Question

the data on ages (in years) and prices (in hundreds of dollars) for 8 cars of a specific model are given:

Age: 8 3 6 9 2 5 6 3
price: 45 210 100 33 267 134 109 235

Fund the linear correlation coefficient r. Use appropriate test to indicate if there is a linear correlation.

Answer 1

(a)

From the given data,the following Table is calculated:

X	Y	XY	X2	Y2
8	45	360	64	2025
3	210	630	9	44100
6	100	600	36	10000
9	33	297	81	1089
2	267	534	4	71289
5	134	670	25	17956
6	109	654	36	11881
3	235	705	9	55225
Total = 42	1133	4450	264	213565

Correlation Coefficient (r) is given by:

(b)

H0:Null Hypothesis: = 0

HA: Alternative Hypothesis: 0

Test statistic is given by:

Take = 0.05

ndf = n - 2 = 8 - 2 =6

From Table, critical values of t = 2.4469

Since the calculated value of t = - 14.3798 is less than critical value of t = - 2.4469, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a linear correlation.