Hypothesis Testing in Multiple Regression

Imagine you are conducting an empirical analysis on the impact of various factors on the sales of a retail store. You decide to use multiple regression analysis to determine which of these factors significantly affect sales. You form the following linear regression model:

$$ Sales = \beta_0 + \beta_1 Price + \beta_2 Advertising + \beta_3 Location + \epsilon $$

After running the regression, you obtain the following coefficients and their respective p-values:

• Price: $\beta_1 = -2.3$, p-value = 0.04
• Advertising: $\beta_2 = 5.8$, p-value = 0.01
• Location: $\beta_3 = 1.2$, p-value = 0.15

You are interested in testing the null hypothesis that each of the predictors is statistically significant at the 5% significance level. Which of the following statements regarding your hypothesis tests is true?