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.

1. Based on the results above, is there a relationship between Price and Carat, and why? Assume =5%.
2. What does the slope, \[{{\hat{\beta }}_{1}}\] = 9349, mean in terms of Price and Carat?
3. What does \[{{\hat{\beta }}_{0}}\] = 1696 mean? Does it have a practical meaning here?
4. Build a 95% confidence interval for the slope. What does it mean?
5. Identify and interpret the coefficient of determination.
6. As a thorough statistician, you produced the following graphs. What is your opinion about the assumptions of the model?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document