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PSU STAT 501 - Stat 501 Final Exam Study Guide

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Stat 501 Final Exam Study GuideThe exam will be a mixture of open-ended, multiple choice, and true/false questions. This guide isintended to help focus your efforts in preparing for the exam, that is, to let you know:• whatyouneedtoknowhowtocalculate;• with what Minitab output you should know;• what hypothesis tests you should know; and• with what general concepts you should know.1 Whatdoyouneedtoknowhowtocalculate?You should:• Know how to use an estimated regression equation to predict a future response or to estimate a meanresponse.• Know the relationship among all the values in the basic analysis of variance table — that is, be able tocalculate any value that is missing from the table from the other values in the table.• Know the relationship among all the values in the lack of fit analysis of variance table — that is, beable to calculate any value that is missing from the table from the other values in the table.• Know how to calculate a 95% confidence interval for β0and β1given the sample estimates b0and b1and the standard errors se (b0) and se (b1) in Minitab output.• Know how to calculate the R2value given SSR and SSTO, or giv en SSE and SSTO.• Knowhowtocalculateaconfidence interval for a single slope parameter in the multiple regressionsetting.• Know how to calculate a sequential sum of squares — reduction in error sum of squares or increase inregression sum of squares.• Know how to obtain a two (or more)-degree-of-freedom sequential sum of squares.• Knowhowtocalculateacoefficient of partial determination.2 W hat Minitab output should y ou know ?You should:• Output from Fitted Line Plot command.• Output from Regression command (that we’ve used)• Output for the lack of fit analysis of variance table.• Correlation matrix output.• Scatter plot matrix output.• Stepwise regression output.• Best subsets regression output.• Logistic regression output (that we’ve used).13 What h ypothesis tests should y ou kno w ?You should know how to specify the null and alternative hy potheses, and be able to draw a conclusion givenappropriate Minitab for each of the following hypothesis tests that we studied:• The t-test or partial F -test for H0: β1=0.• The overall F -test for H0: β1= ··· = βp=0.• The partial F -test for any subset of the slope parameters.• The F -test for lack of fit.• The Ryan-Joiner correlation test for normality of error terms.• The Z-test for testing βjof a logistic regression model is 0.4 What general concepts should y ou know?You should:• Know what a confidence interval is and what a confidence interval tells us.• Know what a hypothesis test is, know how to draw a conclusion about a hypothesis using a P-value, andknow the difference between the t wo types of errors that are possible whenever performing a hypothesistest.• Know the difference between a functional relation and a statistical relation.• Be able to distinguish between the true regression line and an estimated regression line.• Be able to distinguish between population regression parameters¡β0,β1,σ2¢and sample statistics(b0,b1,MSE) .• Know the simple linear regression model and assumptions — “LINE.”• Know that the least squares estimates minimize the sum of the squared distances between the observedresponse, yi, andtheestimatedregressionline,byi.• Know what the estimated intercept and estimated slope parameters tell us.• Know that it is dangerous to extrapolate beyond the scope of the model.• Given a data point (xi,yi), be able to distinguish between the predictor xi, the observed response yi,the fitted (estimated) response byi,theresidualei, and the average response E(Yi).• Know that MSE =1n−2Pni=1(yi− byi)2estimates σ2, the common variance of the many populations.• Know that association between x and y does not imply that x causes the changes in y.• Know the interpretation of the t-statistic for testing β1=0(the number of standard errors b1fallsabove or below the assumed β1=0)• Know the three possible realities when we don’t reject the null H0: β1=0, and know the three possiblerealities when we do reject the null H0: β1=0.• Know that the (linear) LOF test only gives you evidence against linearity. If you reject the null, andconclude lack of linear fit, it doesn’t tell you what (non-linear) regression function would work.• Be able to distinguish between estimating a mean response (confidence interval) and predicting a newobservation (prediction interval).2• Know what factors affect the width of the confidence interval for the mean response.• Know that (and why) a prediction interval for a new observation is wider than a confidence intervalfor the mean response.• Know the formula for a prediction interval depends strongly on the assumption that the error termsare normally distributed, while the formula for the confidence interval is not so dependent on thisassumption for large sample sizes.• Know the relation and distinction between the t-test and the F -test for testing that β1=0.• Understand the general idea of the general linear test approach, and how it is used to derive the lackof fittest.• Know that the coefficient of determination¡R2¢and the correlation coefficient (r) are measures oflinear association (that is, they can be 0 even if there is perfect nonlinear association).• Know how to interpret the R2value.• Know how to calculate the correlation coefficient from the R2value.• Know what various correlation coefficient values mean. There is no other meaningful interpret ationfor the correlation coefficient as there is for the R2value.• Understand why we need to check the assumptions of our model.• Know the six things that can go wrong with the model, and how we can detect the problems usingresiduals vs. fits plots, residuals vs. predictor plots, residuals vs. order plots, and normal probabilityplots.• Understand when transforming the X values might help and when transforming the Y values mighthelp (or when it might be necessary to do both.)• Know how to use an estimated regression equation (confidence interval, or prediction interval) basedon transformed data to predict a future response.• Be able to interpret the coefficien ts of a multiple regression model.• Understand what the scope of the model is in a multiple regression setting.• Be able to define a linear regression model (including the assumptions) in matrix terms. (So, also


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PSU STAT 501 - Stat 501 Final Exam Study Guide

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