanded at a tremendous rate, and its growth and potential seemedlimitless. But sectionalism and the violence of the Civil War threatened to break apart and destroy the boundless possibilities of the United States. As a way of dealing with both the population growth and the massive deaths during the Civil War, Whitman focused on the life cycles of individuals: people are born, they age and reproduce, and they die. Such poems as “When Lilacs Last in the Doory ard Bloom‟d” imagine death as an integral part of life. The speaker of “When Lilacs Last in the Dooryard Bloom‟d” realizes that flowers die in the winter, but they rebloom in the springtime, and he vows to mourn his fallen friends every year just as new buds are appearing. Describing the life cycle of nature helped Whitman contextualize the severe injuries and trauma he witnessed during the Civil War—linking death to life helped give the deaths of so many soldiers meaning.Throughout his poetry, Whitman praised the individual. He imagined a democratic nation as a unified whole composed of unique but equal individuals. “Song of Myself” opens in a triumphant paean to the individual: “I celebrate myself, and sing myself” (1). Elsewhere the speaker of that exuberant poem identifies himself as Walt Whitman and claims that, through him, the voices of many will speak. In this way, many individuals make up the individual democracy, a single entity composed of myriad parts. Every voice and every part will carry the same weight within the single democracy—and thus every voice and every individual is equally beautiful. Despite this pluralist view, Whitman still singled out specific individuals for praise in his poetry, particularly Abraham Lincoln. In 1865, Lincoln was assassinated, and Whitman began composing several elegies, including “O Captain! My Captain!” Although all individuals were beautiful and worthy of praise, some individuals merited their own poems because of their contributions to society and democracy.Whi tman‟s poetry revels in its depictions of the human body and the body‟s capacity for physical contact. The speaker of “Song of Myself” claims that “copulation is no more rank to me than death is” (521) to demonstrate the naturalness of taking pleasure in t he body‟s physical possibilities. With physical contact comes spiritual communion: two touching bodies form one individual unit of togetherness. Several poems praise the bodies of both women and men, describing them at work, at play, and interacting. The s peaker of “I Sing the Body Electric” (1855) boldly praises the perfection of the human form and worships the body because the body houses the soul. This free expression of sexuality horrified some of Whitman‟s early readers, and Whitman was fired from his job at the Indian Bureau in 1865 because the secretary of the interior found Leaves of Grass offensive. Whitman‟s unabashed praise of the male form has led many critics to argue that he was homosexual or bisexual, but the repressive culture of the nineteenth century prevented him from truly expressing those feelings in his work.Many of Whitman‟s poems rely on rhythm and repetition to create a captivating, spellbinding quality of incantation. Often, Whitman begins several lines in a row with the same word or phrase, a literary device called anaphora. For example, the first four lines of “When I Heard the Learn‟d Astronomer” (1865) each begin with the word when. The long lines of such poems as “Song of Myself” and “When Lilacs Last in the Dooryard Bloom‟d” fo rce readers to inhale several bits of text without pausing for breath, and this breathlessness contributes to the incantatory quality of the poems. Generally, the anaphora and the rhythm transform the poems into celebratory chants, and the joyous form and structure reflect the joyousness of the poetic content. Elsewhere, however, the repetition and rhythm contribute to an elegiac tone, as in “O Captain! My Captain!” This poem uses short lines and words, such as heart and father,to mournfully incant anelegy for the assassinated Abraham Lincoln.Throughout Whitman‟s poetry, plant life symbolizes both growth and multiplicity. Rapid, regular plant growth also stands in for the rapid, regular expansion of the population of the United States. In “When Lilacs Last in the Dooryard Bloom‟d,” Whitman uses flowers, bushes, wheat, trees, and other plant life to signify the possibilities of regeneration and re-growth after death. As the speaker mourns the loss of Lincoln, he drops a lilac spray onto the coffin; the act of laying a flower on the coffin not only honors the person who has died but lends death a measure of dignity and respect. The title Leaves of Grass highlights another of Whitman‟s themes: the beauty of the individual. Each leaf or blade of grass possesses its own distinct beauty, and together the blades form a beautiful unified whole, an idea Whitman explores in the sixth section of “Song of Myself.” Multiple leaves of grass thus symbolize democracy, another instance of a beautiful whole composed of individual parts. In 1860, Whitman published an edition of Leaves of Grass that included a number of poems celebrating love between men. He titled this section “The Calamus Poems,” after the phallic calamus plant.Whitman‟s interest in the self ties into his praise of the individual. Whitman links the self to the conception