Two new variables, the market value of the firm (a measure of firm size, in millions of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression: In(Earnings) = 3.86-0.28Female +0.37In(MarketValue) + 0.004 Return, (0.03) (0.04) (0.004) (0.003) n = 46,670, R² = 0.345. If MarketValue increases by 0.82%, what is the increase in earnings? If Market Value increases by 0.82%, earnings increase by The coefficient on Female is now -0.28. Why has it changed from the first regression? OA. Female correlated with the two new included variables. 0.30 % (Round your response to two decimal places.)
Two new variables, the market value of the firm (a measure of firm size, in millions of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression: In(Earnings) = 3.86-0.28Female +0.37In(MarketValue) + 0.004 Return, (0.03) (0.04) (0.004) (0.003) n = 46,670, R² = 0.345. If MarketValue increases by 0.82%, what is the increase in earnings? If Market Value increases by 0.82%, earnings increase by The coefficient on Female is now -0.28. Why has it changed from the first regression? OA. Female correlated with the two new included variables. 0.30 % (Round your response to two decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please answer the third and fourth part
![### Analyzing the Impact of Market Value and Stock Return on Earnings
#### Regression Analysis
In a regression study evaluating the effect of market value (firm size) and stock return (firm performance) on earnings, the following regression equation is used:
\[ \ln(\text{Earnings}) = 3.86 - 0.28\text{Female} + 0.37\ln(\text{MarketValue}) + 0.004\text{Return} \]
\[ \text{Standard errors: } (0.03) \, (0.04) \, (0.004) \, (0.003) \]
\[ n = 46,670, \, R^2 = 0.345 \]
Where:
- ln(Earnings) represents natural logarithm of earnings.
- Female is a binary variable indicating gender.
- ln(MarketValue) is the natural logarithm of the market value of the firm.
- Return is the percentage stock return.
#### Question Analysis
1. **If MarketValue increases by 0.82%, what is the increase in earnings?**
Calculation:
\[ \ln(\text{Earnings}) = 0.37 \times 0.0082 \approx 0.003034 \]
Hence, if MarketValue increases by 0.82%, earnings increase by 0.30%.
2. **Why has the coefficient on Female changed in the second regression?**
Possible reasons:
- **Female** is correlated with variables **ln(MarketValue)** and **Return**.
- The earlier regression might have suffered from omitted variable bias.
- **MarketValue** is crucial in explaining **ln(Earnings)**.
Correct Answer: **D. All of the above.**
#### Assumption for Further Analysis
Assume the second regression's coefficient for Female is accurate. Exclude the Return variable due to its minor effect. Calculate the correlation between **Female** and **ln(MarketValue)** given:
\[ \text{Let } X = \text{Female}, u = \text{MarketValue}, \, \frac{\sigma_u}{\sigma_x} = 0.48. \]
3. **Calculate the Correlation:**
Given:
\[ \text{Correlation } (\rho_{Xu}) = -\frac{0.28}{0.37} \times 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec7d60bf-a428-4edd-b5b3-7ceefcf490fe%2Ff59e4cf6-d868-4e20-9b5a-b51773e04e15%2Fwwblrt8_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing the Impact of Market Value and Stock Return on Earnings
#### Regression Analysis
In a regression study evaluating the effect of market value (firm size) and stock return (firm performance) on earnings, the following regression equation is used:
\[ \ln(\text{Earnings}) = 3.86 - 0.28\text{Female} + 0.37\ln(\text{MarketValue}) + 0.004\text{Return} \]
\[ \text{Standard errors: } (0.03) \, (0.04) \, (0.004) \, (0.003) \]
\[ n = 46,670, \, R^2 = 0.345 \]
Where:
- ln(Earnings) represents natural logarithm of earnings.
- Female is a binary variable indicating gender.
- ln(MarketValue) is the natural logarithm of the market value of the firm.
- Return is the percentage stock return.
#### Question Analysis
1. **If MarketValue increases by 0.82%, what is the increase in earnings?**
Calculation:
\[ \ln(\text{Earnings}) = 0.37 \times 0.0082 \approx 0.003034 \]
Hence, if MarketValue increases by 0.82%, earnings increase by 0.30%.
2. **Why has the coefficient on Female changed in the second regression?**
Possible reasons:
- **Female** is correlated with variables **ln(MarketValue)** and **Return**.
- The earlier regression might have suffered from omitted variable bias.
- **MarketValue** is crucial in explaining **ln(Earnings)**.
Correct Answer: **D. All of the above.**
#### Assumption for Further Analysis
Assume the second regression's coefficient for Female is accurate. Exclude the Return variable due to its minor effect. Calculate the correlation between **Female** and **ln(MarketValue)** given:
\[ \text{Let } X = \text{Female}, u = \text{MarketValue}, \, \frac{\sigma_u}{\sigma_x} = 0.48. \]
3. **Calculate the Correlation:**
Given:
\[ \text{Correlation } (\rho_{Xu}) = -\frac{0.28}{0.37} \times 0
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