Question

Provided below is a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (Y), unit price (X1 in $1,000) and the number of advertising spots (X2) they used on a local television station.

ANOVA Table
DF SS MS F Significance F
Regression 2 655.955
Error 9 182.96
Total 838.917

At α = 0.05 level of significance, what is the F value?

At α = 0.05 level of significance, what is critical F?

At α = 0.05 level of significance, is the regression model significant?

What is the multiple coefficient of determination?

What is the adjusted multiple coefficient of determination?

Answer 1

Answer on Question #57134 – Math – Statistics and Probability

Provided below is a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (Y), unit price (X1 in $1,000) and the number of advertising spots (X2) they used on a local television station.

ANOVA Table

At $\alpha = 0.05$ level of significance, what is the F value?

At $\alpha = 0.05$ level of significance, what is critical F?

At $\alpha = 0.05$ level of significance, is the regression model significant?

What is the multiple coefficient of determination?

What is the adjusted multiple coefficient of determination?

Solution

At $\alpha = 0.05$ level of significance, the F value is

$$F = \frac {M S _ {r e g r}}{M S _ {e r r}} = \frac {\frac {6 5 5 . 9 5 5}{2}}{\frac {1 8 2 . 9 6}{9}} = 1 6. 1 3 4$$

At $\alpha = 0.05$ level of significance, critical F is

$$F _ {c r} = F (2; 9; 0. 0 5) = 4. 2 5 6$$

At $\alpha = 0.05$ level of significance, the regression model is significant,

because $F > F_{\text{crit}}$.

The multiple coefficient of determination is

$$R ^ {2} = 1 - \frac {S S _ {e r r}}{S S _ {t o t a l}} = 1 - \frac {1 8 2 . 9 6}{8 3 8 . 9 1 7} = 0. 7 8 1 9$$

The adjusted multiple coefficient of determination is

$$R _ {a d j} ^ {2} = 1 - \frac {M S _ {e r r}}{M S _ {t o t a l}} = 1 - \frac {\frac {1 8 2 . 9 6}{9}}{\frac {8 3 8 . 9 1 7}{1 1}} = 0. 7 3 3 4$$

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