Question

Linear Regression and Correlation Activity Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age 16 - 19 20-24 25-34 35 - 54 55 - 74 75+ Number of Driver Death per 100,000 38 36 24 20 18 28 1. For each age group, list out the midpoints of the intervals for the x values. (For the 75+ group, use 80. 2. Find the correlation using the formular = η Σχy)-(Σχ)(Σy) Vin Sx2-(2x)][n Xy2-(y)] Fill in the table using x = midpoint and y = number of driver deaths per 100,000. Use the bottom rows for the sums. Then, use the formula to find r. x y y2 ху

Answer 1

clss limi	class boundary	mid point
16-19	15.5-19.5	$\frac{(15.5+19.5)}{2}=17.5$
20-24	19.5-24.5	$\frac{(19.5+24.5)}{2}=22$
25-34	24.5-34.5	$\frac{(24.5+34.5)}{2}=29.5$
35-54	34.5-54.5	$\frac{(34.5+54.5)}{2}=44.5$
55-74	54.5-74.5	$\frac{(54.5+74.5)}{2}=64.5$
75+	74.5+

x	y	X^2	Y^2	XY
17.5	38	306.25	1444	665
22	36	484	1296	792
29.5	24	870.25	576	708
44.5	20	1980.25	400	890
64.5	18	4160.25	324	1161
80	28	6400	784	2240

258

164

14201

4824

6456

total

$r=\frac{[n\sum X_iY_i-(\sum X_i\sum Y_i])}{\sqrt{[n\sum X_i^2-(\sum X_i)^2][n\sum Y_i^2-(\sum Y_i)^2]}}$

$r=\frac{[6\times 6456-(258\times 164])}{\sqrt{[6\times 14201-(258)^2][6\times 4824-(164)^2]}}$

$r=\frac{-3576}{\sqrt{18642\times 2048}}$

r=-0.57874----------------------ans