Hypothesis Testing in Multiple Regression

In a multiple regression analysis, a financial analyst is examining the impact of several independent variables on the dependent variable, which is the annual return of a stock. The analyst has constructed the following regression equation:

$$R = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$$

where:

• $$R$$ is the annual return of the stock,
• $$X_1$$ is the market return,
• $$X_2$$ is the earnings per share (EPS),
• $$\beta_0$$ is the intercept,
• $$\beta_1$$ and $$\beta_2$$ are the coefficients for the independent variables,
• $$\epsilon$$ is the error term.

The analyst wants to test the null hypothesis that $$\beta_1 = 0$$ (market return has no effect) against the alternative hypothesis that $$\beta_1 \neq 0$$. The results of the hypothesis test yield a p-value of 0.03. Based on this information, what can the analyst conclude?