Multiple Regression - Hypothesis Testing Interpretation

Very Hard Multiple Regression Analysis Hypothesis Testing

A financial analyst is conducting a multiple regression analysis to assess the impact of various macroeconomic factors on the stock price of a company. The model includes three independent variables: GDP growth rate (X₁), inflation rate (X₂), and interest rate (X₃). The regression equation is given as:

$$Y = eta_0 + eta_1X_1 + eta_2X_2 + eta_3X_3 + eta$$

Where:

Y is the stock price.
$$eta_0$$ is the intercept.
$$eta_1$$, $$eta_2$$, and $$eta_3$$ are the coefficients for each independent variable.

The analyst conducts a hypothesis test to evaluate the significance of the impact of the independent variables on the stock price. The null hypothesis states that at least one of the coefficients is equal to zero (i.e., $$H_0: eta_1 = eta_2 = eta_3 = 0$$), while the alternative hypothesis states that at least one of them is not equal to zero (i.e., $$H_a: $$At least one $$eta_i e 0$$).

After running the regression, the analyst finds an F-statistic of 9.67 with a p-value of 0.0032. Determine the correct interpretation regarding the null hypothesis based on the results of the test.

There is not enough evidence to reject the null hypothesis, indicating the independent variables do not significantly affect the stock price.

The null hypothesis can be rejected at the 0.05 significance level, suggesting at least one independent variable significantly affects the stock price.

The p-value indicates that all coefficients are statistically significant at the 0.01 level, confirming their impact on the stock price.

Hint

Submitted13.9K

Correct9.9K

% Correct71%