Question: Suppose that you decided to go into the jewelry business. You collected data that relates price (y) to diamond carats (x), ran the model in Minitab, and you obtained the following results.

The regression equation is

Price = - 1696 + 9349 Carat

Predictor Coef SE Coef T P

Constant -1696.2 298.3 -5.69 0.000

Carat 9349.4 794.1 11.77 0.000

S = 331.921 R-Sq = 78.5% R-Sq(adj) = 77.9%

Analysis of Variance

Source DF SS MS F P

Regression 1 15270545 15270545 138.61 0.000

Residual Error 38 4186512 110171

Total 39 19457057

Unusual Observations

Obs Carat Price Fit SE Fit Residual St Resid

33 0.450 1572.0 2511.0 82.6 -939.0 -2.92R

R denotes an observation with a large standardized residual.

a. Based on the results above, is there a relationship between Price and Carat, and why? Assume ?=5%.

b. What does the slope, = 9349, mean in terms of Price and Carat?

c. What does = ?1696 mean? Does it have a practical meaning here?

d. Build a 95% confidence interval for the slope. What does it mean?

e. Identify and interpret the coefficient of determination.

f. As a thorough statistician, you produced the following graphs. What is your opinion about the assumptions of the model?