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	15	31	44

Complete parts (a) through (e), given Σx = 372, Σy = 113, Σx² = 24814, Σy² = 3311, Σxy = 8351, and r ≈ 0.935.

(a) Draw a scatter diagram displaying the data.

Selection Tool

Line

Ray

Segment

Circle

Vertical Parabola

Horizontal Parabola

Point

No Solution

Help

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

5

10

15

20

25

30

35

40

45

50

Clear Graph

Delete Layer

Fill

WebAssign Graphing Tool

Graph LayersToggle Open/Closed

• After you add an object to the graph you can use Graph Layers to view and edit its properties.

(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

Part b)

ΣX = 372
ΣY = 113
ΣX * Y = 8351
ΣX2 = 24814
ΣY2 = 3311

r = 0.935

Part c)

Equation of regression line is Ŷ = a + bX


b = 0.769
a =( Σ Y - ( b * Σ X) ) / n
a =( 113 - ( 0.7686 * 372 ) ) / 6
a = -28.818
Equation of regression line becomes Ŷ = -28.818 + 0.769 X

Part e)

Coefficient of Determination
= 0.874
Explained variation = 0.874* 100 = 87.4%
Unexplained variation = 1 - 0.874* 100 = 12.6%

Part f)

When X = 70
Ŷ = -28.818 + 0.769 X
Ŷ = -28.818 + ( 0.769 * 70 )
Ŷ = 25.01