of poetry throughout his work, envisioning the self as the birthplace of poetry. Most of his poems are spoken from the first person, using the pronoun I. The speaker of Whitman‟s most famous poem, “Song of Myself,” even assumes the name Walt Whitman, but nevertheless the speaker remains a fictional creation employed by the poet Whitman. Although Whitman borrows from his own autobiography for some of the speaker‟s experiences, he also borrows many experiences from popular works of art, music, and literature. Repeatedly the speaker of this poem exclaims that he contains everything and everyone, which is a way for Whitman to reimagine the boundary between the self and the world. By imaging a person capable of carrying the entire world within him, Whitman can create an elaborate analogy about the ideal democracy, which would, like the self, be capable of containing the whole world.Song of Myself(Excerpt)1I celebrate myself, and sing myself,And what I assume you shall assume,For every atom belonging to me as good belongs to you.I loafe and invite my soul,I lean and loafe at my ease observing a spear of summer grass.My tongue, every atom of my blood, form'd from this soil, this air,Born here of parents born here from parents and their parents the same,I, now thirty-seven years old in perfect health begin,Hoping to cease not till death.Creeds and schools in abeyance,Retiring back a while sufficed at what they are, but never forgotten,I harbor for good or bad, I permit to speak at every hazard,Nature without check with original energy.2Houses and rooms are full of perfumes, the shelves are crowded with perfumes,。

Cp11.a:Stochastic error term: Stochastic error term is a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs.B:Linear : An equation is linear if plotting the function in terms of X and Y generates a straight line,c: Slope coefficient(β)shows the response of Y to a one-unit increase in X.d:: a linear regression model which has more than one independent variables .e:. Expected value：the expression β0+β1x is called the deterministic component of the regression equation ,this deterministic component can also be thought of as the expected value of Y given X.f:Residual: the difference between the estimated value of the dependent variable and the actual value of the dependent variable is defined as the residualCP2P43:a: Ordinary Least Squares is a regression estimation technique that calculates theβs so as to minimize the sum of the squared residuals.b:multivariate regression coefficient indicates the change in the dependent variable associated with a one-unit increase in the independent variable in question.c: total sum of squares is the squared variations of Y around its mean as a measure of the amount of variation to be explained by the regression. The explained sum of squares is the amount if the squared deviation of Yi from its mean that is explained by the regression line. Residual sum of squares is the unexplained in an empirical sense by the estimated regression equation.d: coefficient of determination is the ratio of the explained sum of squares to the total sum of squares.e: degrees of freedom is the excess of the number of observations(N) over the number of coefficients(including the intercept estimated (K+1).f: R^2 is the coefficient of determination.Chapter 31.a. Review the literature and develop the theoretical model.Specify the model.Hypothesize the expected signs of coefficient.Collect data.Estimate and evaluate the equation.Document the results.b. Apply other researchers’ model to my data set.c. Any mistakes in the specification of a model.d. The excess of the number of observations over the number of coefficient s to be estimated.Chapter 41.a. The regression model is linear.The error term has a zero population mean.All explanatory variables are uncorrelated with the err termObservations of the err term are uncorrelated with each other.The error term has a constant varianceNo explanatory variable is a perfect linear function of any other explanatory variables.The error term is normally distributed.b. An error term satisfying Assumption through one to five.c. A normal distribution with a mean equal to zero and a variance equal to one.d. SE is the square root of the estimated variance of β s.e. An estimate β is an unbiased estimator if its sampling distribution has as its expected value the true value of β.f. Best Linear Unbiased Estimator.g. The probability distribution of these β values across different samples. Chapter 51.a. A statement of the values that the researcher does not expect.b. A statement of the values that the researcher expects.c. We reject a true null hypothesisd. Indicate the probability of observing an estimated t-value greater than the critical t-value if the null hypothesis were correct.e. In which the alternative hypothesis has values on both sides if null hypothesis.f. When testing a hypothesis, you have to calculate a sample statistic and compare it with a critical value selected in advance.g. A value that divides the acceptance region from the rejection region when testing a null hypothesis.h. It is a ratio of departure of an estimated parameter from its notional value and its standard error.i. A range which contains the true value of an item a specified percentage of the time.j. A p-value for a t-score is the probability of observing a t