Question

A jeweler prices diamonds on the basis of quality (with values from 0 to 8, with 8 being flawless and 0 containing numerous imperfections) and color (with values from 1 to 10, with 10 being pure white and 1 being yellow). Based on the price per carat (in hundreds of dollars) of the following 11 diamonds of approximately the same weight, determine the relationship between quality (X1), color (X2) and price (Y).

Color Quality Price

7 5 65

3 7 38

5 8 51

8 1 38

9 3 55

5 4 43

4 0 25

2 6 33

8 7 71

6 4 51

9 2 49

1)Identify the correlation coefficient and the coefficient of interpretation, and comment on the strength of the linear relationship (very strong, strong, somewhat strong, not strong)

2) Determine the regression equation

3) Make one prediction of the dependent variable, y, by substituting values into the independent variables, x

4) Identify the result of the test for significance of the regression equation

Answer 1

1) The karl pearson correlation coefficient is

The relation between Color and price is 0.625

The relation between Color and Quality is -0.334

The relation between price and quality is 0.431

2)

The regression equation is
Price = 1.75 + 4.90 Color + 3.76 Quality

3) The output from MINITAB is

The p-value of color and quality is less than alpha 0.05 There the both variables are significant

4) P-value of regression is 0.000 < alpha 0.05 so we reject H0

Thus we conclude that the regression is best fit to the given data