Stat 501 Midterm Exam #1 Study GuideThe exam will be a mixture of open-ended, multiple choice, and true/false questions. This guide isintended to help focus your e¤orts in preparing for the exam, that is, to let you know:² what you need to know how to calculate;² with what Minitab output you should know;² what hypothesis tests you should know; and² with what general concepts you should know.1 What do you need to know how to calculate?You should:² Know how to use an estimated regression equation to predict a future response or to estimate a meanresponse.² 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.² Know the relationship among all the values in the lack of …t analysis of variance table – that is, beable to calculate any value that is missing from the table from the other values in the table.² Know how to calculate a 95% con…dence interval for ¯0and ¯1given the sample estimates b0and b1and the standard errors se (b0) and se (b1) in Minitab output.² Know how to calculate the R2value given SSR and SST O; or given SSE and SSTO:2 What Minitab output should you know?You should:² Know basic Minitab output from Fitted Line Plot command.² Know basic Minitab output from Regression command (estimated regression equation, t-test table forparameters, s =pMSE, R2, the analysis of variance table, etc.)² Know Minitab output for a con…dence interval for a mean response and a prediction interval for a newobservation.² Know Minitab output for the lack of …t analysis of variance table.3 What hypothesis tests should you know?You should know how to specify the null and alternative hypotheses, and be able to draw a conclusion givenappropriate Minitab for each of the following hypothesis tests that we studied:² The t-test for H0: ¯1= 0:² The F -test for H0: ¯1= 0:² The F -test for lack of …t.² The Ryan-Joiner correlation test for normality of error terms.14 What general concepts should you know?You should:² Know what a con…dence interval is and what a con…dence interval tells us.² Know what a hypothesis test is, know how to draw a conclusion about a hypothesis using a P -value,and know the di¤erence between the two types of errors that are possible whenever performing ahypothesis test.² Know the di¤erence between a functional relation and a statistical relation.² Be able to distinguish between the true regression line and an estimated regression line.² Be able to distinguish between population regression parameters¡¯0; ¯1; ¾2¢and sample statistics(b0; b1; MSE) :² Know the simple linear regression model and assumptions – “LINE.”² Know that the least squares estimates minimize the sum of the squared distances between the observedresponse, yi; and the estimated regression line, byi.² Know what the estimated intercept and estimated slope parameters tell us.² Know that it is dangerous to extrapolate beyond the scope of the model.² Given a data point (xi; yi), be able to distinguish between the predictor xi, the observed response yi,the …tted (estimated) response byi, the residual ei, and the average response E(Yi).² Know that MSE =1n ¡2Pni=1(yi¡ byi)2estimates ¾2; the common variance of the many populations.² Know that association between x and y does not imply that x causes the changes in y:² Know the interpretation of the t-statistic for testing ¯1= 0 (the number of standard errors b1fallsabove or below the assumed ¯1= 0)² Know the three possible realities when we don’t reject the null H0: ¯1= 0; and know the three possiblerealities when we do reject the null H0: ¯1= 0:² Know that the (linear) LOF test only gives you evidence against linearity. If you reject the null, andconclude lack of linear …t, it doesn’t tell you what (non-linear) regression function would work.² Be able to distinguish between estimating a mean response (con…dence interval) and predicting a newobservation (prediction interval).² Know what factors a¤ect the width of the con…dence interval for the mean response.² Know that (and why) a prediction interval for a new observation is wider than a con…dence intervalfor the mean response.² Know the formula for a prediction interval depends strongly on the assumption that the error termsare normally distributed, while the formula for the con…dence interval is not so dependent on thisassumption for large sample sizes.² Know the relation and distinction between the t-test and the F -test for testing that ¯1= 0.² Understand the general idea of the general linear test approach, and how it is used to derive the lackof …t test.² Know that the coe¢cient of determination¡R2¢and the correlation coe¢cient (r) are measures oflinear association (that is, they can be 0 even if there is perfect nonlinear association).² Know how to interpret the R2value.2² Know how to calculate the correlation coe¢cient from the R2value.² Know what various correlation coe¢cient values mean. There is no other meaningful interpretationfor the correlation coe¢cient as there is for the R2value.² Understand why we need to check the assumptions of our model.² Know the six things that can go wrong with the model, and how we can detect the problems usingresiduals vs. …ts plots, residuals vs. predictor plots, residuals vs. order plots, and normal
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