score that big or bigger if the null hypothesis were true.CHAPTER 61.a. The omitted variable is an important explanatory variable that has been left outof a regression equation.b. The irrelevant variable is the variable included in an equation that doesn’t belong there.c. The specification bias is the bias caused by leaving a variable out of an equation.d. sequential specification search 6.4.2e. The specification error results from choosing the incorrect independent variables, the incorrect functional form and the incorrect form of the stochastic error term.f. The four valid criteria are to help decide whether a given variable belongs in the equation:g. expected bias 6.1.3CP71.a. Elasticity of Y with respect to X, the percentage change in the dependent variable caused by a 1 percent increase in the independent variable, holding the other varia bles in the equation constant can be calculated.b. In a doublelog functional form, the natural log of Y is the dependent variables an d the natural log of X is the independent variable.c. The semiology functional form is a variant of double-log equation in which some but not all of the variables are expressed in terms of their natural logsd. Polynomial functional forms express Y as a function of independent variables, so me of which are raised to powers other than one.e. The inverse functional form expresses Y as a function of the reciprocal of one or more of the independent variables.f. A slope dummy is a dummy variable that is multiplied by an independent variabl e to allow the slope of the relationship between the dependent variable and the pa rticular independent variable to change, depending on whether or not a particular condition is met.g. The natural log of a number is its logarithm to the base of the mathematical cons tant e, where e is an irrational and transcendental number approximately equal to2.718.h. The omitted condition, forms the basis against which the included conditions are compared.i. An interaction term is an independent variable in a regression equation that is th e multiple of two or more other independent variables.j. A form that is linear in the variables should be used unless a specific hypothesis s uggestions otherwise.k. An equation is linear in the coefficients only if the coefficients appear in their si mplest form, they are not raised to any powers and not multiplied or divided by ot her coefficients, and do not themselves include some sort of function.。

Chapter 13 – 5
Stating Research and Null Hypotheses
• The research hypothesis (H1) proposes that the two variables are related in the population. • The null hypothesis (H0) states that no association exists between the two cross-tabulated variables in the population, and therefore the variables are statistically independent.
Chapter 13 – 13
The Sampling Distribution of Chi-Square
• The distributions are positively skewed. The research hypothesis for the chi-square is always a one-tailed test. • Chi-square values are always positive. The minimum possible value is zero, with no upper limit to its maximum value. • As the number of degrees of freedom increases, the χ2 distribution becomes more symmetrical.
Chapter 13 – 3
Hypothesis Testing with Chi-Square

OBJECTIVES:After completing this chapter, you should be able to❖D iscuss the general idea of analysis of variance.❖U se the one-way ANOVA technique to determine ifthere is a significant difference among two or moremeans.❖U se the two-way ANOVA technique to determine ifthere is a significant difference in the main effects.3.1: INTRODUCTION➢The analysis of variance (ANOVA) is a procedure used to test whether difference exists between two or more population means for interval data.➢To do this, the technique analyzes the sample variance.➢The F test can also be used to test the equality of two means. But since it is equivalent to the t test in this case, the t test is usually used instead of the F test when there are only two means.➢There are several reasons why the t test should not be done to test three means or more:1.When one is comparing two means at a time, therest of the means under study are ignored. Withthe F test, all the means are comparedsimultaneously.2.When one is comparing two means at a time andmaking all pairwise comparisons, the probabilityof rejecting the null hypothesis when it is true isincreased, since the more t tests that areconducted, the greater is the likelihood ofgetting significant different by chance alone.3.The more means there are to compare, the moret test are needed. (For example: For thecomparison of 3 means two at a time, 3 t testsare required. For the comparison of 5 means twoat a time, 10 tests are required. And for thecomparison of 10 means two at a time, 45 testsare required.)➢The F test can only show whether or not a difference exists but not where the difference lies.F DISTRIBUTION➢ If two independent samples are selected from two normally distributed populations in which thevariance are equal (σ12 = σ22 ) and if the variances s 12 and s 22 are compared as 2122s s, the sampling distribution of the ratio of the variances is called the F distribution.➢ Characteristics of F distribution.▪ F cannot be negative because variances are always positive or zero and it is a continuous distribution. ▪ The F distribution is positively skewed.