Question 1

A simple regression analysis linking a dependent variable y to an independent variable x is conducted with 20 observations.The p-value value for t_stat in the  = 0 hypothesis test turns out to be .0162.The p-value value for F_stat in the same test must be A)1 - .0162 = .9838. B)2 times .0162 = .0324 C).0162. D)statistically significant at the 1% significance level. E)none of the above

Accepted Answer

In simple linear regression, the p-value for the t-test of the slope coefficient (testing the hypothesis that β = 0) and the p-value for the F-test (testing the overall significance of the regression) are the same. Therefore, if the p-value for the t-test is .0162, the p-value for the F-test is also .0162.

Question 2

1% of the values in an F distribution with numerator degrees of freedom= 5 and denominator degrees of freedom = 22 are greater than ___.
A)3.988
B)2.661
C)4.102
D)3.939
E)2.699

Accepted Answer

The answer of 1% of the values in an F...

Question 3

A regression analysis involved 4 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the numerator degrees of freedom should be
A)15
B)4
C)2
D)16
E)none of the above

Accepted Answer

The numerator degrees of freedom for an F-test in regression analysis is equal to the number of independent variables, which in this case is 4.

Question 4

In multiple regression analysis
A)there can be any number of dependent variables but only one independent variable
B)there must be only one independent variable
C)the coefficient of determination must be larger than 1
D)there can be several independent variables, but only one dependent variable
E)none of the above

Accepted Answer

In multiple regression analysis, the model is designed to predict the outcome of a single dependent variable based on the values of two or more independent variables. This allows for the examination of how multiple factors may influence a single outcome.

Question 5

A simple regression analysis linking dependent variable y to independent variable x is conducted with 25 observations.The value of F_stat used to test the $\beta$= 0 null hypothesis turns out to be 12.7.The value of t_stat for the x coefficient is A)15 B)3.56 C)12.7 D)161.29 E)cannot be determined from the information given

Accepted Answer

The t-statistic for the x coefficient can be derived from the F-statistic in a simple linear regression with one independent variable using the relationship $ t^2 = F $. Therefore, $ t = \sqrt{12.7} \approx 3.56 $.

Question 6

A simple regression analysis linking dependent variable y to independent variable x is conducted with 20 observations.The F ratio used to test the  = 0 null hypothesis indicates that the slope coefficient is statistically significant at the 5% significance level.The value of t_stat for the x coefficient will also show that the slope coefficient is A)statistically significant at the 2.5% significance level. B)greater than F C)statistically significant at the 5% significance level. D)statistically significant at the 1% significance level. E)none of the above

Accepted Answer

In simple linear regression, the t-test for the slope coefficient and the F-test for the overall model significance will give the same p-value. Therefore, if the F-test shows the slope is significant at the 5% level, the t-test will also show significance at the 5% level.

Question 7

A regression analysis involved 5 independent variables and 15 observations..In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be
A)9
B)10
C)14
D)4
E)none of the above

Accepted Answer

The denominator degrees of freedom in a regression analysis is calculated as the total number of observations minus the number of parameters being estimated (including the intercept). Here, it is 15 observations minus 6 parameters (5 independent variables plus the intercept), which equals 9.

Question 8

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 12 are greater than ___.
A)3.634
B)4.451
C)6.112
D)6.226
E)3.490

Accepted Answer

The answer of 5% of the values in an F...

Question 9

A regression analysis involved 6 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be
A)26
B)13
C)14
D)25
E)none of the above

Accepted Answer

The answer of A regression analysis involved 6 independent variables...

Question 10

A multiple regression analysis uses 5 independent variables and 15 observations.The F ratio for testing the 'all s are 0' null hypothesis turns out to be statistically significant at the 5% significance level.It must be true that ____ of the regression coefficients are (is) statistically significant at the 5% level.
A)all
B)at least one
C)most
D)none
E)none of the above

Accepted Answer

The answer of A multiple regression analysis uses 5 independent...

Question 11

A regression analysis involved 6 independent variables and 27 observations.The t distribution in which we will find the critical value of t for testing the significance of each of the independent variable coefficients will have
A)20 degrees of freedom
B)21 degrees of freedom
C)26 degrees of freedom
D)27 degrees of freedom
E)none of the above

Accepted Answer

The degrees of freedom for the t distribution in a regression analysis is calculated as the number of observations minus the number of parameters being estimated. Here, it is 27 observations minus 6 independent variables (plus 1 for the intercept), which equals 20 degrees of freedom.

Question 12

In an F distribution with numerator degrees of freedom of 4 and denominator degrees of freedom of 8, 99% of the values are less than ______ .
A)3.838
B)6.041
C)7.006
D)14.799

Accepted Answer

The 99th percentile of an F-distribution with 4 numerator degrees of freedom and 8 denominator degrees of freedom is approximately 7.006.

Question 13

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 17 are greater than ___.
A)3.758
B)2.576
C)2.549
D)3.812
E)3.197

Accepted Answer

The answer of 5% of the values in an F...

Quiz 12: Multiple Regression

A simple regression analysis linking a dependent variable y to an independent variable x is conducted with 20 observations.The p-value value for t_stat in the  = 0 hypothesis test turns out to be .0162.The p-value value for F_stat in the same test must be

1% of the values in an F distribution with numerator degrees of freedom= 5 and denominator degrees of freedom = 22 are greater than ___.

A regression analysis involved 4 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the numerator degrees of freedom should be

In multiple regression analysis

A simple regression analysis linking dependent variable y to independent variable x is conducted with 25 observations.The value of F_stat used to test the $\beta$ = 0 null hypothesis turns out to be 12.7.The value of t_stat for the x coefficient is

A regression analysis involved 5 independent variables and 15 observations..In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 12 are greater than ___.

A regression analysis involved 6 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A regression analysis involved 6 independent variables and 27 observations.The t distribution in which we will find the critical value of t for testing the significance of each of the independent variable coefficients will have

In an F distribution with numerator degrees of freedom of 4 and denominator degrees of freedom of 8, 99% of the values are less than ______ .

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 17 are greater than ___.