Linear Regression Statistics and Analysis

Linear regression is a statistical technique that is used to learn more about the relationship between an independent (predictor) variable and a dependent (criterion) variable. When you have more than one independent variable in your analysis, this is referred to as multiple linear regression. In general, regression allows the researcher to ask the general question â€Å"What is the best predictor of†¦?† For example, let say we were studying the causes of obesity, measured by body mass index (BMI). In particular, we wanted to see if the following variables were significant predictors of a person’s BMI: number of fast food meals eaten per week, number of hours of television watched per week, the number of minutes spent exercising per week, and parents’ BMI. Linear regression would be a good methodology for this analysis. The Regression Equation When you are conducting a regression analysis with one independent variable, the regression equation is Y a b*X where Y is the dependent variable, X is the independent variable, a is the constant (or intercept), and b is the slope of the regression line. For example, let’s say that GPA is best predicted by the regression equation 1 0.02*IQ. If a student had an IQ of 130, then, his or her GPA would be 3.6 (1 0.02*130 3.6). When you are conducting a regression analysis in which you have more than one independent variable, the regression equation is Y a b1*X1 b2*X2 †¦ bp*Xp. For example, if we wanted to include more variables to our GPA analysis, such as measures of motivation and self-discipline, we would use this equation. R-Square R-square, also known as the coefficient of determination, is a commonly used statistic to evaluate the model fit of a regression equation. That is, how good are all of your independent variables at predicting your dependent variable? The value of R-square ranges from 0.0 to 1.0 and can be multiplied by 100 to obtain a percentage of variance explained. For example, going back to our GPA regression equation with only one independent variable (IQ)†¦Let’s say that our R-square for the equation was 0.4. We could interpret this to mean that 40% of the variance in GPA is explained by IQ. If we then add our other two variables (motivation and self-discipline) and the R-square increases to 0.6, this means that IQ, motivation, and self-discipline together explain 60% of the variance in GPA scores. Regression analyses are typically done using statistical software, such as SPSS or SAS and so the R-square is calculated for you. Interpreting the Regression Coefficients (b) The b coefficients from the equations above represent the strength and direction of the relationship between the independent and dependent variables. If we look at the GPA and IQ equation, 1 0.02*130 3.6, 0.02 is the regression coefficient for the variable IQ. This tells us that the direction of the relationship is positive so that as IQ increases, GPA also increases. If the equation were 1 - 0.02*130 Y, then this would mean that the relationship between IQ and GPA was negative. Assumptions There are several assumptions about the data that must be met in order to conduct a linear regression analysis: Linearity: It is assumed that the relationship between the independent and dependent variables is linear. Though this assumption can never be fully confirmed, looking at a scatterplot of your variables can help make this determination. If a curvature in the relationship is present, you may consider transforming the variables or explicitly allowing for nonlinear components.Normality: It is assumed that the residuals of your variables are normally distributed. That is, the errors in the prediction of the value of Y (the dependent variable) are distributed in a way that approaches the normal curve. You can look at histograms or normal probability plots to inspect the distribution of your variables and their residual values.Independence: It is assumed that the errors in the prediction of the value of Y are all independent of one another (not correlated).Homoscedasticity: It is assumed that the variance around the regression line is the same for all values of the independent variables. Source StatSoft: Electronic Statistics Textbook. (2011). http://www.statsoft.com/textbook/basic-statistics/#Crosstabulationb.

Why Has Utopian Literature Remained Popular Essay - 856 Words

All works of Utopian literature are designed to present ideologies and protest. Through this they have maintained their popularity whilst retaining the ability to reformulate. This ability to reformulate itself has created a way for authors to explore and investigate ideologies and protests whilst keeping the issues contextual to the time. More has done this extremely well, establishing the genre at the beginning of the 16th century, in his novella Utopia. By using Rafael as the narrator he successfully presents his alternative of a communistic style state where everyone is equal, whilst keeping him safe; also convincing them that it was a non-fiction text and as a result protecting himself from punishment. He did this so successfully that†¦show more content†¦But what the play is really doing is making us question the gender roles that currently exist. * De Groen does this by cleverly switching the roles of men and women in the imaginary society of the late twentieth centur y. * For example, in the imaginary society, women have the powerful jobs such as doctor and men are in lesser roles such as the orderly in the hospital. * In the opening scene Audra, the doctor, is a woman portrayed with traditional male characteristics, strong and dominant, unemotional, and says to Wayne â€Å"you’re cute, you’re funny, you make me laugh, and when I can get you to shut up, I like going to bed with you. That’s all there is to it†. * Wayne is portrayed as traditionally female, needy and emotional because he wants more from the relationship. Catch 22 uses its odd and dysfunctional characters and plots to portray the absurdity of war. * For example, in one scene Colonel Cathcart is feeling generous and tries to promote the absurdly named Major Major Major Major but he is rebuked by his superiors as they only have one Major Major Major Major and don’t want to lose him. Colonel Cathcart then sulkily threatens to bust Major Major Major Major down to Lieutenant and is teased by his colleague Colonel Corn who points out that they probably won’t let him do this either, for the same reason. * In another scene, Doc Daneeka isShow MoreRelatedThes Benevolent Association, The Knights Of Labor And The Farmers Union1223 Words   |  5 Pagesfarming and ranching. Free labor, supported by the legalized human enslavement led to a successful agricultural enterprise within the republic. 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Renaissance Quizz Essay Research Paper Example For Students