▪ The F distribution is a family of curves based on the degrees of freedom of the variance of the numerator and the degrees of freedom of the variance of the denominator.▪ Its values range from 0 to ∞. As F → ∞, the curve approaches the X-axis but never touches it.➢ Formula for the F test:2122s F s =where s 12 is the larger of the two variances.➢The F test has two terms for the degree of freedoms: that of the numerator, n1-1 and that of thedenominator, n2-1, where n1 is the sample size from which the larger variance was obtained.3.2: ONE WAY ANALYSIS OF VARIANCE➢Assumption for the F test to compare three or more means:1.The populations from which the samples wereobtained must be normally or approximatelynormally distributed.2.The samples must be independent of each other.3.The variances of the populations must be equal.Example 1:Fifteen fourth-grade students were randomly assign to three groups to experiment with three differentmethods of teaching arithmetic. At the end of thesemester, the same test was given to all 15 students.The table gives the scores of students in the threegroups.➢In the F test, two different estimates of the population variance are made.➢The first estimate is called the between-group variance, and it involves finding the variance of the means.➢The second estimate, the within-group variance, is made by computing the variance using all the data and it is not affected by differences in the means.➢If there is no difference in the means, the between group variance will be approximately equal to the within-group variance, and F test value will be close to 1 → The null hypothesis will not be rejected.➢However, when the means differ significantly, the between-group variance will be much larger than the within-group variance, the F test will be significantly greater than 1 → The null hypothesis will be rejected.1. Hypothesis Statement➢ To test the difference among the means, the following hypothesis should be used.012:...k H μμμ===, where k is the number of groups 1:H At least two means differ2. Test Statistic1SSAMSA k F SSE MSE n k-==-➢ Total Sum of Squares, SST• The total variability in the data.• SST found using the following formula:()222211 or anijijiji j x SST x nX SST xn===-=-∑∑∑∑∑• SST can be partitioned into 2 component parts: the treatment sum of square, SSA and the error sum of square, SSE.SST=SSA + SSE➢ Treatment Sum of Squares, SSA• The sum of squares between groups.()()()2221or aij i i i i i x x SSA n X X SSA n n =⎡⎤⎢⎥=-=-⎢⎥⎣⎦∑∑∑∑➢ Error Sum of Squares, SSE• Sum of squares within groups.()()2221s or ii i ij ix SSE n SSE x n ⎡⎤⎢⎥=-=-⎢⎥⎣⎦∑∑∑∑or SSE = SST – SSA➢ Mean Squares• The mean squares values are equal to the sum of squares divided by the degree of freedom.and 1SSA SSEMSA MSE k n k ==--➢ANOVA Summary TableSource Sum of df Mean FSquares SquaresTreatment SSA k-1 MSAMSA FMSE =Error SSE n-k MSE_________________________________________ Total SST3.Critical Value➢Fα;k-1,n-k4.Decision Rule➢Reject H0 if F > Fα;k-1,n-k5.ConclusionExample 2:Reconsider Example 1. At the 1% significance level, test the claim that there is no different among the means.∑x 1=324 ∑x 2=369 ∑x 3=388 ∑x=1081 ∑x 2=80709 n 1=5 n 2=5 n 3=5 n=1522223243693881081432.133355515SSA ⎡⎤=++-=⎢⎥⎣⎦ 222324369388807092372.8555SSE ⎡⎤=-++=⎢⎥⎣⎦ or21081807092804.933315SST =-=ANOVA table:Source Sum ofdf Mean F SquaresSquaresTreatment 432.1333 2 216.0667 1.09Error 2372.8000 12 197.7333_______________________________________ Total 2804.93330123:H μμμ==H 1: At least two means differ. F 0.01;2,12 = 6.93F=1.09 < F 0.01;2,12 = 6.93 Do not reject H 0There is enough evidence to conclude that there is no different among the means.Exercise:1. How does an MBA major affect the number of job offers received? An MBA student randomly sampled four recent graduates in each of Finance, Marketing and Management and asked each of them to report the number of job offers. Can we conclude at the 5% significance level that there are different in the number of job offers between the three MBA majors?Finance Marketing Management 3 1 8 1 5 5 4 3 4 1 4 62.Spam is the price we pay to be capable of easilycommunicating using e-mail. Does spam affect everyone equally? In a preliminary study, university professors, administrators and students were randomly sampled. Each person was asked to count the number of Spam messages received that day.The results follow. Can we infer at the 2.5% significance level that the differing university communities differ in the amount of Spam they receive in their e-mail?Professors Administrators Students3 9 518 10 150 16 44 12 187 5 12SPSS Output for One-way ANOVA1. A study was conducted to determine the lifetime ofthree brands of battery towards 12 torch lights. Base on the information (in hours), test the claim that there is a different in mean lifetime among the three brands ofbattery.Brand A 8.7 8.2 8.1Brand B 9.1 9.2 9.4 9.6 9.2Brand C 9.4 9.4 9.4 8.8Output3.A management scientist believes that one way ofjudging whether a computer came equipped with enough memory is to determine the age of the computer. In a preliminary study, random sample of computer users were asked to identify the brand of computer and its age (in months). The categorized responses are shown here. Do these data provide sufficient evidence to conclude that there are differences in age between the computer brands?Use =0.05.IBM DELL Hewlett Packard Other17 8 6 2410 4 15 1213 21 8 15。