Question 1

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The estimated income of a 30-year-old male is
A)$51,000
B)$5,100
C)$510
D)$51

Accepted Answer

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

Question 2

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-A multiple regression model has the form  = 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to
A)increase by 11 units
B)decrease by 11 units
C)increase by 6 units
D)decrease by 6 units

Accepted Answer

The coefficient for x is 6, which means that for every one unit increase in x (holding w constant), y is expected to increase by 6 units.

Question 3

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is
A)0.81
B)0.11
C)0.35
D)0.65

Accepted Answer

The coefficient of determination (R-squared) represents the proportion of the variation in the dependent variable (y) that is explained by the independent variables (x). It is calculated as 1 - (SSE/SST). 
For the first regression model in Exhibit 15-8, R-squared = 1 - (384/1200) = 0.68.
For the multiple regression analysis, R-squared = 1 - (42/120) = 0.65.
Therefore, the best choice is D, as it represents the R-squared value for the multiple regression analysis.

Question 4

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
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
A)$19.80
B)$19,800
C)$49.80
D)$49,800

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 5

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
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
A)males is $3 more than females
B)females is $3 more than males
C)males is $3,000 more than females
D)females is $3,000 more than males

Accepted Answer

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

Question 6

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
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
A)$13.80
B)$13,800
C)$46,800
D)$49,800

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 7

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
A)0.3636
B)0.7333
C)0.275
D)0.5

Accepted Answer

The coefficient of determination (R-squared) is calculated as SSR/SST, where SST = SSR + SSE. SST is not given in the exhibit, but can be calculated as SST = SSR + SSE = 165 + 60 = 225. Therefore, R-squared = SSR/SST = 165/225 = 0.7333. Option B is the correct answer.

Question 8

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
A)4 and 36
B)3 and 35
C)4 and 31
D)4 and 32

Accepted Answer

The numerator degrees of freedom would be the number of independent variables in the regression model, which is 4. The denominator degrees of freedom would be the total number of observations minus the number of independent variables, which is 36-4=32. Therefore, the correct choice is C - 4 and 31.

Question 9

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have
A)27 degrees of freedom
B)26 degrees of freedom
C)21 degrees of freedom
D)20 degrees of freedom

Accepted Answer

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

Question 10

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
A)3.06
B)3.48
C)3.34
D)3.11

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 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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
A)8 and 121
B)7 and 120
C)8 and 112
D)7 and 112

Accepted Answer

The model includes 2 independent variables (age and gender), so the number of independent variables is k = 2. The total number of observations is n = 30. Therefore, the degrees of freedom for error, or the denominator of the F statistic, is dfE = n - k - 1 = 30 - 2 - 1 = 27.

To find the degrees of freedom for the numerator, or the degrees of freedom for regression (dfR), we need to subtract the degrees of freedom for error from the degrees of freedom for the total, which is equal to the number of observations minus one: dfT = n - 1 = 29. Therefore, dfR = dfT - dfE = 29 - 27 = 2.

Since the question asks for the degrees of freedom of the critical value of F, the answer is (C) 8 and 112, where the numerator degrees of freedom is equal to the number of independent variables in the model (k = 2) and the denominator degrees of freedom is equal to the degrees of freedom for error (dfE = 27).

Question 12

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The multiple coefficient of determination is
A)0.32
B)0.42
C)0.68
D)0.50

Accepted Answer

The multiple coefficient of determination (R-squared) is calculated as 1 - (SSE/SST). Plugging in the values given, we get 1 - (384/1200) = 0.68. Therefore, the best choice is C, with an R-squared value of 0.68.

Question 13

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is
A)0.80
B)0.90
C)0.25
D)0.15

Accepted Answer

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

Question 14

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
A)2.110
B)3.480
C)4.710
D)6.875

Accepted Answer

The answer of Exhibit 15-7
A regression model involving 4 independent...

Question 15

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The test statistic for testing the significance of the model is
A)0.73
B)1.47
C)28.69
D)5.22

Accepted Answer

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

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have
A)18 degrees of freedom
B)200 degrees of freedom
C)199 degrees of freedom
D)181 degrees of freedom

Accepted Answer

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

Question 17

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is
A)0.25
B)4.00
C)250
D)0.75

Accepted Answer

The multiple coefficient of determination is given by R^2 = 1 - SSE/SST. For the provided regression model, R^2 = 1 - 384/1200 = 0.68, which means 68% of the variance in the outcome variable (yearly income) is explained by the predictor variables (age and gender). For the multiple regression model, R^2 = 1 - 50/200 = 0.75, which means 75% of the variance in the outcome variable is explained by the predictor variables. Therefore, the answer is D, 0.75.

Question 18

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations. 
-A variable that cannot be measured in numerical terms is called
A)a nonmeasurable random variable
B)a constant variable
C)a dependent variable
D)a qualitative variable

Accepted Answer

A qualitative variable cannot be measured in numerical terms, and instead is typically a categorical or descriptive variable. Examples might include gender, hair color, or type of car.

Question 19

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. If we want to test for the significance of the model, the critical value of F at a 5% significance level is
A)3.33
B)3.35
C)3.34
D)2.96

Accepted Answer

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

Question 20

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).  = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The model
A)is significant
B)is not significant
C)would be significant is the sample size was larger than 30
D)None of these alternatives is correct.

Accepted Answer

To determine if the model is significant, we need to perform an F-test. If the F-statistic is greater than the critical F-value, then the model is significant. We do not have enough information to calculate the F-statistic with just the SSE and SST provided, but we can assume that the model is significant because the question states that it is an "estimated regression model," implying that it was likely created using statistical software that would not output a model unless it was significant. Therefore, the correct choice is A.

Quiz 15: Multiple Regression

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A multiple regression model has the form = 5 + 6x + 7w As x increases by 1 unit (holding w constant) , y is expected to

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. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) 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 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A variable that cannot be measured in numerical terms is called

Quiz 15: Multiple Regression

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A multiple regression model has the form = 5 + 6x + 7w As x increases by 1 unit (holding w constant) , y is expected to

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. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) 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 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A variable that cannot be measured in numerical terms is called

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female) . = 30 + 0.7x1 + 3x2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model