Financial Risk Manager Part 1
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Q.3344 An analyst wishes to establish the relationship between corporate revenue (Yₜ) and the average years of experience per employee (Xₜ) and comes up with the following model.
Yₜ = 0.45 + 0.78Xₜ
The analyst also observes that the standard error of the coefficient of the average years of experience per employee is 0.65. In order to test the null hypothesis that the average years of experience per employee have no effect on corporate revenue, what is the correct statistic to calculate?
Explanation:
Explanation
In both single and multiple regression analysis, we use the t-test to determine whether a specific independent variable has a significant effect on the dependent variable at a given level of confidence.
Hypothesis Testing Framework:
- H₀: β₁ = 0 (Average years of experience per employee have no effect on corporate revenue)
- H₁: β₁ ≠ 0 (Average years of experience per employee have a significant effect on corporate revenue)
Test Statistic Calculation:
The t-statistic is computed as:
t = (estimated β₁ - hypothesized β₁) / standard error of β₁
= (0.78 - 0) / 0.65
= 1.2
t = (estimated β₁ - hypothesized β₁) / standard error of β₁
= (0.78 - 0) / 0.65
= 1.2
Why t-test is appropriate:
- The t-test is specifically designed for testing individual regression coefficients
- It assesses whether a single independent variable's coefficient is statistically different from zero
- The F-test is used for testing the overall significance of the regression model (all coefficients simultaneously)
- Chi-square test is used for categorical data and goodness-of-fit tests
- Durbin Watson test is used for detecting autocorrelation in regression residuals
Decision Rule:
Compare the calculated t-statistic (1.2) with the critical t-value from the t-distribution table at the desired significance level and appropriate degrees of freedom to determine if we reject or fail to reject the null hypothesis.