Question 1

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. We want to test whether the parameter $\beta$₁ is significant. The test statistic equals

Accepted Answer

The test statistic for determining the significance of a parameter is typically calculated as the estimated coefficient divided by its standard error. The value of 2.8 suggests that this is the calculated test statistic for $\beta$₁.

Question 2

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test of significance for the parameter $\beta$₁ at the 1% level. The null hypothesis should be

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Question 3

Exhibit 15-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 15-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is

Accepted Answer

To test for the significance of the model, we need to perform an F-test with the following hypotheses: 
H0: β1 = β2 = β3 = β4 = 0 (the model has no explanatory power)
Ha: at least one βi is not equal to 0 (the model has explanatory power)
Under the null hypothesis, the expected value of SSR divided by its degrees of freedom (4) is equal to the expected value of SSE divided by its degrees of freedom (n-5=10) which is the error variance (σ2). In other words, SSR/4 and SSE/10 should be about the same. If the model has no explanatory power, then any variation in the dependent variable is due to random error, and the R-squared should be close to 0. Therefore, we can compute the F-statistic as follows:
F = (SSR/4) / (SSE/10) ≈ R2/(1-R2) * (n-5)/4 ~ F(4,10)
where R2 = 1 - SSE/TSS and TSS is the total sum of squares, which can be expressed as TSS = SSR + SSE. 
Plugging in the numbers from the exhibit, we get:
F = (165/4) / (60/10) ≈ 0.69 * 2 = 1.38
To find the critical F-value from the table with α=0.05 and (df1=4, df2=10), we look at the intersection of the row for df1=4 and the column for df2=10, which gives us Fcrit = 3.48.
Since our computed F (1.38) is smaller than the critical F (3.48), we fail to reject the null hypothesis and conclude that the model is not significant at the 95% confidence level.

Question 4

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Accepted Answer

The F value at the 5% significance level is typically determined by the degrees of freedom for the numerator and the denominator. Without specific degrees of freedom provided, option C (3.81) is a common critical value for many F-distributions at the 5% level.

Question 5

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

Accepted Answer

The degrees of freedom for the sum of squares explained by the regression (SSR) is equal to the number of independent variables in the model.

Question 6

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Accepted Answer

Based on the output, the p-value is less than 0.05, which indicates that there is significant evidence to reject the null hypothesis. Therefore, we can conclude that there is a relationship among the variables at the 5% level.

Question 7

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Question 8

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on X₁ is that

Accepted Answer

The coefficient on X₁ indicates that a one unit change in X₁ will lead to a 25.625 unit increase in Y when all other variables are held constant. This is the interpretation of a regression coefficient in general, and is particularly applicable when the multiple regression analysis has controlled for the effects of other explanatory variables.

Question 9

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. We want to test whether the parameter $\beta$₁ is significant. The test statistic equals

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Question 10

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Accepted Answer

The test statistic used to determine if there is a relationship among the variables is given by the F-statistic, which in this case is 5.

Question 11

Exhibit 15-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (XS1U1B11S1U1B0) and their gender (XS1U1B12S1U1B0) (0 if male and 1 if female).  Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. From the above function, it can be said that the expected yearly income of

Accepted Answer

The answer of Exhibit 15-8
The following estimated regression model was...

Question 12

Exhibit 15-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 15-7. The coefficient of determination is

Accepted Answer

The coefficient of determination (R-squared) is SSR/SST, where SST is the total sum of squares. Since SST = SSR + SSE, we can calculate SST as 165 + 60 = 225. Therefore, R-squared = SSR/SST = 165/225 = 0.7333. The best choice is B, which is the correct value of the coefficient of determination.

Question 13

Exhibit 15-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 15-7. The test statistic from the information provided is

Accepted Answer

The test statistic for the overall significance of the regression model is calculated using the formula F = (SSR/k) / (SSE/(n-k-1)), where k is the number of independent variables and n is the sample size. Here, k = 4 and n = 15. So, F = (165/4) / (60/(15-4-1)) = 6.875.

Question 14

Exhibit 15-5
Below you are given a partial Minitab output based on a sample of 25 observations. 
-Refer to Exhibit 15-5. The t value obtained from the table to test an individual parameter at the 5% level is

Accepted Answer

The answer of Exhibit 15-5
Below you are given a partial...

Question 15

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The estimated regression equation is

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Question 16

Exhibit 15-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (XS1U1B11S1U1B0) and their gender (XS1U1B12S1U1B0) (0 if male and 1 if female).  Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The yearly income of a 24-year-old male individual is

Accepted Answer

We can use the estimated regression model to estimate the yearly income of a 24-year-old male individual as follows:
Y = b0 + b1*X1 + b2*X2
where Y is the dependent variable (yearly income in $1,000s), X1 is the age of the individual, X2 is the gender (0 if male), and b0, b1, and b2 are the estimated regression coefficients.

Substituting X1 = 24 and X2 = 0 into the regression model, we get:
Y = -8.4 + 0.32*24 + 1.8*0
Y = -8.4 + 7.68
Y = -0.72

This estimate does not make sense because it is negative. This suggests that the estimated regression model may not be a good fit for the data, or that the relationship between income, age, and gender is not accurately captured by the model.

Alternatively, we can use the SST and SSE values to calculate the coefficient of determination (R-squared) as follows:
R-squared = 1 - SSE/SST
R-squared = 1 - 384/1200
R-squared = 0.68

This suggests that the model explains 68% of the total variation in income, and 32% of the variation is unexplained. However, we cannot use this information to estimate the income of a specific individual.

Question 17

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations. 
-Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Question 18

Exhibit 15-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (XS1U1B11S1U1B0) and their gender (XS1U1B12S1U1B0) (0 if male and 1 if female).  Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The yearly income of a 24-year-old female individual is

Accepted Answer

The regression model is Y = b0 + b1X1 + b2X2, where X1 is age and X2 is gender (0 for male and 1 for female). From the model, we can see that the coefficient b1 represents the change in yearly income associated with a one-year increase in age, while the coefficient b2 represents the difference in yearly income between females and males, holding age constant.

To predict the yearly income of a 24-year-old female individual, we plug in X1 = 24 and X2 = 1 into the regression model: Y = b0 + b1(24) + b2(1) = 16.80 + 0.50(24) + 2.50(1) = 19.80.

However, note that the question asks for the yearly income in thousands of dollars, so the answer is $19,800 (option D).

Question 19

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. Carry out the test of significance for the parameter $\beta$₁at the 5% level. The null hypothesis should be

Accepted Answer

The t-statistic for $\beta$₁ is -2.33, and the critical value for a two-tailed test at the 5% level is -2.064. Since the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis.

Question 20

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The interpretation of the coefficient of X₁ is that

Accepted Answer

The answer of Exhibit 15-6
Below you are given a partial...

Quiz 15: Multiple Regression

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test of significance for the parameter β\betaβ 1 at the 1% level. The null hypothesis should be

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 15-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on X1 is that

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 15-7. The coefficient of determination is

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 15-7. The test statistic from the information provided is

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. The t value obtained from the table to test an individual parameter at the 5% level is

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The estimated regression equation is

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. Carry out the test of significance for the parameter β\betaβ 1at the 5% level. The null hypothesis should be

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The interpretation of the coefficient of X1 is that

Exhibit 15-5 Below you are given a partial Minitab output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on X₁ is that

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The interpretation of the coefficient of X₁ is that