A financial analyst is conducting a multiple regression analysis to evaluate the impact of three independent variables (X 1 , X 2 , and X 3 ) on a dependent variable (Y). The regression output provides the following coefficients: Coefficient for X 1 = 0.5, Coefficient for X 2 = 1.2, Coefficient for X 3 = -0.3. The analyst wishes to test the null hypothesis that X 2 does not have any effect on Y (H 0 : β 2 = 0) at a significance level of 0.05. The t-statistic for X 2 is calculated to be 2.60, with a critical t-value of 2.045 for 25 degrees of freedom. What can the analyst conclude from this hypothesis test?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Hypothesis Testing in Multiple Regression

Hard Multiple Regression Analysis Hypothesis Testing

A financial analyst is conducting a multiple regression analysis to evaluate the impact of three independent variables (X₁, X₂, and X₃) on a dependent variable (Y). The regression output provides the following coefficients:
Coefficient for X₁ = 0.5, Coefficient for X₂ = 1.2, Coefficient for X₃ = -0.3.
The analyst wishes to test the null hypothesis that X₂ does not have any effect on Y (H₀: β₂ = 0) at a significance level of 0.05. The t-statistic for X₂ is calculated to be 2.60, with a critical t-value of 2.045 for 25 degrees of freedom.
What can the analyst conclude from this hypothesis test?

The null hypothesis can be rejected, indicating X2 has a statistically significant impact on Y.

The null hypothesis cannot be rejected, indicating X2 does not have a statistically significant impact on Y.

There is insufficient information to determine the impact of X2 on Y.

Hint

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