Question

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 39% of all fatal accidents of 17-year-olds are due to speeding.

x	17	27	37	47	57	67	77
y	39	22	22	12	10	7	5

Complete parts (a) through (e), given

Σx = 329, Σy = 117, Σx² = 18,263, Σy² = 2807, Σxy = 4059, and r ≈ −0.933.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx	=
Σy	=
Σx2	=
Σy2	=
Σxy	=
r	=

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x	=
y	=
	=	+   x

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =
explained	%
unexplained	%

(f) Predict the percentage of all fatal accidents due to speeding for 60-year-olds. (Round your answer to two decimal places.)
__________________ %

Answer 1

b)

Sl.No.	x	y	x^2	y^2	xy
1	17	39	289	1521	663
2	27	22	729	484	594
3	37	22	1369	484	814
4	47	12	2209	144	564
5	57	10	3249	100	570
6	67	7	4489	49	469
7	77	5	5929	25	385
Total	Σx = 329	Σy = 117	Σx2 = 18263	Σy2 = 2807	Σxy =4059

Sxx	2800
Syy	851.43
Sxy	-1440

correlation coefficeint r = = -0.933

c)

= 47

= 16.71

b = Sxy/Sxx = -1440/2800 = -0.514

a = = 16.71 - (-0.514)*47 = 40.868

y = 40.868 - 0.514* x

e) R2 = (b*Sxy)/Syy = -0.514*(-1440)/851.43 = 0.869

r2 =

0.869

explained 86.9 %

unexplained 13.1%

f) given x = 60

y = 40.868 - 0.514* 60 = 10.03