Question

4 7. Following are age and price data for 6 randomly selected Civics between 1 and 6 years old. Here, denones age in years, and y denotes price in thousands of dollars. 15 x = Age y=Price x2 gy 1 20 20 2 1 19 2 0 16 ll. 4 5 16 12 Eu711 46 1202

- Calculate the linear correlation coefficient and comment on the strength or weakness of the linear correlation between x and y

Answer 1

From the given data:

	Age(x)	Price(y)	x^2	y^2	xy
	1	20	1	400	20
	2	19	4	361	38
	4	16	16	256	64
	5	16	25	256	80
Total	12	71	46	1273	202

The correlation coefficient is given by:

r = η(Στy) – (Στ) * (Σ9) - V[n Σ2 - (Σ)2][n Σy2 - (ΣΗ)2

T = 4* 202 - 12 * 71 [4* 46 - (12)214 * 1273 - (71)2]

808 - 851 [184 - 144] [5092 - 5041]

Pe 40 * 51

-44 T= 2040

了= 45 16635916

$r=-0.974176374$

$r=-0.97$

The correlation coefficient indicates that there is a strong negative linear relationship between age and price.