Name: Class: Date: Rand Final Pop 2 Multiple Choice Identify the choice that best completes the statement or answers the question. Scenario 12-1 A high school guidance counselor wonders if it is possible to predict a student s GPA in their senior year from their GPA in the first marking period of their freshman year. She selects a random sample of 15 seniors from the graduating class of 468 and records both full-year GPA in their senior year ( Senior ) and first-marking-period GPA in their freshman year ( Fresh ). A computer regression analysis and a residual plot of these data are given below. Constant 1.6310 0.5328 3.06 0.009 Fresh 0.5304 0.1789 2.96 0.011 S = 0.3558 R-Sq = 40.3% R-Sq(adj) = 35.7% 1. Use Scenario 12-1. Which of the following is the estimate from this sample for the standard deviation of the sampling distribution of slopes? A. 0.1789 B. 0.3558 C. 0.5304 D. 0.5328 E. 1.6310 1
Name: Scenario 12-2 Can we predict annual household electricity costs in a specific region from the number of rooms in the house? Below is a scatterplot of annual electricity costs (in dollars) versus number of rooms for 30 randomly-selected houses in Michigan, along with computer output for linear regression of electricity costs on number of rooms. Constant 406.9 164.8 2.47 0.020 Rooms 58.45 24.77 2.36 0.026 S = 246.735 R-Sq = 16.6% R-Sq(adj) = 13.6% 2. Use Scenario 12-2. Both the scatterplot and the residual plot indicate that residuals for 3 rooms and 8 and 9 rooms tend to be lower than residuals for 4 through 7 rooms. Which condition for regression inference is not satisfied in this case? A. Mean Annual Electricity costs is a linear function of Number of rooms. B. Observations for each household are independent. C. For each number of rooms, the distribution of annual electricity costs is roughly Normal. D. The variance of annual electricity costs is roughly equal for each number of rooms. E. The data come from a random sample. 3. Use Scenario 12-2. Which value in the computer output is the estimate from this sample for the standard deviation of the residuals? A. 24.77 B. 58.45 C. 164.8 D. 246.735 E. This quantity is not provided by the computer output. 2
Name: 4. Use Scenario 12-2. Which of the following statements is a correct interpretation of information in this computer output? A. A one-room house is predicted to have annual electricity costs of $58.45. B. For each additional room a house has, predicted annual electricity costs increase by $58.45. C. For each additional room a house has, predicted annual electricity costs increase by $24.77. D. The standard deviation in annual electrical costs for houses in this sample is $246.735. E. The standard deviation in annual electrical costs for houses in this sample is $24.77. Scenario 12-3 Are high school students who like their English class more likely to enjoy their history class as well? Here is a regression analysis and residual plot for 30 randomly-selected students who were asked to rate how much they liked both English and history on a 0 to 5 scale (a higher rating means the student liked the subject more). [Data from 2004-5 Census at Schools survey in Canada]. Constant 1.1867 0.5574 2.13 0.042 English 0.5254 0.1995 2.63 0.014 S = 1.37707 R-Sq = 19.8% R-Sq(adj) = 17.0% 5. Use Scenario 12-3. We wish to perform a t-test for regression slope. What is the test statistic for this test? A. 0.014 B. 0.1995 C. 1.37707 D. 2.13 E. 2.63 3
Name: 6. Use Scenario 12-3. Assuming that the conditions for inference have been met, which of the following represents a 99% confidence interval for the rate of change in history rating for a one-unit change in English rating? A. B. C. D. E. Scenario 12-5 Can we predict annual household electricity costs in a specific region from the number of rooms in the house? Below is computer output for a regression of annual electricity costs (in dollars) on number of rooms for 30 randomly-selected houses in Michigan. Assume the conditions for regression inference have been met. 7. Use Scenario 12-5. Which of the following represents the proportion of variation in annual electricity costs that is accounted for by the regression of annual electricity costs on number of rooms? A. 0.020 B. 0.026 C. 0.166 D. E. 4