Question

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 _____

Answer 1

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