Regression Analysis: Emergency Calls To The New York Auto Club

Example of Regression Analysis: Emergency Calls to the New York Auto Club The AAA Club of New York provides many services to its members, including travel planning, traffic safety classes and discounts on insurance. The service with the highest profile is its Emergency Road Service (ERS). If a club member’s car breaks down, the member can tell the Club to send out a tow truck for assistance. This service is especially useful in the winter months, when Club members can be stranded with frozen locks, dead batteries, weather induced accidents and spinning tires.

If the weather is very bad, the Club can be overwhelmed with calls. By tracking the weather conditions the Club can divert resources from other Club activities to the ERS for projected
We will investigate this with data from the second-half of January in 1993 and 1994. The Club reports the number of ERS calls answered each day as a percentage of the monthly ERS calls (Pcalls). We have also recorded the forecast daily low temperature. The data is in ers.JMP.

The percentage of the January calls for 1/16/93 and 1/17/93 are 3.6% and 2.7% respectively. This suggests that the resources necessary on the 17th would be about 75%=2.7/3.6 of those necessary on the 16th. Thus 25% of those people working for the ERS on the 16th could be reassigned or given a rest day. The advantage of considering percentage of the monthly ERS calls rather than the actual number of ERS calls is that it adjusts for the total level of calls for that month due to the cumulative effects of weather. It is difficult to measure and take into account the cumulative effects of weather.

Step I. Define the question of interest. We would like to be able to make point predictions and make prediction intervals for Pcalls based on the forecast daily low temperature. This will help the Club best allocate its staff based on the forecast daily low
Total 27 21.846601 0.0016

Parameter Estimates
Term Estimate Std Error t Ratio Prob>|t|
Intercept 4.7895287 0.389303 12.30 <.0001
Forecast Low Temperature -0.052302 0.01481 -3.53 0.0016

Distributions
Residuals Percentage Calls

The four assumptions of the simple linear regression model are (1) linearity – the mean of E(Y|X) is a straight line function of X; (2) constant variance – the standard deviation of Y|X is the same for all X; (3) normality – the distribution of Y|X is normal; (4) independence – the observations are all independent.

We check linearity by looking at the residual plot. There is no clear pattern in the mean of the residuals as X changes , so linearity appears reasonable. We also check constant variance by looking at the residual plot. There is no clear pattern in the spread of the residuals as X changes, so constant variance appears reasonable. We check normality by looking at a normal quantile plot of the residuals. All of the points fall within the 95% confidence bands, indicating that normality appears