Stat 501 Midterm Exam #1 Study GuideThis is the study guide for the written exam on 25 Feb 2004. The exam will be a mixture of open-ended, multiple c h oice, and true/false questions. You cannot use any notes or textbooksduring the exam. This guide i s intended to help focus your efforts in preparing for the exam,that is, to let you know:• what you need to know how to calculate;• what Minitab output you should know;• what hypothesis tests you should know; and• what general concepts you should know.1 Whatdoyouneedtoknowhowtocalculate?You should:• K now how to use an estimated regression equation to predict a future response or to estimatea mean response.• Know the relationship among all the values in the basic 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 the relationship among all the values in the lac k of fit analysis of variance table — thatis, be able to calculate any value that is missing from the table from the other values in thetable.• Kn ow how to calculate a 95% confidence interval for β0and β1given the sample estimatesb0and b1and the standard errors se (b0) and se (b1) in Minitab output.• Know how the R2value is calculated either from SSR and SSTO, or from SSE and SSTO.• K now how to make the calculations that are necessary to get meaningful interpretations ofthe slope parameter under log-transformed data.• Kn ow how to use an estimated regression equation based on transformed data to predict afuture response (prediction interval) or estimate a mean response (confidence interval).2 W hat Minitab output sho uld y ou know?You should:• Kn ow basic Minitab output from Fitted Line Plot command.• Know basic Minitab output from Regression command (estimated regression equation, t-testtable for parameters, s =√MSE, R2, the analysis of variance table, etc.)• Know Minitab output for a confidence interval for a mean response and a prediction intervalfor a new observation.• Know Minitab output for the lack of fit analysis of variance table.13 What h ypothesis tests should you know ?You should know how to specify the null and alternative hy potheses, and be able to draw a con-clusion given appropriate Minitab for eac h of the following hypothesis tests that we studied:• The t-test for H0: β1=0.• The F -test for H0: β1=0.• The t-test for H0: ρ =0.• The F -test for lack of fit.• The Ryan-Joiner correlation test for normality of error terms.You should also know when it is okay (that is, what conditions must be at least approximatelymet) to use each test.4 What general concepts should you know?You should:• K now the type of research question each statistical procedure we studied can answer.• Know what a confidence interval is and what a confidence in terval tells us.• Know what a h ypothesis test is, know how to draw a conclusion about a hypothesis using aP -value, and know the difference between the two t ypes of errors that are possible wheneverperforming a h ypothesis test.• Know the difference betw een 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 samplestatistics (b0,b1,MSE) .• Know the simple linear regression model and assumptions — “LINE.”• Understand the principle of least squares estimation. That is, know that the least squaresestimates minimize the sum of the squared distances between the observed response, yi, andthe estimated regression line, 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,theobservedresponse yi,thefitted (estimated) response byi, the residual ei, and the mean response µY.• Know that MSE =1n−2Pni=1(yi− byi)2estimates σ2, the common variance of the manypopulations.• 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 β1=0(the number of standard errorsb1falls above or below the assumed β1=0)• Know the three possible realities when we don’t reject the null H0: β1=0, and know thethree possible realities when we do reject the null H0: β1=0.• Be able to distinguish between estimating a mean response (confidence interval) and predict-ing a new observation (prediction in terval).• 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 confidenceinterval for the mean response.• Know the formula for a prediction interval depends strongly on the assumption that theerror terms are normally distributed, while the formula for the confidence interval is not sodependent on this assumption for large sample sizes.• Understand the “derivation” of the F -test for testing H0: β1=0. That is, understand thedecomposition of the total sum of squares, and how the expected mean squares tell us to usethe ratio MSR/MSE to conduct the test.• Know the relation and distinction between the t-test and the F -test for testing that β1=0.• Know that the (linear) LOF test only gives you evidence against linearity. If you reject thenull, and conclude lack of linear fit, it doesn’t tell you what (non-linear) regression functionwould work.• Understand the “derivation” of the linear lac k of fit test. That is, understand the decompo-sition of the error sum of squares, and how the expected mean squares tell us to use the ratioMSLF/MSPE to test for lack of linear fit.• Know that the coefficien t of determination¡R2¢and the correlation coefficient (r) are mea-sures of linear association (that is, they can be 0 even if there is perfect nonlinear association).• Know how to interpret the R2value.• Understand the cautions necessary in using the R2value as a way of assessing the strengthof the linear association.• Know how to calculate the correlation coefficient r from the R2value.• Know what various correlation coefficient values mean. There is no other meaningful inter-pretation for the correlation coefficient as there is for the R2value.• Know the t-test for testing that β1=0,theF -test for testing that β1=0,
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