Question

city code	%drivers21	fatal accidents/1000
1	12	1.309
2	5	0
3	12	2.539
4	9	2.003
5	11	2.034
6	14	4.08
7	13	2.639
8	9	0.124
9	6	0
10	10	1.145
11	13	2.719
12	18	3.128
13	10	1.676
14	17	3.769
15	14	2.639
16	13	1.449
17	12	3.121
18	10	2.616
19	9	0.788
20	14	2.631
21	10	1.887
22	12	1
23	9	0.652
24	12	1.209
25	15	0.775
26	9	0.23
27	20	4.814
28	9	1.172
29	11	1.015
30	16	3.333
31	16	2.607
32	14	2.154

** I HAVE POSTED THIS QUESTION A SECOND TIME FOR 13,14 and 15, because this question is too long for 1 answer! ** Please Answer 9,10,11, and 12 as they are simply related. 13, 14, 15 can be done in the next question!***

Question B In a study of the role of young drivers in automobile accidents, data on percentage of licensed drivers under the age of 21 and the number of fatal accidents per 1000 licenses were determined for 32 cities. The data are stored in Table B. The first column contains a number as the city code, the second column contains the percentage of drivers who are under 21, and the third column contains the number of fatal accidents per 1000 drivers. The primary interest is whether or not the number of fatal accidents is dependent upon the proportion of licensed drivers that are under 21. Copy the data into the EXCEL worksheet, name the columns, and view the data. 9. Which city (number) had the highest number of fatal accidents per 1000 licensed drivers? Example 1 Plot the number of fatal accidents as a function of percentage of drivers under 21. Based on the plot, try to anticipate whether or not the following analysis will show that there is a significant increase or decrease in number of fatalities with increases in percentage of drivers under 21 Example 27) LABORATORY ASSIGNMENTS Regression analysis, where one variable depends on another, can be used to predict levels of a dependent variable for specified levels of an independent variable. Use the EXCEL REGRESSION command to calculate the intercept and slope of the least-squares line, as well as the analysis of variance associated with that line. Fill in the following table and use the results to answer the next few questions. Carefully choose your independent and dependent variables and input them correctly using EXCEL's regression command. In this example, the percentage of drivers under the age of 21 affects the number of Fatals/1000 licenses. The regression equation (least-squares line) is Fatals/1000 licenses- 90 under 21 (intercept) (slope) Analysis of variance Source DF MS Regression Residual (Error) 30 10. What is the estimated increase in number of fatal accidents per 1000 licenses due to a one percent increase in the percentage of drivers under 21 (i.e. the slope)? I l. what is the standard deviation of the estimated slope? 12. What is the estimated number of fatal accidents per 1000 licenses if there were no drivers under the age of 21 (i.e. the y intercept)? 13. What percentage of the variation in accident fatalities can be explained by the linear relationship with drivers under 21 (i.e. 100 × the unadjusted coefficient of determination)? 14. Should the hypothesis that the slope does not differ from zero (no effect of young drivers on fatals) be rejected (1) or not (0) based on a test at the 1% significance level (i.e. is the p-value from the ANOVA less than 0.01)? 15. What are the degrees of freedom for the standard error of estimate (and the standard deviation of the slope); i.e. what are the error degrees of freedom? Example 29

Answer 1

9)

City 27 had the highest number of fatal accidents per 1000 licensed driver.

scatter plot y-0.2907x-15546 R 0.6254 -1 8 10 12 14161820 22 % driver 21

there is a significant increase number fatalities with increase % driver 21

fatals/1000licensed = -1.5742 + 0.2907 % under 21

Source	DF	Sum of Squares	Mean Square	F Statistic	P-value
Regression (between ŷi andyibar)	1	28.9021	28.9021	49.0189	8.838e-8
Residual (between yi and ŷi)	30	17.6884	0.5896
Total(between yi andyibar)	31	46.5905	1.5029

10) increase fatal accidents 0.2907/1000 licenses due to one percent increase of the % under 214

11) square root of [( residual)/ (n-2)]

= square root of [(17.6884)/(32-2)]

= 0.76786

12) fatals/1000licensed = -1.5742 + 0.2907 % under 21

fatals/1000licensed = -1.5742 + 0.2907 * 0

so, fatals/1000licensed = -1.5742

13) R square (R²) equals 0.6203. It means 62.03 % variation of fatalities explained by % under 21.

14) Ho: slope = 0

Ha: slope $\neq$ 0

t stat = slope / SE

	Coeff	SE	t-stat	lower t0.025(30)	upper t0.975(30)	Stand Coeff	p-value	VIF
intercept	-1.5742	0.5164	-3.0483	-2.6288	-0.5195	0.000	0.004772
slope	0.2907	0.04152	7.0014	0.2059	0.3755	0.7876	8.838e-8	1.0000

t stat = 7.0014 and p value is 8.838e-8 means % under 21 has a significant effect on fatalitis because p value < 0.01.

15) n-2 = 32-2 = 30