Reading 12- LOS e (Part 1) : Q1- 3

1.Consider the following analysis of variance (ANOVA) table:

The F-statistic for the test of the fit of the model is closest to:

A)   0.10.

B)   0.25.

C)   10.00.

D)   0.20.

The correct answer was C)

F = MSR/MSE = 20 / 2 = 10.

2.A dependent variable is regressed against three independent variables across 25 observations. The regression sum of squares is 119.25, and the total sum of squares is 294.45. The following are the estimated coefficient values and standard errors of the coefficients.

What is the p-value for the test of the hypothesis that all three of the coefficients are equal to zero?

A)   lower than 0.025.

B)   Between 0.025 and 0.05.

C)   Between 0.05 and 0.10.

D)   Greater than 0.10.

The correct answer was A)

This test requires an F-statistic, which is equal to the ratio of the mean regression sum of squares to the mean squared error. The mean regression sum of squares is the regression sum of squares divided by the number of independent variables, which is 119.25 / 3 = 39.75. The residual sum of squares is the difference between the total sum of squares and the regression sum of squares, which is 294.45 − 119.25 = 175.20. The denominator degrees of freedom is the number of observations minus the number of independent variables, minus 1, which is 25 − 3 − 1 = 21. The mean squared error is the residual sum of squares divided by the denominator degrees of freedom, which is 175.20 / 21 = 8.34. The F-statistic is 39.75 / 8.34 = 4.76, which is higher than the F-values (with 3 numerator degrees of freedom and 21 denominator degrees of freedom) of 3.07 at the 5% level of significance and higher than the F-value of 3.82 at the 2.5% level of significance. The conclusion is that the p-value must be lower than 0.025. Remember the p-value is the probability that lies above the computed test statistic for upper tail tests or below the computed test statistic for lower tail tests.

3.Consider the following analysis of variance (ANOVA) table:

The F-statistic for the test of the fit of the model is closest to:

A)   0.10.

B)   0.25.

C)   0.20.

D)   10.00.

The correct answer was D)

F = MSR/MSE = 20 / 2 = 10.