Multiple Linear Regression

Question 1 of 15

1. Question

Questions 1-5 refer to the following information:

A financial analyst is conducting a multiple linear regression analysis to determine the factors that influence the stock price of a particular company. The analyst uses the following independent variables in the regression model:

Earnings per share (EPS)
Book value per share (BVPS)
Price-to-earnings ratio (P/E)
Return on equity (ROE)

The analyst collects data for 50 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	24.25	1.23	19.72	0.000
EPS	0.98	0.07	13.64	0.002
BVPS	1.15	0.08	14.29	0.001
P/E	0.57	0.11	5.20	0.042
ROE	-0.75	0.06	-12.27	0.003
R-squared	0.80
Adjusted R-squared	0.78
Standard Error	5.12

Calculate the predicted stock price for a quarter where the company has an EPS of 1.20, BVPS of 10.50, P/E of 20, and ROE of 0.12.

29.75
31.04
33.89

Question 2 of 15

2. Question

Questions 1-5 refer to the following information:

A financial analyst is conducting a multiple linear regression analysis to determine the factors that influence the stock price of a particular company. The analyst uses the following independent variables in the regression model:

Earnings per share (EPS)
Book value per share (BVPS)
Price-to-earnings ratio (P/E)
Return on equity (ROE)

The analyst collects data for 50 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	24.25	1.23	19.72	0.000
EPS	0.98	0.07	13.64	0.002
BVPS	1.15	0.08	14.29	0.001
P/E	0.57	0.11	5.20	0.042
ROE	-0.75	0.06	-12.27	0.003
R-squared	0.80
Adjusted R-squared	0.78
Standard Error	5.12

Calculate the 95% confidence interval for the coefficient of the P/E variable.

(0.35, 0.79)
(0.14, 1.00)
(0.12, 0.89)

Question 3 of 15

3. Question

Questions 1-5 refer to the following information:

A financial analyst is conducting a multiple linear regression analysis to determine the factors that influence the stock price of a particular company. The analyst uses the following independent variables in the regression model:

Earnings per share (EPS)
Book value per share (BVPS)
Price-to-earnings ratio (P/E)
Return on equity (ROE)

The analyst collects data for 50 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	24.25	1.23	19.72	0.000
EPS	0.98	0.07	13.64	0.002
BVPS	1.15	0.08	14.29	0.001
P/E	0.57	0.11	5.20	0.042
ROE	-0.75	0.06	-12.27	0.003
R-squared	0.80
Adjusted R-squared	0.78
Standard Error	5.12

What is the meaning of the p-value for the coefficient of an independent variable in the regression model?

It measures the size of the coefficient relative to its standard error.
It measures the significance of the coefficient.
It measures the goodness of fit of the regression model.

Question 4 of 15

4. Question

Questions 1-5 refer to the following information:

A financial analyst is conducting a multiple linear regression analysis to determine the factors that influence the stock price of a particular company. The analyst uses the following independent variables in the regression model:

Earnings per share (EPS)
Book value per share (BVPS)
Price-to-earnings ratio (P/E)
Return on equity (ROE)

The analyst collects data for 50 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	24.25	1.23	19.72	0.000
EPS	0.98	0.07	13.64	0.002
BVPS	1.15	0.08	14.29	0.001
P/E	0.57	0.11	5.20	0.042
ROE	-0.75	0.06	-12.27	0.003
R-squared	0.80
Adjusted R-squared	0.78
Standard Error	5.12

Calculate the F-statistic for the regression model.

38.44
42.56
46.78

Question 5 of 15

5. Question

Questions 1-5 refer to the following information:

A financial analyst is conducting a multiple linear regression analysis to determine the factors that influence the stock price of a particular company. The analyst uses the following independent variables in the regression model:

Earnings per share (EPS)
Book value per share (BVPS)
Price-to-earnings ratio (P/E)
Return on equity (ROE)

The analyst collects data for 50 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	24.25	1.23	19.72	0.000
EPS	0.98	0.07	13.64	0.002
BVPS	1.15	0.08	14.29	0.001
P/E	0.57	0.11	5.20	0.042
ROE	-0.75	0.06	-12.27	0.003
R-squared	0.80
Adjusted R-squared	0.78
Standard Error	5.12

What is the difference between R-squared and adjusted R-squared, and why is adjusted R-squared preferred in some cases?

R-squared is a measure of how well the regression line fits the data, while adjusted R-squared takes into account the number of independent variables and sample size. Adjusted R-squared is preferred in some cases because it penalizes the addition of irrelevant independent variables to the model.
R-squared is a measure of how well the independent variables explain the variation in the dependent variable, while adjusted R-squared takes into account the correlation between the independent variables. Adjusted R-squared is preferred in some cases because it corrects for multicollinearity.
R-squared is a measure of how well the regression line fits the data, while adjusted R-squared takes into account the distribution of the dependent variable. Adjusted R-squared is preferred in some cases because it corrects for non-normality of the dependent variable.

