Question

Perform a t test using the critical value approach for the significance of β₁. Use a level of significance of 0.05.

Perform a t test using the critical value approach for the significance of β₂. Use a level of significance of 0.05.

The estimated regression equation for a model involving two independent variables and 65 observations is:

yhat = 55.17+1.1X₁ -0.153X₂

Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, S_b1 = 0.33, S_b2 = 0.20.

Answer 1

a) Ho: B1 = 0
Ha: B1 =/ 0

t-statistic = Coefficient/Standard Error = 1.1/0.33 = +3.33
t-critical value at 0.05 significance level and df = 65 - 2 - 1 = 62 is: +2.00 and -2.00

As t-statistic= 3.33>2.00, we can reject the null hypothesis. Hence, we can conclude that the coefficient of X1 is significantly different than zero.

b) Ho: B2 = 0
Ha: B2 =/ 0

t-statistic = Coefficient/Standard Error = -0.153/0.20 = -0.765
t-critical value at 0.05 significance level and df = 65 - 2 - 1 = 62 is: +2.00 and -2.00

As t-statistic= -0.765 is not less than -2.00, we fail to reject the null hypothesis. Hence, we can conclude that the coefficient of X2 is not different than zero.