+ 70% 3 1b) Cak On the graph below complete the scatterplot of the 12 Toyotas' ages (1-5 years) on the X axis against their asking price (10-18 $K) on the Y axis. Draw a rough best-fitting straight line through the plot, making sure it passes through the point (X,Y). (3 pts) Price (SK) 18 16 15 14 13 12 11 10 1.00 M tv 2.00 3.00 4.00 5.00 Age ZA W N P -+ 70% 4 1c) It appears that age and asking price are related. Is it a positive or negative linear relationship? What indicates that it is either positive or negative? (2 pts) 1d) Does it appear to be a strong or weak relationship? Why do you say this? (2 pts) 1e) Using the numbers you've computed in 1a), calculate the covariance between X and Y using the formula found near the top of p. 192 in section 9.3 (also found at the bottom of p. 573 in Appendix C. (3 pts) 1f) COVxy = Calculate the standard deviations of X and Y (Sx & Sy) using either of the two formulas found in the middle of p. 89 in Section 5.6 and on p. 572. (6 pts) Sx= Sy= tv all Z A W P 5 1g) Calculate the correlation coefficient (to 3 decimal places) between age and price using the definitional formula for r given near the middle of p. 192 in Section 9.4 and the top of p. 574. (3 pts) 1h) Calculate the correlation coefficient (to 3 decimal places) between age and price using the computational formula for r given near the bottom of p. 192 in section 9.4. (3 pts) 11) Do your answers from 1g) and 1h) match (within rounding error)? (If not, you've made a calculation error) (1 pt) 1j) If we want to know if age and price are negatively correlated for the population of used 1-5 year-old Corollas, what are the symbolic forms of the null and the (directional) alternative hypotheses (see p. 205 in Section 9.10)? (2 pts) 1k) Ho: H: What are the degrees of freedom for this problem (see p. 231 in Section 10.2)? df = (1 pt) 11) Assume = .05. What is the critical value of the correlation coefficient (from Table E.2)? r.05 (_) (2 pts) 1m) What is your decision with respect to the null hypothesis? Why do you make this decision? (2 pts) 1n) What do you conclude about the relationship (i.e., significant/not significant; positive/negative) between the age of a used Corolla and its asking price? (2 pts) E W N 6 2a) Calculate the coefficient of determination for this data. (2 pts) 2b) Given the above, what percentage of the variability in asking price is attributable to the variability in the car's age (see pp. 242-243 in Section 10.4)? % (1 pt) 2c) Can you interpret this to mean that a little more than two-thirds of the variability in asking price is caused by the vehicle's age? Why or why not? (2 pts) 3a) For the above example, compute the regression equation for predicting the asking price (Y) from the age (X) of the Corollas. First, use the equations to calculate the slope and intercept as given on p. 233 in Section 10.3 and p. 574 in Appendix C. (6 pts) b= a= What is your final regression equation (should take the same form as the formula near the middle of p. 234 in Section 10.3). [You should get a predicted Y value of 6.72 (within rounding error) for an X value of 7. If not, you have made an error somewhere] (1 pt) L C W N 3b) 7 Using the above regression equation, predict the asking price for a 1-year-old Corolla, and for a 4-year-old Corolla. (6 pts) 1-year-old Corolla: 3c) 4-year-old Corolla: Your answers should fit on the regression line in your scatterplot (1b). If not, you've made an error somewhere on your graph or calculations. In Lab 9 (and on p. 234 in Section 10.3) it is explained how to interpret the slope and intercept. Given the regression equation from 3a) how would you interpret the slope with respect to the predicted asking price of Corollas? (1 pt) How would you interpret the intercept with respect to the predicted asking price of Corollas? stv (1 pt) W P 2 For each calculation question (starting with 1e), you must show the formula used, the substitution of numbers into the formula, and your final answer (rounded off to two decimal places). 1a) The data given below represent the age (in years) and asking price (in thousands of dollars, rounded off) for a sample of 12 used Toyota Corollas (sedan, blue or silver exterior, automatic transmission) advertised on AutoTrader.ca on a randomly chosen day. Calculate the means of X and Y and complete the calculations in the table, including the column sums on the shaded 2nd to bottom row. The last row helps you identify the term. Hint: SP should equal -40. If yours doesn't, you've made a math error somewhere. (10 pts) V# Age Price (X) M (X-X) (Y-Y) (X-X) (Y-Y) (X-X) (Y-Y) x Y XY 1 2 18 -1 4 4 324 2 4 12 1 -2 16 16 144 3 4 11 1 -3 16 121 4 3 17 0 3 9 289 5 3 14 0 0 9 196 62 17 -1 3 4 289 7 2 16 -1 2 4 256 00 6 4 10 1 -4 16 16 100 5 11 2 -3 25 25 121 10 1 17 -2 3 1 289 11 1 15 -2 1 1 225 12 5 10 2 -4 25 100 (X-X) (Y-Y) E(X-X)2 (Y-Y) E(X-X)(Y-Y) EXEY EXY X = = Y =