1. The parameters to be estimated in the simple linear regression model Y u+fx+s c-N(0,o) are: a) a, B. G bja, B. c c) a, b, s d) E, 0, a 2. We can measure the proportion of the variation explained by the regression model by: ajr b) R' c) o d) F 3. The MSE is an estimator of: aje b) 0 c) 02 dj Y 4. In multiple regression with p predictor variables, when constructing a confidence interval for any B, the degrees of freedom for the tabulated value of t should be: a) n-1 b) n-2 c) n- p-1 d) p-1 5. In a regression study, a 95% confidence interval for , was given as: (-5.65, 2.61). What would a test for Ho: B1 0 vs Ha: Biz0 conclude? a) reject the null hypothesis at a 0.05 and all smaller a b) fail to reject the null hypothesis at a 0.05 and all smaller a c) reject the null hypothesis at a 0.05 and all larger a d) fail to reject the null hypothesis at a 0.05 and all larger a 6. In simple linear regression, when B is not significantly different from zero we conclude that: a) X is a good predictor of Y b) there is no linear relationship between X and Y c) the relationship between X and Y is quadratic d) there is no relationship between X and Y 7. In a study of the relationship between X-mean daily temperature for the month and Y-monthly charges on electrical bill, the following data was gathered: X 20 30 50 60 80 90 Which of the following seems the most likely model? Y 125 110 95 90 110 130 a) Y-a +fx+c b) Y-a +Ax+E c) Y-a +B,x+pix +E d) Ya+pixtexte Bro 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 x b) a change in x causes a change in y c) changes in x are not related to changes in y d) changes in x are associated to changes in y 9. 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 response b) somewhat smaller than the corresponding confidence interval for the mean response ") one unit larger than the corresponding confidence interval for the mean response d) one unit smaller than the corresponding confidence interval for the mean response15. Match the statements below with the corresponding terms from the list. a) multicollinearity b) extrapolation c) R adjusted d) quadratic regression e) interaction f) residual plots g) fitted equation h) dummy variables i) cause and effect j) multiple regression model k) R 1) residual m) influential points n) outliers Used when a numerical predictor has a curvilinear relationship with the response. Worst kind of outlier, can totally reverse the direction of association between x and y. Used to check the assumptions of the regression model. Used when trying to decide between two models with different numbers of predictors. Used when the effect of a predictor on the response depends on other predictors. Proportion of the variability in y explained by the regression model. Is the observed value of y minus the predicted value of y for the observed x.. A point that lies far away from the rest. Can give bad predictions if the conditions do not hold outside the observed range of x's. Can be erroneously assumed in an observational study. ja+bixitbzxz+...+boxp Problem that can occur when the information provided by several predictors overlaps. Used in a regression model to represent categorical variables.Let the following model describe the true relationship between variables y, I and 2: y = Bot Bix+ Bzz + 1 (1) 1. (5 points) Assume availability of a sample (;, r;, 2;), i = 1. ....n. Discuss under which conditions the OLS estimates of 8, and 8, are unbiased.2. (3 points) Suppose we are particularly interested in estimating 3, but we only have information on a random sample for (yi, r; ), i = 1, . . ., n. Under which conditions would it be correct to estimate the model y = Bo+ Bir tu
