Journalists are trying to find out the main factors used by a railway company in establishing dynamic pricing for tickets. One of the possible regression models, based on the information on 20 tickets, is y = Price for a railway ticket ($) x₁ = Number of days before departure x₂ = Weekday (1 = Fri/Sat/Sun, 0 = Mon/Tue/Wen/Thu) x₃ = Distance (km) x₄ = Demand (1 to 5 scale) Using the Minitab output results from fitting this model, carry out the model utility test at a 0.05 significance level. A) P-value 0.05, there is a useful linear relationship between y and each of the three predictors. E) P-value 0.05, there is no useful linear relationship between y and at least one of the predictors.

Question

Journalists are trying to find out the main factors used by a railway company in establishing dynamic pricing for tickets. One of the possible regression models, based on the information on 20 tickets, is y = Price for a railway ticket ($) x₁ = Number of days before departure x₂ = Weekday (1 = Fri/Sat/Sun, 0 = Mon/Tue/Wen/Thu) x₃ = Distance (km) x₄ = Demand (1 to 5 scale) Using the Minitab output results from fitting this model, carry out the model utility test at a 0.05 significance level. A) P-value < 0.05, there appears to be a useful linear relationship between y and at least one of the three predictors. B) P-value < 0.05, there appears to be a useful linear relationship between y and each of the three predictors. C) P-value > 0.05, there is no useful linear relationship between y and any of the predictors. D) P-value > 0.05, there is a useful linear relationship between y and each of the three predictors. E) P-value > 0.05, there is no useful linear relationship between y and at least one of the predictors.

Quizplus · Accepted Answer

The model utility test aims to determine if there is a useful linear relationship between the response variable and at least one of the predictors. The null hypothesis is that there is no useful linear relationship, and the alternative hypothesis is that there is a useful linear relationship. The test is performed using an F-test, and the p-value is compared to the significance level (0.05 in this case). From the given Minitab output, the p-value for the F-test is less than 0.05. Therefore, we reject the null hypothesis and conclude that there appears to be a useful linear relationship between y and at least one of the predictors.

Journalists Are Trying to Find Out the Main Factors Used