Question

Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 32.4 34.5 36.1 44.0 47.8 y 29.6 31.4 32.0 42.1 42.2

(a) Verify that Σx = 194.8, Σy = 177.3, Σx2 = 7764.06, Σy2 = 6439.37, Σxy = 7067.1, and r ≈ 0.978. Σx Σy Σx2 Σy2 Σxy r

(b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t critical t

(c) Verify that Se ≈ 1.4904, a ≈ -0.1182, and b ≈ 0.9132. Se a b

(d) Find the predicted dealer invoice when the list price is x = 41 (thousand dollars). (Use 2 decimal places.)

(e) Find a 95% confidence interval for y when x = 41 (thousand dollars). (Use 2 decimal place.) lower limit upper limit

(f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t

(g) Find a 95% confidence interval for β and interpret its meaning. (Use 3 decimal places.) lower limit upper limit

Answer 1

a) Correlation coefficient is r=0.9779

b) r>0