Question

In: Statistics and Probability

An auto manufacturing company wanted to investigate how the price of one of its car models...

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.

Age

8

3

6

9

2

5

6

3

Price

18

96

48

22

149

40

35

98

Compute the coefficient of determination.

Round your answer to two decimal places.

The coefficient of determination is _____

Solutions

Expert Solution

Solution:

X Y XY X^2 Y^2
8 18 144 64 324
3 96 288 9 9216
6 48 288 36 2304
9 22 198 81 484
2 149 298 4 22201
5 40 200 25 1600
6 35 210 36 1225
3 98 294 9 9604

n 8
sum(XY) 1920.00
sum(X) 42.00
sum(Y) 506.00
sum(X^2) 264.00
sum(Y^2) 46958.00
Numerator -5892.00
Denominator 6452.17
r -0.9132
r square 0.8339
Xbar(mean) 5.2500
Ybar(mean) 63.2500
SD(X) 2.5000
SD(Y) 46.4414
b -16.9310
a 152.1379

The coefficient of determination is,

r2 = 0.83


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