Several states have argued that the 65-mph speed limit has no justification and have refused to enforce it. The federal Department of Transportation (DOT) believes that the 65-mph limit saves lives. To illustrate its contention, the department regressed the number of traffic fatalities (Y) last year in a state on the state’s population (X1), the number of days of snow cover (X2), and the average speed of all cars (X3). The results are shown below. Table 10: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .821 a .780 .613 3.258 a. Predictors: (Constant), population, days of snow, average speed Table 11: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1.4 2.957 .473 .584 Population .00029 .00003 .0034 9.667 .000 Days of Snow 2.4 .62 .759 3.871 .000 Average Speed 10.3 1.1 1.438 9.364 .000 a. Dependent Variable: Number of Traffic Fatalities From the results shown above, write the regression equation. What proportion of variation in the number of traffic fatalities can be explained by the regression model? With all else being equal, how many lives would be saved in a state if the average speed were reduced from 75 to 65 mph? Does reducing the average speed of cars have a statistically significant impact? Explain.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Several states have argued that the 65-mph speed limit has no justification and have refused to enforce it. The federal Department of Transportation (DOT) believes that the 65-mph limit saves lives. To illustrate its contention, the department regressed the number of traffic fatalities (Y) last year in a state on the state’s population (X₁), the number of days of snow cover (X₂), and the average speed of all cars (X₃). The results are shown below.

Table 10: Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.821 ^a	.780	.613	3.258
a. Predictors: (Constant), population, days of snow, average speed

Table 11: Coefficients

Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	1.4	2.957		.473	.584
Population	.00029	.00003	.0034	9.667	.000
Days of Snow	2.4	.62	.759	3.871	.000
Average Speed	10.3	1.1	1.438	9.364	.000
a. Dependent Variable: Number of Traffic Fatalities

From the results shown above, write the regression equation.
What proportion of variation in the number of traffic fatalities can be explained by the regression model?
With all else being equal, how many lives would be saved in a state if the average speed were reduced from 75 to 65 mph?
Does reducing the average speed of cars have a statistically significant impact? Explain.

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