Testing Significance in Multiple Regression

In a multiple regression analysis, a financial analyst is testing whether the independent variables significantly contribute to explaining the variance in the dependent variable, which represents the returns of a portfolio. The model is specified as follows:

$$ R_t = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon_t $$

where:

$$ R_t $$ = return of the portfolio,

$$ X_1 $$ = market return,

$$ X_2 $$ = interest rate,

and $$ \epsilon_t $$ is the error term.

The analyst performs a hypothesis test for the coefficients $$ \beta_1 $$ and $$ \beta_2 $$ using a significance level of 0.05. The null hypothesis for both coefficients is:

$$ H_0: \beta_1 = 0 \quad \text{and} \quad H_0: \beta_2 = 0 $$

After conducting the test, the analyst finds the following results:

For $$ \beta_1 $$: t-statistic = 3.2

For $$ \beta_2 $$: t-statistic = 1.8

Assuming that the critical t-value for a two-tailed test at 0.05 significance level is approximately 2.10, determine the appropriate conclusion regarding the significance of the independent variables.