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 17 92 52 20 143 43 34 99

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	17	136	64	289
3	92	276	9	8464
6	52	312	36	2704
9	20	180	81	400
2	143	286	4	20449
5	43	215	25	1849
6	34	204	36	1156
3	99	297	9	9801

n	8
sum(XY)	1906.00
sum(X)	42.00
sum(Y)	500.00
sum(X^2)	264.00
sum(Y^2)	45112.00
Numerator	-5752.00
Denominator	6212.23
r	-0.9259
r square	0.8573
Xbar(mean)	5.2500
Ybar(mean)	62.5000
SD(X)	2.5000
SD(Y)	44.1717
b	-16.5287
a	149.2759

r = -0.9259

The coefficient of determination is 0.86