Question

For the accompanying data set, (a) draw a scatter diagram of the data, (b) compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y. Click the icon to view the data set Click the icon to view the critical values table (a) Draw a scatter diagram of the data. Choose the correct graph below. OA. ов. Ос. OD. A 10 A 10- 10- 1 Question Viewer

Answer 1

a) Scatter Plot: Correct answer: Option (D) Graph / Plot

Scatterplot of Y vs X 9 8 7 5 > 5 4 3 2 . 0 1 3 4 5 N 6 7 8 9 X

b) From the given data

	X	Y	X^2	Y^2	XY
	2	8	4	64	16
	6	2	36	4	12
	1	6	1	36	6
	7	9	49	81	63
	9	5	81	25	45
Total:	25	30	171	210	142

The correlation coefficient r is computed using the following expression: r= SSXY SSXX SSyy where SSXY -3xx -+ (2x) (3) 2 72 n 1 SSxx = x ΣΧ n i=1 SSyy = Y; - r- () In this case, based on the data provided, we get that 1 SSXY 142 (25 x 30) = -8 5 1 SSxx 171 (25)2 = 46 1 SSyy = 210 (30)2 = 30 Therefore, based on this information, the sample correlation coefficient is computed as follows T = SSXY SSXX SSyy -8 46 x 30 = -0.215

c) H0: There is no correlation between X and Y

H1: There is correlation between X and Y

Criticla vlaue = 0.878 at n - 2 = 5 - 2 = 3 df

since r value < r critical value so we accept the H0

Thus we conclude that there is no correlation between X and Y