MAT210 Quiz2 erences Mailings Review View Developer Helpell me what you w The fo
ID: 3072974 • Letter: M
Question
MAT210 Quiz2 erences Mailings Review View Developer Helpell me what you w The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Age Group | Number of | # of Female # of Male Number Drivers (in Fatal Thousands) Crashes Thousands) Crashes 12 6424 6941 Drivers (in of Fatal 74 227 5180 5016 8595 12 6139 6816 17664 20063 2742 19984 2113 1531 2780 80687990 20406 7990 2 19898 14340 4527 14441 8194 4803 2022 7118 2285 1514 938 980 2274 8400 5375 There were two least-squares regressions created, one for male drivers and number of fatal crashes, and one for female drivers and number of fatal crashes. The regression lines are as follows: Imae0.3248x+99.4488 and yremate -0.1045x +514.152. Use the data table and regression equations above to answer the following questions: 1. How many licensed drivers male drivers are under the age of 16? 2. Interpret the slope and y-intercept for the least-squares regression equation for males. 3. Interpret the slope and y-intercept for the least-squares regression equation for females. The correlation between number of female drivers in thousands and number of fatal crashes is 0.836. Is there enough evidence to say that there is a linear relationship? Why? The correlation between number of female drivers in thousands and number of fatal crashes is 0.836. What is the coefficient of determination for the female regression equation? Interpret this value. 4. 5. 6. How many fatal accidents would you expect from the age group of 16-20 year old 7. How many fatal accidents would you expect from the age group of 16-20 year old 8. How might an insurance company use any of the information provided in this problem? males? females?Explanation / Answer
(5) R: output
> x=c(12,6139,6816,17664,20063,19984,14441,8400,5375)
> y=c(77,2113,1531,2780,2742,2285,1514,938,980)
> l=lm(y~x)
> summary(l)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-508.97 -438.41 -95.74 304.70 957.43
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 514.15197 335.14018 1.534 0.16887
x 0.10448 0.02591 4.033 0.00498 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 530.6 on 7 degrees of freedom
Multiple R-squared: 0.6991, Adjusted R-squared: 0.6561
F-statistic: 16.26 on 1 and 7 DF, p-value: 0.004978
The female regression equation is y^female = 0.1045*x + 514.152 .
The coefficient of determination for the female regression equation is 0.6991.
Interpretation: R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.
R-squared = Explained variation / Total variation
R-squared is always between 0 and 100%:
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