A multiple regression analysis produced the following tables. Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$₁ = 0,the critical t value is ____. A) ± 1.753 B) ± 2.110 C) ± 2.131 D) ± 1.740 E) ± 2.500

Question

Quizplus · Accepted Answer

To find the critical t value for this multiple regression analysis, we need to use the formula:

t = (b - 0) / SEb

where b is the estimated regression coefficient, SEb is the standard error of the coefficient, and 0 is the null hypothesis value.

Looking at the tables provided, we can see that the variable of interest is X1, with an estimated regression coefficient of -4.347 and a standard error of 1.677.

Using the formula above, we can calculate the t value:

t = (-4.347 - 0) / 1.677 = -2.588

To find the critical t value, we need to use a t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables (including the intercept). In this case, we have n = 20 and k = 2.

Using a t-table or calculator with 18 degrees of freedom and a significance level of 0.05, we find the critical t value to be ±2.131.

Therefore, the correct answer is C.

A Multiple Regression Analysis Produced the Following Tables α\alphaα = 005 to Test the Null Hypothesis H0

A Multiple Regression Analysis Produced the Following Tables $\alpha$ = 005 to Test the Null Hypothesis H₀