Question

110. A study in transportation safety collected data on 42 North American cities. From each city, two of the variables recorded were X = percentage of licensed drivers who are under 21 years of age, and Y = the number of fatal accidents per year per 1000 licenses. Below is the output from the data: Parameter Std. Estimate Error T Statistic p-value Intercept -1.59741 0.371671 -4.29792 0.0001 Slope 0.287053 0.0293898 9.76711 Unknown Correlation Coefficient = 0.839387 R-squared = 70.4571 percent Standard error of estimate = 0.58935 35

a) What is the formula for the regression function?

b) Interpret the slope of the regression equation.

c) Construct an 95% interval to predict y when x = 14, and explain what it means in the context of the problem.

d) Advanced question? What is the p value for the slope in this problem? Calculate it and show your work? Based on this analysis, can we conclude that the number of fatal accidents is linearly related to the percentage of licensed drives? Justify your answer showing all work. What is the null and the alternative hypothesis?

Answer 1

a) What is the formula for the regression function?

b1 = r*(sy/sx)

b0 = ybar - b1*xbar

The regression equation is:

y = b0 + b1*x

b) Interpret the slope of the regression equation.

For every increase in percentage of licensed drivers who are under 21 years of age, the number of fatal accidents per year per 1000 licenses will increase by 0.287053.

c) Construct an 95% interval to predict y when x = 14, and explain what it means in the context of the problem.

Predicted values for: Fatal Accidents per 1000
		95% Confidence Interval
Percent Under 21	Predicted	lower	upper
14	2.421331	2.210525	2.632136

The 95% confidence interval to predict y when x = 14 is between 2.210525 and 2.632136.

d) Advanced question? What is the p value for the slope in this problem? Calculate it and show your work? Based on this analysis, can we conclude that the number of fatal accidents is linearly related to the percentage of licensed drives? Justify your answer showing all work. What is the null and the alternative hypothesis?

The test statistic = 0.287053/0.0293898 = 9.76711

The p-value is 0.0000.

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the number of fatal accidents is linearly related to the percentage of licensed drives.

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