The administrator of the National Highway Traffic Safety...

The administrator of the National Highway Traffic Safety Administration (NHTSA) wants to know if the different types of vehicles in a state have a relationship to the highway death rate in the state. She has asked you to develop multiple regression analyses to determine if the average vehicle weight, the percentage of imported cars, the percentage of light trucks, and the average car age are related to crash deaths in automobiles and pickups. The data for the analysis are located in the data file named Vehicle Travel State. A description of the variables is contained in the Chapter 11 appendix. a. Prepare a correlation matrix for crash deaths and the predictor variables. Note the simple relationships between crash deaths and the predictor variables. In addition, indicate any potential multicollinearity problems between the predictor variables. b. Prepare a multiple regression analysis of crash deaths on the potential predictor variables. Remove any nonsignificant predictor variables, one at a time, from the regression model. Indicate your best final model. c. State the conclusions from your analysis and discuss the conditional importance of the variables in terms of their relationship to crash deaths.

The administrator of the National Highway Traffic Safety Administration (NHTSA) wants to know if the different types of vehicles in a state have a relationship to the highway death rate in the state. She has asked you to develop multiple regression analyses to determine if the average vehicle weight, the percentage of imported cars, the percentage of light trucks, and the average car age are related to crash deaths in automobiles and pickups. The data for the analysis are located in the data file named Vehicle Travel State. A description of the variables is contained in the Chapter 11 appendix.
a. Prepare a correlation matrix for crash deaths and the predictor variables. Note the simple relationships between crash deaths and the predictor
variables. In addition, indicate any potential multicollinearity problems between the predictor variables.
b. Prepare a multiple regression analysis of crash deaths on the potential predictor variables. Remove any nonsignificant predictor variables, one at a time, from the regression model. Indicate your best final model.
c. State the conclusions from your analysis and discuss the conditional importance of the variables in terms of their relationship to crash deaths.

Transcript

00:01 National highway transportation safety administration runs crash tests in which stock automobiles are crashed into a wall at 35 miles per hour, with dummies in both the passenger and driver's seats.

00:11 The thor alpha crash dummy is capable of recording 134 channels of data on the impact of this crash at various sites in the dummy.

00:19 In this test, 335 cars are crashed.

00:22 The response variable is a measure of head injury.

00:25 Researchers want to know if which seat the dummy is in affects head injury severe.

00:31 Severity, as well as whether the type of car affects severity.

00:39 Here are the partial locks plots for the two different seat, the driver's seat and the passenger seat, and the six different size classifications, compact, light, medium, mini pickup, and van.

00:49 An interaction plot shows that you can see the interaction plot, and then you can see the scatter plot of residuals versus predictive values as well.

01:06 So with all that information, we want to say the hypothesis about the the main effects, both numerically and in words.

01:15 And the null hypotheses state of the effect, whether it's gamma or tau, of the level, is the same on the response for each category, while the alternative hypothesis states that not all variable levels have the same effect on the response.

01:38 So let's say for the first gamma will say is the seat.

01:44 So the null hypothesis would be that they are equal, and the alternative is that not all c levels have the same effect on response...

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