Question

Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth.

{(0, 10.8), (3, 11.3), (5, 11.2), (−4, 10.7), (1, 9.3)}

Answer 1

Let the regression line be:

ŷ =a+bX

	X	Y	X*Y	X2	Y2
	0	10.8	0	0	116.64
	3	11.3	33.9	9	127.69
	5	11.2	56	25	125.44
	-4	10.7	-42.8	16	114.49
	1	9.3	9.3	1	86.49
Sum =	5	53.3	56.4	51	570.75

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope b and the y-intercept a)are obtained as follows:

Therefore, we find that the regression equation is:

Y=10.5926+0.0674X

inear correlation coefficient:

r=

r=

r=

r=

r=0.285

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