SCENARIO 18-2 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 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( ), the amount of insulation in inches ( ), the number of windows in the house ( ), and the age of the furnace in years ( ).Given below are the EXCEL outputs of two regression models.
-Referring to Scenario 18-2 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test j =1, 2,..., 4 using Model 1?
A)Do not reject and conclude that the 4 independent variables have significant individual linear effects on heating costs.
B)Reject and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs.
C)Do not reject and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.
D)Reject and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.

Question

SCENARIO 18-2 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 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (  ), the amount of insulation in inches (  ), the number of windows in the house (  ), and the age of the furnace in years (  ).Given below are the EXCEL outputs of two regression models. 
-Referring to Scenario 18-2 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test  j =1, 2,..., 4 using Model 1?
A)Do not reject and conclude that the 4 independent variables have significant individual linear effects on heating costs. 
B)Reject and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs. 
C)Do not reject and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. 
D)Reject and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.

Quizplus · Accepted Answer

The null hypothesis for each individual variable is that its coefficient is equal to zero, while the null hypothesis for the group of variables is that all coefficients in the regression equation are equal to zero. The p-values for all four variables in Model 1 are less than 0.01, indicating that we can reject each individual null hypothesis and conclude that each independent variable has a significant linear effect on heating costs. For the F-test of the entire model, the p-value is also less than 0.01, indicating that we can reject the null hypothesis and conclude that the set of independent variables taken as a group has a significant linear effect on heating costs. Therefore, the correct answer is B: reject 11ebc114_12e0_2cc9_8acb_51276137d8c1_TB8562_11 and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs. The null hypothesis for each individual t-test is that the corresponding coefficient is equal to 0, while the alternative hypothesis is that the coefficient is not equal to 0. In Model 1, all four t-tests have p-values less than 0.01, which means that we reject the null hypothesis for each individual t-test and conclude that each independent variable has a significant linear effect on heating costs. The null hypothesis for the F-test is that all four coefficients are equal to 0, while the alternative hypothesis is that at least one coefficient is not equal to 0. The p-value for the F-test in Model 1 is less than 0.01, which means that we reject the null hypothesis and conclude that the group of independent variables (daily minimum outside temperature, insulation, number of windows, and age of furnace) has a significant linear effect on heating costs. Therefore, the best choice is B.

SCENARIO 18-2 One of the Most Common Questions of Prospective