Question 6 of 15

6. Question

Questions 6-10 refer to the following information:

A researcher is conducting a multiple linear regression analysis to examine the factors that affect a company’s revenue. The following independent variables are used in the regression model:

Advertising spending (AdSpend)
Number of employees (NumEmp)
Customer satisfaction score (CSat)
Price of the product (Price)

The researcher collects data for 100 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	1850	350	5.29	0.000
AdSpend	125	30	4.13	0.002
NumEmp	80	15	5.14	0.001
CSat	500	120	4.17	0.001
Price	-300	40	-7.50	0.000
R-squared	0.75
Adjusted R-squared	0.73
Standard Error	1000

What is the significance of the p-value for the AdSpend variable?

The AdSpend variable is statistically significant at a 0.05 significance level.
The AdSpend variable is not statistically significant at a 0.05 significance level.
The p-value for the AdSpend variable cannot be determined from the information provided.

Question 7 of 15

7. Question

Questions 6-10 refer to the following information:

A researcher is conducting a multiple linear regression analysis to examine the factors that affect a company’s revenue. The following independent variables are used in the regression model:

Advertising spending (AdSpend)
Number of employees (NumEmp)
Customer satisfaction score (CSat)
Price of the product (Price)

The researcher collects data for 100 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	1850	350	5.29	0.000
AdSpend	125	30	4.13	0.002
NumEmp	80	15	5.14	0.001
CSat	500	120	4.17	0.001
Price	-300	40	-7.50	0.000
R-squared	0.75
Adjusted R-squared	0.73
Standard Error	1000

What is the primary consequence of heteroskedasticity in a regression model?

It makes the coefficient estimates biased and inconsistent.
It makes it difficult to interpret the coefficient estimates.
It makes it difficult to estimate the standard error of the coefficient estimates.

Question 8 of 15

8. Question

Questions 6-10 refer to the following information:

A researcher is conducting a multiple linear regression analysis to examine the factors that affect a company’s revenue. The following independent variables are used in the regression model:

Advertising spending (AdSpend)
Number of employees (NumEmp)
Customer satisfaction score (CSat)
Price of the product (Price)

The researcher collects data for 100 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	1850	350	5.29	0.000
AdSpend	125	30	4.13	0.002
NumEmp	80	15	5.14	0.001
CSat	500	120	4.17	0.001
Price	-300	40	-7.50	0.000
R-squared	0.75
Adjusted R-squared	0.73
Standard Error	1000

What is the variance inflation factor (VIF) for the Revenue variable in the regression model?

1.20
4.00
2.00

Question 9 of 15

9. Question

Questions 6-10 refer to the following information:

A researcher is conducting a multiple linear regression analysis to examine the factors that affect a company’s revenue. The following independent variables are used in the regression model:

Advertising spending (AdSpend)
Number of employees (NumEmp)
Customer satisfaction score (CSat)
Price of the product (Price)

The researcher collects data for 100 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	1850	350	5.29	0.000
AdSpend	125	30	4.13	0.002
NumEmp	80	15	5.14	0.001
CSat	500	120	4.17	0.001
Price	-300	40		0.000
R-squared	0.75
Adjusted R-squared	0.73
Standard Error	1000

Calculate the t-value for the coefficient of the Price variable.

-4.50
3.75
-7.50

Question 10 of 15

10. Question

Questions 6-10 refer to the following information:

A researcher is conducting a multiple linear regression analysis to examine the factors that affect a company’s revenue. The following independent variables are used in the regression model:

Advertising spending (AdSpend)
Number of employees (NumEmp)
Customer satisfaction score (CSat)
Price of the product (Price)

The researcher collects data for 100 quarters and performs the regression analysis. The following output is obtained:

Regression Output:

	Coefficient	Std. Error	t-stat	p-value
Intercept	1850	350	5.29	0.000
AdSpend	125	30	4.13	0.002
NumEmp	80	15	5.14	0.001
CSat	500	120	4.17	0.001
Price	-300	40	-7.50	0.000
R-squared	0.75
Adjusted R-squared	0.73
Standard Error	1000

What is the consequence of autocorrelation in the residuals of a regression model?

It can make the coefficient estimates biased and inconsistent.
It can make it difficult to interpret the coefficient estimates.
It can lead to incorrect hypothesis testing.

Question 11 of 15

11. Question

Questions 11-15 refer to the following information:

Regression Analysis: Revenue versus AdSpend, NumEmp, CSat, Price

Analysis of Variance Table

Source	SS	df	F	p-value
Regression	4,785,500	4	191.74	<0.001
Residual	7,214,500	95
Total		99

What is the total sum of squares (SST) in the regression model?

4,785,500
7,214,500
12,000,000

Question 12 of 15

12. Question

Questions 11-15 refer to the following information:

Regression Analysis: Revenue versus AdSpend, NumEmp, CSat, Price

Analysis of Variance Table

Source	SS	df	F	p-value
Regression	4,785,500	4	191.74	<0.001
Residual	7,214,500	95
Total	12,000,000	99

What is the mean square for regression (MSR) in the regression model?

1,196,375
75,994
14,413,000

Question 13 of 15

13. Question

Questions 11-15 refer to the following information:

Regression Analysis: Revenue versus AdSpend, NumEmp, CSat, Price

Analysis of Variance Table

Source	SS	df	MS	p-value
Regression	4,785,500	4	1,196,375	<0.001
Residual	7,214,500	95	75,994
Total	12,000,000	99

What is the F-statistic for the regression model?

4.20
15.10
191.74

Question 14 of 15

14. Question

Question 15 of 15