Question 13 4 pts Many high school students take either the SAT or the ACT. However, some students take both. Data were collected from 100 students who took both college entrance exams. The average SAT score was 920 with a standard deviation of 170. The average ACT score was 20 with a standard deviation of 5. The correlation coefficient r between these two variables equals 0.82. To predict the SAT score from a student's ACT score, what is the equation of the least-squares regression line? Show your work for full credit. Question 14 4 pts A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their beginning salary is Y 2500+ 2.1X where Y is the current salary, and X is the beginning salary. Jay started working for the company earning $ 30,000. He currently earns $60,000. What is the residual for Jay (assuming no extrapolation error)? Show your work for full credit. Question 15 4 pts In a study of cars that may be considered classics (all built in the 1970s), the least-squares regression line of mileage (in miles per gallon) on vehicle weight (in thousands of pounds) is calculated to be mileage = 45 - 7.5 weight The mileage for a small Chevy is predicted to be 22 miles per gallon. What was the weight (lbs) of this car? Show your work for full credit. Question 16 2 pts It is widely believed that a person's level of fitness prior to undergoing corrective knee surgery is an important factor in the speed of rehabilitation following surgery. A study was undertaken with 24 randomly selected male subjects who were to undergo such surgery. The physical fitness status of each subject before the surgery was categorized as being: below average, average, or above average. Following surgery the number of days spent in physical therapy by each patient until fully rehabilitated was measured. If the null hypothesis for the ANOVA F test is that the population mean number of days spent in physical therapy are equal for all three physical fitness status. What is the alternative hypothesis? The three population mean number of days spent in physical therapy are all different from each other. The population mean number of days spent in physical therapy is shorter for above average than the other two groups. The population mean number of days spent in physical therapy is longer for below average than the other two groups. Not all three population mean number of days spent in physical therapy are equal to each other. Question 11 4 pts In a study of 2000 model cars, a researcher computed the least-squares regression line of price (in collars) on horsepower. He obtained the following equation of this regression line. Price = -7000+ 170 x horsepower Based on the least-squares regression line, what would we predict the cost of a 2000 model car with horsepower equal to 230 to be (assuming no extrapolation error)? Show your work for full credit. Question 12 4 pts In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least-squares regression line was Y 10+ 0.85 X where Y represents the final exam score, and X is the midterm exam score. Suppose Jay scores an 83 on the midterm exam. What would be the predicted value of his score on the final exam (assuming no extrapolation error)? Show your work for full credit.