Question

For the data set below (a) Determine the least-squares regression line. (b) Compute th x30405060 70 y 113 100 87 85 67 (a) Determine the least-squares regression line (Round to four decimal places as needed)

Answer 1

a) suppose our regression line be ,

y=a+bx ; where b=

a= $\overline{y}-b\overline{x}$

by the excel table we have b=(-1070)/(1000) . and a= 90.4-(-1.07 * 50)

= -1.07 =143.9

hence our least squared regression line is ,  y= 143.9+( -1.07)x

b) The sum of the squared residuals for the least squares regression line will be ,

$\sum (\hat{y}-a-b*x)^{2}$

=46.3

CALCULATIONS >>>>>>>>>>>>>>>>>

X	Y	X-50	Y-90.4	(X-50)*(Y-90.4)	(X-50)^2		Y-143.9+(1.07*X)	(Y-143.9+(1.07*X))^2
30	113	-20	22.6	-452	400		1.2	1.44
40	100	-10	9.6	-96	100		-1.1	1.21
50	87	0	-3.4	0	0		-3.4	11.56
60	85	10	-5.4	-54	100		5.3	28.09
70	67	20	-23.4	-468	400		-2	4
x_bar        = 50	y_bar= 90.4			SUM= -1070	SUM= 1000			sum=    46.3