Airlines on time. Airlines strive to be on time, in part, because customers can refer to government-published statistics to select flights that are most often on time. We have data for 19 airlines for March 2006 reporting the following variables:

On Time (number of on-time arrivals)

Cancelled (number of cancelled flights)

Diverted (number of diverted flights)

Carrier (number of delays due to the carrier)

Weather (number of delays due to weather)

NAS Delay (Delays due to the National Airspace System (traffic control))

Late Arrival (number of delays due to late arrival of equipment or crew)

Here’s a regression model.

Dependent variable is: On Time R-squared 93.9% R-squared (adjusted) 90.8%

s 5176 with 19 7 12 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 4947151273 6 824525212 30.8 Residual 321546284 12 26795524

b) It seems from the scatterplot that Diverted would be a good predictor of On Time, but that seems not to be the case. Why do you think the coefficient of Diverted is not significant in the first regression?

c) How does the second regression explain this apparent contradiction?

d) Find the value of the Variance Inflation Factor statistic for Diverted in the first regression.

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Variable Intercept Coeff SE (Coeff) t-ratio P-value 1357.10 2316 0.586 0.5687 Cancelled -18.5514 6.352 -2.92 0.0128 Diverted 39.5623 95.59 0.414 0.6863 Carrier 10.9620 3.104. 3.53 0.0041 Weather 10.4637 9.462 1.11 0.2905 NAS Delay 2.46727 1.091 2.26 0.0431 Late Arrival 4.64874 1.445 3.22 0.0074 a) In view of its P-value, can we interpret the coefficient of Diverted? Here's a scatterplot of On Time vs. Diverted and another regression. Note that Diverted is the response variable in this second regression. On Time 60000 45000 30000 15000 + 0 25 50 75 100 Diverted Dependent variable is: Diverted R-squared 85.6% = R-squared (adjusted) = 80.0% s = 15.02 with 19 6 13 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value Intercept -1.65088 6.703 -0.246 0.8093 Cancelled -0.016896 0.0178 -0.948 0.3604 Carrier 0.013823 0.0081 1.70 0.1136 Weather 0.050714 0.0236 2.15 0.0509 Late Arrival 6.33917e-3 0.0038 1.67 0.1196 NAS Delay 7.09830e-3 0.0025 2.86 0.0133