Question

1) True or False? We use Femlab (labor force participation rate among females) to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. By the Excel ANOVA table on the overall significance below (some information is missing but can be worked out for the full information ANOVA table), it must be the case that the SSR is 5377.836 and SST is 54745.225.

Source of variation	Sum of Squares	Degrees of Freedom	Mean Square	F-Statistic
Regression		1	5377.836
Residual	49367.389
Total		49

2) Based off the table presented above, We use Femlab (labor force participation rate among females) to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. By the Excel ANOVA table on the overall significance below, the MSE must be equal to

a) 1028.487

b) 2140.525

c) 865.231

d) 3148.792

3) Based off the table presented above, We use Femlab (labor force participation rate among females) to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. By the Excel ANOVA table on the overall significance below, the F statistic must be equal to

a) 1.364

b) 3.547

c) 5.229

d) 8.523

4) True or False? We use Femlab (labor force participation rate among females) to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. By the Excel ANOVA table on the overall significance below, we fail to reject the null hypothesis that the overall fit of this model is poor, because the F statistic is less than the F critical value in a right tailed-test, at α ൌ 0.05 (Hint: you can use the Excel function F.INV.RT(α, df1, df2) to find the critical value) Based off the table presented above

Answer 1

Solution:

Given:

Source of variation	Sum of Squares	Degrees of Freedom	Mean Square	F-Statistic
Regression		1	5377.836
Residual	49367.389
Total		49

Question 1)

By the Excel ANOVA table on the overall significance below (some information is missing but can be worked out for the full information ANOVA table), it must be the case that the SSR is 5377.836 and SST is 54745.225.

Since MSR = 5377.84 and df for regression is 1

thus

MSR = SSR / dfregression

5377.836 = SSR / 1

SSR = 5377.836

Thus

SST = SSR + SSE

SST = 5377.836 + 49367.389

SST = 54745.225

Thus given statement is True.

Question 2)

By the Excel ANOVA table on the overall significance below, the MSE must be equal to____?

df for total = df_total = 49

df for error = df_error = df_total + df_regression

df_error = 49 - 1

df_error = 48

thus

MSE = SSE / df_error

MSE = 49367.389 / 48

MSE = 1028.487

Thus correct answer is: a) 1028.487

Question 3)

By the Excel ANOVA table on the overall significance below, the F statistic must be equal to_____?

F statistic = MSR / MSE

F statistic = 5377.836 / 1028.487

F statistic = 5.229

Thus correct answer is: c) 5.229

Question 4)

By the Excel ANOVA table on the overall significance below, we fail to reject the null hypothesis that the overall fit of this model is poor, because the F statistic is less than the F critical value in a right tailed-test, at α = 0.05

Find F critical value using Excel command:

=F.INV.RT( probability , df1 , df2)

=F.INV.RT( α , df_regression , df_error )

=F.INV.RT( 0.05 , 1 , 48 )

=4.043

Thus F critical value = 4.043

Since F test statistic value = 5.229 > F critical value = 4.043, we reject null hypothesis H0 at 0.05 level of significance.

Thus given statement is False.