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To interpret the effect of \( X_4 \) on the dependent variable in this multiple regression analysis:

- \( X_4 \) is a qualitative (dummy) variable, which means it can take only the values of 0 or 1.
- The coefficient for \( X_4 \) is \(-9.976\), indicating the effect of \( X_4 = 1 \) on the dependent variable.

When \( X_4 \) changes from 0 to 1, the dependent variable is expected to **decrease by 9.976 units**, all else being equal. This is because a coefficient of \(-9.976\) implies a reduction of that amount when \( X_4 \) takes the value 1.

Thus, the correct answer is:

**The dependent variable will decrease by 9.976 units.**

Would you like further details or explanations? Here are 5 related questions:

1. What is the significance of the p-value for \( X_4 \) in this analysis?
2. How does a dummy variable like \( X_4 \) affect the regression model?
3. How should we interpret the coefficient of \( X_3 \) despite its large standard error?
4. What impact does the intercept have in this regression model?
5. How do we assess the overall goodness-of-fit for this regression model?

**Tip:** The p-value helps assess whether the effect of a variable is statistically significant. If it's less than a threshold (commonly 0.05), the variable is considered to have a significant effect on the dependent variable.

A multiple regression analysis showed the following results of the individual independent variables. X4 is a qualitative variable (i.e., it takes on the value 0 or 1). If X4 is equal to one, what is the variable's effect on the dependent variable?

In this regression analysis problem, learn how the coefficient of a qualitative variable (X4) impacts the dependent variable. The solution involves understanding dummy variables, statistical significance (p-values), and interpreting coefficients. Appropriate for undergraduate students studying statistics or econometrics.

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