Math Problem Statement

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?

Group of answer choices

The dependent variable will increase by 9.976 units.

The dependent variable will increase by 2*9.976 units.

The dependent variable will decrease by 9.976 units.

The dependent variable will not be affected because the coefficient on X4 cannot be said to be statistically different than zero

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? Group of answer choices: 1. The dependent variable will increase by 9.976 units. 2. The dependent variable will increase by 2*9.976 units. 3. The dependent variable will decrease by 9.976 units. 4. The dependent variable will not be affected because the coefficient on X4 cannot be said to be statistically different than zero.

Solution

The coefficient for X4X_4 is −9.976-9.976, with a statistically significant p-value (p=0.024p = 0.024, which is less than the common significance threshold of 0.05). This indicates that X4X_4 has a significant effect on the dependent variable.

Since X4X_4 is a qualitative (dummy) variable that takes the value 0 or 1, when X4=1X_4 = 1, the dependent variable will decrease by 9.976 units compared to when X4=0X_4 = 0.

Correct Answer:

The dependent variable will decrease by 9.976 units.

Would you like further clarification on how dummy variables work in regression or the interpretation of p-values? Here are some related questions:

  1. What does it mean when a variable's coefficient is statistically significant?
  2. How are dummy variables constructed in regression analysis?
  3. How does the p-value affect the interpretation of a regression coefficient?
  4. What is the role of the intercept in a regression model?
  5. How do qualitative variables impact regression outcomes?

Tip: Always examine both the coefficient and its p-value to determine a variable's impact and statistical significance in a regression model.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Statistical Significance
Dummy Variables

Formulas

Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε

Theorems

Hypothesis testing for regression coefficients

Suitable Grade Level

Undergraduate level

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