Question 1

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -Referring to Table 14-17,which of the following is the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables? A)H₁ : All β_j≠ 0 for j = 0,1,2 B)H₁ : All β_j≠ 0 for j = 1,2 C)H₁ : At least one of β_j≠ 0 for j = 0,1,2 D)H₁ : At least one of β_j ≠ 0 for j = 1,2

Accepted Answer

The correct alternative hypothesis for testing the significance of the relationship between the dependent variable and the explanatory variables is that at least one of the coefficients of the explanatory variables (excluding the intercept) is not equal to zero.

Question 2

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the alternative hypothesis H₁ : At least one of β_j ≠ 0 for j = 1,2 implies that the number of weeks a worker is unemployed due to a layoff is related to all of the explanatory variables.

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 3

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the null hypothesis H₀ : β₁= β₂= 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by some of the explanatory variables.

Accepted Answer

The null hypothesis H₀ : β₁= β₂= 0 implies that both the age of the worker and the dummy variable for management position have no effect on the number of weeks a worker is unemployed due to a layoff, not just some of the explanatory variables. Therefore, the statement is false.

Question 4

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the null hypothesis H₀ : β₁ = β₂ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not related to any of the explanatory variables.

Accepted Answer

The null hypothesis H₀: β₁ = β₂ = 0 suggests that the coefficients of the explanatory variables are zero, indicating no relationship between the unemployment duration and the explanatory variables.

Question 5

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year-old and is a manager.

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 6

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,estimate the mean number of weeks being unemployed due to a layoff for a worker who is a thirty-year-old and is a manager.

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 7

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -Referring to Table 14-17,which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable? A)H₀ : β₁ = 0 B)H₀: β₁≠ 0 C)H₀ : β₂ = 0 D)H₀: β₂ ≠ 0

Accepted Answer

The null hypothesis for testing the effect of age on the number of weeks a worker is unemployed, while controlling for other variables, is that the coefficient of age (β₁) is equal to zero, indicating no effect.

Question 8

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-True or False: Referring to Table 14-17,the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable.

Accepted Answer

Looking at the "t-Value" for the Age variable in the regression output, we see that it is equal to -2.04. To test whether this coefficient is statistically significant, we refer to the "Pr > |t|" column. This value tells us the probability of observing a t-value as extreme or more extreme than what we observed, assuming the null hypothesis is true (i.e., that the true coefficient is equal to 0). In this case, we see that the "Pr > |t|" value for Age is 0.0424, which is less than 0.10. This means we can reject the null hypothesis at the 10% level of significance and conclude that age does have a statistically significant effect on the number of weeks a worker is unemployed due to a layoff, holding constant the effect of the other independent variable (i.e., Manager).

Question 9

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,which of the following is a correct statement?
A)On average,those who are in a management position are estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of age.
B)On average,those who are in a management position are estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of age.
C)On average,those who are in a management position are estimated to stay jobless shorter by approximately 22.5761 weeks while holding constant the effects of age.
D)On average,those who are in a management position are estimated to stay jobless longer by approximately 22.5761 weeks while holding constant the effects of age.

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 10

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the null hypothesis H₀ : β₁ = β₂ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by any of the explanatory variables.

Accepted Answer

The null hypothesis H₀: β₁ = β₂ = 0 suggests that the coefficients of the explanatory variables are zero, indicating that these variables do not have a statistically significant effect on the dependent variable, which in this context is the number of weeks a worker is unemployed.

Question 11

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,which of the following is a correct statement?
A)37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager.
B)37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size.
C)37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance.
D)37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables.

Accepted Answer

The statement refers to the adjusted R-squared value, which accounts for the number of predictors and sample size when explaining the variation in the dependent variable.

Question 12

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,what is the value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 13

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -Referring to Table 14-17,which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable? A)H₁ : β₁ = 0 B)H₁ : β₁ ≠ 0 C)H₁: β₂= 0 D)H₁: β₂ ≠ 0

Accepted Answer

The correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable is H₁ : β₁ ≠ 0. This is because we want to know if there is a significant relationship between age and the number of weeks unemployed, and the inequality symbol (≠) allows for either a positive or negative relationship. A null hypothesis would be β₁ = 0, which would mean there is no significant relationship between age and the number of weeks unemployed.

Question 14

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,which of the following is a correct statement?
A)40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager.
B)40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size.
C)40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance.
D)40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables.

Accepted Answer

The statement correctly interprets the R-squared value as the percentage of variation in the dependent variable that can be explained by the independent variables, without any adjustment for sample size or significance level, and without specifying the control of other variables.

Question 15

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,which of the following is a correct statement?
A)On average,a worker who is a year older is estimated to stay jobless shorter by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable.
B)On average,a worker who is a year older is estimated to stay jobless longer by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable.
C)On average,a worker who is a year older is estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable.
D)On average,a worker who is a year older is estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable.

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 16

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-True or False: Referring to Table 14-17,there is sufficient evidence that age has an effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable at a 10% level of significance.

Accepted Answer

The coefficient for the Age variable is significant with a p-value of 0.032, which is less than the 10% level of significance. Therefore, we can conclude that age has a significant effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable.

Question 17

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,what is the standard error of estimate?

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 18

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the null hypothesis H₀: β₁ = β₂ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not related to one of the explanatory variables.

Accepted Answer

The null hypothesis H₀: β₁ = β₂ = 0 implies that both age and management position are not significant predictors of the number of weeks a worker is unemployed due to a layoff. This means that the variables are not unrelated, but rather that they do not have a significant impact on the outcome variable.

Question 19

TABLE 14-17
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no).
The results of the regression analysis are given below: 
-Referring to Table 14-17,what is the p-value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

Accepted Answer

The answer of TABLE 14-17
Given below are results from the...

Question 20

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -Referring to Table 14-17,which of the following is the correct null hypothesis to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables? A)H₀: β₀ = β₁ = β₂ = 0 B)H₀ : β₁ = β₂= 0 C)H₀ : β₀= β₁= β₂ D)H₀ : β₁ = β₂

Accepted Answer

The null hypothesis for testing the significance of the relationship between the dependent variable and the explanatory variables in a regression model is that all the coefficients of the explanatory variables are equal to zero, indicating no relationship.

Quiz 14: Introduction to Multiple Regression