STA 3024 Practice Problems for Exam 2 Fall 2007Please Note: Answering all of these questions is not necessarily sufficient for a decent grade.You must first study, using your book as well as your notes. These questions are notintended to cover everything, but aim to give you an idea about the questions you mayhave in the test. You are responsible from everything in the text as well as the notes. Solveas many problems as you can from your text AFTER CAREFULLY READING IT.Read questions very carefully. For each question, choose the best answer then explain (toyourself) in a sentence why you chose that as the correct answer and why the other optionsare wrong. Solutions will be posted soon. 1. The parameters to be estimated in the simple linear regression model Y = β0 + β1x + ε with theassumption ε ~ N(0, σ) are:a) β0, β1, σ2b) β0, β1, ε c) b0, b1, s2d) ε, 0, σ22. We can measure the proportion of the variation explained by the regression model by:a) r b) R2c) σ2d) F3. The MSE is an estimator of:a) ε b) 0 c) σ2d) Y 4. In multiple regression with p predictor variables, when constructing a confidence interval for anyβi, the degrees of freedom for the tabulated value of t should be:a) n – 1 b) n – 2 c) n – p – 1 d) p – 15. In a regression study, a 95% confidence interval for β1 was given as: (– 5.65, 2.61). What is thedecision for testing H0: β1 = 0 vs. Ha: β1  0?a) Reject the null hypothesis at α = 0.05 and all smaller αb) Fail to reject the null hypothesis at α = 0.05 and all smaller αc) Reject the null hypothesis at α = 0.05 and all larger αd) Fail to reject the null hypothesis at α = 0.05 and all larger α6. In simple linear regression, when we decide that β1 is not significantly different from zero weconclude that:a) X is a good predictor of Yb) There is no linear relationship between X and Yc) The relationship between X and Y is quadraticd) There is no relationship between X and Y e) Y is a good predictor of XSTA 3024 Practice Questions, Fall 2007, Page 1 of 147. In a study of the relationship between X = mean daily temperature for the month and Y =monthly charges on electrical bill, the following data were gathered: X 20 30 50 60 80 90Y 125 110 95 90 110 130Which of the following seems the most likely model? a) Y = β0 + β1x + ε with β1 < 0 b) Y = β0 + β1x + ε with β1 > 0c) Y = β0 + β1x + β2x2 + ε with β2 < 0 d) Y = β0 + β1x + β2x2 + ε with β2 < 0 8. If a predictor variable x is found to be highly significant we would conclude that:a) A change in y causes a change in xb) A change in x causes a change in yc) Changes in x are not related to changes in yd) Changes in x are associated to changes in y9. At the same confidence level, a prediction interval for a new response is always;a) Somewhat larger than the corresponding confidence interval for the mean responseb) Somewhat smaller than the corresponding confidence interval for the mean responsec) One unit larger than the corresponding confidence interval for the mean responsed) One unit smaller than the corresponding confidence interval for the mean response10. Both the prediction interval for a new response and the confidence interval for the meanresponse are narrower when made for values of x that are:a) Closer to the mean of the x’sb) Further from the mean of the x’sc) Closer to the mean of the y’sd) Further from the mean of the y’s11. In the regression model Y = β0 + β1x + ε the change in Y for a one unit increase in x:a) Will always be the same amount, β0b) Will always be the same amount, β1c) Will depend on the error term d) Will depend on the level of x12. In a regression model with a dummy variable without interaction there can be:a) More than one slope and more than one intercept b) More than one slope, but only one interceptc) Only one slope, but more than one interceptd) Only one slope and one intercept13. In a multiple regression model, where the x's are predictors and y is the response,multicollinearity occurs when:a) The x's provide redundant information about yb) The x's provide complementary information about y c) The x's are used to construct multiple lines, all of which are good predictors of yd) The x's are used to construct multiple lines, all of which are bad predictors of y14. Write the prediction equation given the following results from a sample of 100 (NOFORMULAS GIVEN)STA 3024 Practice Questions, Fall 2007, Page 2 of 1415. Match the statements below with the corresponding terms from the list. a) Multicollinearity b) Extrapolationc) R2 adjusted d) Quadratic regressione) Interaction f) Residual plotsg) Fitted equation h) Dummy variablesi) Cause and effect j) multiple regression modelk) R2l) Residualm) Influential points n) Outliersi. ____ Used when a numerical predictor has a curvilinear relationship with the responseii. ____ Worst kind of outlier, can totally reverse the direction of association between x and y.iii. ____ Used to check the assumptions of the regression model.iv. ____ Used when trying to decide between two models with different numbers of predictors.v. ____ Used when the effect of a predictor on the response depends on other predictors.vi. ____ Proportion of the variability in y explained by the regression model.vii. ____ Is the observed value of y minus the predicted value of y for the observed x..viii. ____ a point that lies far away from the rest.ix. ____ can give bad predictions if the conditions do not hold outside the observed range of x's. x. ____ can be erroneously assumed in an observational study.xi. ____ y = β0 +β1x1 + β2x2 +...+βpxp + ε ε ~ N(0,σ2)xii. ____ yˆ= b0 +b1x1 + b2x2 +...+bpxpxiii. ____ Problem that can occur when the information provided by several predictors overlaps.xiv. ____ Used in a regression model to represent categorical variables.STA 3024 Practice Questions, Fall 2007, Page 3 of 14mean stdev correlationx 163.5 16.2 – 0.774y 874.1 54.2Questions 16 – 19 Palm readers claim to be able to tell how long your life will be by looking at aspecific line (called life-line) on your hand. The following is a plot of age of person at death (inyears) vs. length of life-line on the right hand (in cm) for a sample of 28 (dead) people. Age 16. If we fit a simple linear