TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672
-True or False: Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3.To determine whether X₂ is a significant explanatory variable,you would compute an observed t-value of -5.0.

Question

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model.

Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672
-True or False: Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3.To determine whether X₂ is a significant explanatory variable,you would compute an observed t-value of -5.0.

Quizplus · Accepted Answer

To determine whether X₂ is a significant explanatory variable, we need to compute the t-value using the formula t=b/se, where b is the regression coefficient for X₂ and se is its standard error. Therefore, incorporating the given values, we get t=(-1.5)/0.3=-5.0. Since this t-value is greater than the critical t-value (at the 5% significance level) of -2.086 for 118 degrees of freedom (from the EXCEL output), we can reject the null hypothesis and conclude that X₂ is a significant explanatory variable. Hence, the given statement is true.

TABLE 14-6 One of the Most Common Questions of Prospective House Buyers