Question

<16	12	227	12	77
16-20	6,424	5,180	6,139	2,11
21-24	6,916	5,016	6.816	1,538
25-34	18,068	8.594	17,664	2,780
35-44	20,406	7,990	20,076	2,742
45-54	19,898	7,120	19,984	2,285
55-64	14,339	4,527	14,441	1,514
65-74	8,194	2,274	8,418	938
>74	4,803	2,022	5,375	961

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts ​(a) through ​(c) below

​(a) Find the​ least-squares regression line for males treating the number of licensed drivers as the explanatory​ variable, x, and the number of fatal​ crashes, y, as the response variable. Repeat this procedure for females.

(b) Interpret the slope of the​ least-squares regression line for each​ gender, if appropriate. How might an insurance company use this​ information?

(c) Was the number of fatal accidents for 16 to 20-year-old males above or below​ average? Was the number of fatal accidents for 21 to 24-year-old males above or below​ average? Was the number of fatal accidents for males greater than 74 years old above or below​ average? How might an insurance company use this​ information? Does the same relationship hold for​ females?

Answer 1

a)

Using Excel

data -> data analysis -> regression

for males

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.5230
R Square	0.2735
Adjusted R Square	0.1698
Standard Error	2599.6163
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	17812089.1578	17812089.1578	2.6357	0.1485
Residual	7	47306034.1674	6758004.8811
Total	8	65118123.3252
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	1586.8909	1624.8078	0.9767	0.3613	-2255.1690
male	0.2027	0.1249	1.6235	0.1485	-0.0925

y^ = 1586.8909 + 0.2027 x

For Female

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8127
R Square	0.6605
Adjusted R Square	0.6120
Standard Error	625.5302
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5329726.0918	5329726.0918	13.6210	0.0077
Residual	7	2739016.1304	391288.0186
Total	8	8068742.2222
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	410.9512	350.2433	1.1733	0.2790	-417.2426
female	0.1015	0.0275	3.6907	0.0077	0.0365

y^ = 410.9512 + 0.1015 x

(b) (1) If the number of male licensed drivers increases by 1 (thousand), then the number of fatal crashes increases by 0.2027 on average. (round to 4 decimals)

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(b2)
(2) If the number of female licensed drivers increases by 1 (thousand), then the number of fatal crashes increases by 0.1015 on average.

c)

Observation	Predicted fatal crashes	Residuals
<16	1589.323692	-1362.323692
16-20	2889.237641	2290.762359
21-24	2988.981506	2027.018494
25-34	5249.842449	-5241.248449
35-44	5723.82854	2266.17146
45-54	5620.840972	1499.159028
55-64	4493.856935	33.14306534
65-74	3248.072278	-974.0722779
>74	2560.609988	-538.609988

The number of fatal accidents for 16 to 20 year old males was (abovbe average/below average).The number of fatal accidents for 21 to 24 year old males was (above avergae/below average). The number of fatal accidents for males greater than 74 years was (above avergae/below average).

Does the same relationship hold true for females?

Yes.