Hypothesis Testing in Multiple Regression Analysis

Hard Multiple Regression Analysis Hypothesis Testing

XYZ Corp is conducting a multiple regression analysis to evaluate the relationship between its advertising spending ($Y$) and sales revenue ($X_1$) while controlling for other factors such as economic conditions ($X_2$) and competitor marketing efforts ($X_3$). The regression model is represented as:

$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \epsilon$

After fitting the model, the following hypothesis tests are established:

1. $H_0: \beta_1 = 0$ (The advertising spending has no effect on sales revenue)

2. $H_a: \beta_1 \neq 0$ (The advertising spending has an effect on sales revenue)

XYZ tested this hypothesis using a t-test and obtained a t-statistic of 2.45 and a p-value of 0.015. Assuming a significance level of 0.05, what is the appropriate conclusion regarding the null hypothesis?

Reject the null hypothesis, since the p-value is less than 0.05.

Fail to reject the null hypothesis, since the t-statistic is not significant.

Cannot determine rejection without knowing the degrees of freedom.

Hint

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