In a multiple regression with 5 predictors in a sample of 56 U.S. cities, what would be the critical value for an F
test of overall significance at a= .05?
A. 2.45
B. 2.37
C. 2.40
D. 2.56
To find the critical value for an F test of overall significance, we need to use the F-distribution table or statistical software.
The F test of overall significance tests whether there is a significant relationship between the predictors and the dependent variable in a multiple regression analysis.
In this case, since we have 5 predictors and 56 observations, we have a total of 56 - 5 - 1 = 50 degrees of freedom for the numerator (numerator degrees of freedom represent the number of predictors minus one) and 56 - 1 = 55 degrees of freedom for the denominator (denominator degrees of freedom represent the total sample size minus the number of predictors).
To find the critical value at a significance level of 0.05, we can consult an F-distribution table or use statistical software. Let's assume we are using a two-tailed test.
Looking at the F-distribution table or using statistical software, we find that the critical value for an F test with 50 degrees of freedom for the numerator and 55 degrees of freedom for the denominator at a significance level of 0.05 is approximately 2.41.
Therefore, among the given options, the closest value to 2.41 is option C (2.40).