Question

Use StatKey or other technology to find the regression line to predict Y from X using the following data. 6 2 7 3 6 4 Y 3 1.5 2 Click here to access StatKey Round your answers to three decimal places. х. The regression equation is Y Click if you would like to Show Work for this question: Open Show Work et

Answer 1

for simple linear regressior Y^=a+b*X=-0.47+0.82X

a=(sum(y)*sum(x²)-sum(x)*sum(xy))/(n*sum(x²)-(sum(x))²)=-0.47

b=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x²)-(sum(x))²)=0.82

s.n.	x	y	x2	y2	xy
1	3	2	9	4	6
2	5	3	25	9	15
3	2	1.5	4	2.25	3
4	7	6	49	36	42
5	6	4	36	16	24
sum=	23	16.5	123	67.25	90

following regression analysis information can also be generated using data analysis in ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.950276
R Square	0.903025
Adjusted R Square	0.8707
Standard Error	0.643242
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	11.55872	11.55872	27.93583	0.01321
Residual	3	1.241279	0.41376
Total	4	12.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.47093	0.769268	-0.61218	0.583695	-2.91908	1.977222
X Variable 1	0.819767	0.155099	5.285436	0.01321	0.326172	1.313363