Question

Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.

x	37	47	57	67	77	87
y	5	8	10	18	29	42

Complete parts (a) through (e), given Σx = 372, Σy = 112, Σx² = 24814, Σy² = 3118, Σxy = 8224, and r ≈ 0.955.

(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

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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 failing to yield the right of way for 70-year-olds. (Round your answer to two decimal places.)
%

Answer 1

b)

Sample Correlation coefficient (r):

r = 0.955

C)

Calculation:

For Slope:

b = 0.73

For Intercept:

a = 18.67 - 0.73*62.00

a = -26.68

Therefore, the least square regression line would be,

= -26.68 + 0.73(X)

d)

Scatter Plot:

Coefficient of Determination (r2) = 0.9552 = 0.911 = 91.1%

r2 = 0.911

Explained = 91.1%

Unexplained = 100% - 91.1% = 8.9%

f)

The least square regression line would be,

= -26.68 + 0.73(X)

Put, X = 70

= -26.68 + 0.73*70

= 24.52