Question

x 3 12 6 20 14 Y55 35 45 10 15 The estimated regression equation for these data is - 62.25 -2.75x. (a) Compute SSE, SST, and SSR using equations SSE - ELY,-9.), SST = Ely-7), and SSR-369,-7) SSE - 18.75 SST = 1490 SSR - 0361.25 Compute the coefficient of determination (Round your answer to three decimal places.) 2-10.919 Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large f it is at least 0.55.) The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least sou The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the le squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the le squares line. The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squ (c) Compute the sample correlation coefficient. (Round your answer to three decimal places.) [0.959

please help me with b

Answer 1

	X	Y	X-Xbar	Y-Ybar	(X - Xbar)*(Y-Ybar)	(X-Xbar)^2	(Y-Ybar)^2	Y^ = 62.25-2.75*X	(Y^-Ybar)^2	(Y-Y^)^2
	3	55	-8	23	-184	64	529	54	484	1
	12	35	1	3	3	1	9	29.25	7.5625	33.0625
	6	45	-5	13	-65	25	169	45.75	189.0625	0.5625
	20	10	9	-22	-198	81	484	7.25	612.5625	7.5625
	14	15	3	-17	-51	9	289	23.75	68.0625	76.5625
SUM	55	160			-495	180	1480	160	1361.25	118.75
Mean	11	32
n	5
k	2				slope (m)	-2.75	SUM((X - Xbar)*(Y-Ybar))/SUM(X-X bar)^2
					Interept(b)	62.25	(SUM(Y)-m*SUM(X))/n
					Regression equation	Y^ = 109.9-1.19*X	Y^=mx+b
Source	df		SS		MS		F		P value
Regression	1	k-1	1361.25	SUM(Y^-Ybar)^2	1361.25	SSR/dfR	34.38947368	MSR/MSE	0.009888707	From F table
Error	3	n-k	118.75	SUM(Y-Y^)^2	39.58333333	SSE/dfE
Total	4	n-1	1480	SUM(Y-Ybar)^2

b)

Coefficient of determination (r^2) = SSR/SST = 1361.25/1480 = 0.9198

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least so

c)

Correlation coefficient (r) = -SQRT(r^2) = -0.959 (r value is negative why because we have negative slope)

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least so