Financial Risk Manager Part 1
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An analyst uses the following regression model to explain stock returns:
Dependent variable:
ASR = Annual stock returns (%)
Independent variables:
MCP = Market capitalization (divided by $1 million to simplify modeling)
SEF = Stock exchange firm, where SEF = 1 if the stock is that of a firm listed on the New York Stock Exchange and SEF = 0 if not listed
FMR = Forbes magazine ranking (FMR = 4 is the highest ranking)
The following table presents the regression results:
| Coefficient | Standard Error | |
|---|---|---|
| Intercept | 0.6330 | 1.11 |
| MCP | 0.0840 | 0.0130 |
| SEF | 0.5101 | 0.1235 |
| FMR | 0.7000 | 0.3241 |
Based on the results in the table above, which of the following is the correct regression equation?
Explanation:
Explanation
The correct regression equation uses the Coefficient values from the table, not the Standard Error values. The regression equation follows the format:
ASR = Intercept + β₁(MCP) + β₂(SEF) + β₃(FMR)
From the table:
- Intercept coefficient = 0.6330
- MCP coefficient = 0.0840
- SEF coefficient = 0.5101
- FMR coefficient = 0.7000
Therefore, the correct regression equation is: ASR = 0.6330 + 0.0840(MCP) + 0.5101(SEF) + 0.7000(FMR)
Why other options are incorrect:
- Option A: Missing the intercept term (0.6330)
- Option C: Uses standard error (1.11) instead of the intercept coefficient (0.6330)
- Option D: Uses all standard errors instead of coefficients
Key Points:
- Coefficients represent the estimated parameters in the regression model
- Standard Errors are used for hypothesis testing and confidence intervals, not for the regression equation itself
- The intercept represents the expected value of ASR when all independent variables are zero