Renaissance Quizz Essay Research Paper Renaissance What was one of the chief aims of Italian Renaissance art? Realistic portrayal of individual persons, especially the human nude What was considered to be most important in education of Christian Ladies? Domesticity or asceticism What is a fresco? Method of painting water-based pigments on freshly applied plaster, usually on wall surfaces. What was the purpose of liberal education? Liberal studies were viewed as the key to freedom, which allowed humans to achieve heir goals and reach their full potential. What was the aim off humanist education? Humanist education was thought as being an important factor to the preparation of life. Its main goal was to improve the lives of citizens and help their communities. What did Donated do in Rome? With Michelson he produced a series of works, including the tomb of Pope John XIII in the Baptistery, Florence, and the tomb of Cardinal Britannica in S. Angelo a Nil, Naples. What was Renaissance art influenced by? Humanism What did Renaissance artists seek to imitate? They tried to imitate nature and real life in their work. In politics, the Renaissance contributed the development of the conventions of diplomacy, and in science an increased reliance on observation. Historians often argue this intellectual transformation was a bridge between the Middle Ages and the Modern era. Although the Renaissance saw revolutions in many intellectual pursuits, as well as social and political upheaval, it is perhaps best known for its artistic placements and the contributions of such polymaths as Leonardo dad Vinci and Michelangelo, who inspired the term Renaissance man. As a cultural movement, it encompassed innovative flowering of Latin and vernacular literatures, beginning with the 14th-century resurgence of learning based on classical sources, which contemporaries credited to Patriarch, the development of linear perspective and other techniques of rendering a more natural reality in painting, and gradual but widespread educational reform. Renaissance quiz By legislation

John P. Parker free essay sample

His Promised Land: The Autobiography of John P. Parker, Former Slave And Conductor on the Underground Railroad. When we think of the conductors of the Underground Railroad many think of Harriet Tubman and her only, but if we study history carefully we will find out that she is not the only conductor worth mentioning. John P. Parker has to be one of the most underappreciated figures not only in African American history but American history in general. If everyone was aware of this true American hero’s story, without question he would be a household name. The autobiography of John P. Parker is very well written and will have any reader on the edge of their seat throughout the entire book. The accounts of his experiences both as a slave and as a conductor of the Underground Railroad are extremely descriptive and would make any reader feel like they were right there with Mr. We will write a custom essay sample on John P. Parker or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Parker feeling his pain, anger, pride, bravery, and even his humor. Although there are many themes that you can find in this book, we are going to focus on his bravery, cleverness, and freedom as the three themes to discuss. The first theme we are going to discuss is freedom. John Parker’s life includes many experiences that would influence his love and aspiration for freedom. At the young age of eight years old, he was sold and forced to walk from Norfolk, Virginia to Richmond, Virginia chained to an old man who would be whipped to death. â€Å"This experience set him on fire with hatred and desire to gain his freedom† (p. 20). John Parker was owned by a doctor who had sons that would smuggle books to him. The doctor would also encourage Mr. Parker to learn the trade of iron molding. This situation would influence his aspiration for freedom because he had the ability to read and also knew the trade of iron molding and was fully aware of his potential as a free man. When John Parker finally did get his freedom, he moved to Cincinnati, Ohio where he would help others on their journey to freedom. In Cincinnati he would have his first experience helping runaways get their freedom when he helped a local barber by rescuing his family from slavery. This was the first of many successful rescue missions. The next theme we will talk about will be cleverness. Mr. Parker was so clever that he could easily avoid authority as well as slave owners and even managed to convince a widow to purchase him from his master for $1,800 and was able to purchase his freedom from the widow in just 18 months by working in the iron foundry. John Parker was a very brilliant and clever man that lived a double life. By day he would work as an iron molder and by night he would take slaves across the Ohio River. He was a brilliant inventor with patents to a sugar mill, tobacco press, and soil pulverizer. Parker was a terrific businessman also. He was the owner of a foundry and blacksmith shop at a time when many black businesses were failing. The final theme that we will cover will be bravery. John Parker was very heroic and resilient. For almost fifteen years John Parker helped slaves escape to freedom as a conductor on the Underground Railroad. The dangers of getting caught helping slaves escape include jail time or even death. A good example of John Parker’s bravery would be when he snatched a whip out of a white nurse’s hand and began beating her because she was physically abusing her patients and Mr. Parker had had enough. This was particularly brave because no slave in their right mind would ever strike a white woman and still be around to talk about it. Perhaps the bravest thing about John Parker was that even after he had acquired his freedom he still risked his life and freedom day and night just to make sure other slaves had the same opportunity as he had. In conclusion, this book gives a realistic understanding of what a conductor of the Underground Railroad would experience assisting slaves to freedom. He was truly a Jack of all trades because he was a slave, an inventor, a freedom fighter, and a businessman. I am ashamed to say that I did not know who John P. Parker was prior to reading this book, but at the same time I am proud that I now have knowledge of this great hero in American history. It really surprises me that his story is not much popular. 750 words