Question

67. Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16-19 38 20-24 36 25-34 24 35-54 20 55-74 18 75+ 28 Table 12.19 a For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80) b using ages as the independent variable and "Number of driver deaths per 100.000" as the dependent variable, make a scatter plot of the data c Calculate the least squares (best-ft) line. Put the equation in the form of f a+ bx d. Find the correlation coefficient. Is it significant? e. Predict the number of deaths for ages 40 and 60 t Based on the given data, is there a linear relationship between age of a driver and driver fataity rate? g what is the slope of the least squares (best-fit) line? Interpret the slope

Answer 1

Mid point:

Age	Frequency	midpoint
16 - 19	38	17.5
20 - 24	36	22
25 - 34	24	29.5
35 - 54	20	44.5
55 - 74	18	64.5
75+	28	80

Formula :

Age	Frequency	midpoint
16 - 19	38	=(LEFT(A2,2)+RIGHT(A2,2))/2
20 - 24	36	=(LEFT(A3,2)+RIGHT(A3,2))/2
25 - 34	24	=(LEFT(A4,2)+RIGHT(A4,2))/2
35 - 54	20	=(LEFT(A5,2)+RIGHT(A5,2))/2
55 - 74	18	=(LEFT(A6,2)+RIGHT(A6,2))/2
75+	28	80

B)

Frequency 40 35 漠) 25 20 15 10 yー-3.0857x + 38.133 R0.4882

c) Correlation Coefficeint

0.699

R-squared in the chart is 0.4882

Calculating R:

sqrt(o.4882) = 0.699

r = 0.699

e) predict the number of deaths in the age of 40 and 60

x =40

Regression equation is y = -3.0857x + 38.133

y = -3.0857*40 + 38.133

y = -85.30

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x =60

y = -3.0857*60 + 38.133

y = -147.01

f)

Relationship:

There is a negative linear relationship between Age and driver fatality rate

g) slope:

-3.0857 is the slope of the linear regression

(check the above graph)

Frequency midpoint 38 36 24 20 18 28 2 16 19 3 20 24 4 25 34 5 35 -54 6 55-74 7 75+ 17.5 29.5 44.5 64.5 80 Frequency У -3.0857x + 38.133 R2 0.4882 35 30 25 20 15 10 0.699 Correlation Coefficient 0