Question

Find the multiple regression equation for the data given below.

x1: -3, -2, -1, 2 ,3

x2: -4, 1, -1, -1, 2

y: 1, -9, 1, 13, 8

The equation is y^= _____+ ______ x1 + _____ x2.

Answer 1

For the given data using Regression in Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.999565338
R Square	0.999130865
Adjusted R Square	0.998261731
Standard Error	0.346825963
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	276.5594235	138.2797	1149.57	0.000869135
Residual	2	0.240576497	0.120288
Total	4	276.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.890243902	0.162495346	11.6326	0.007309	1.191082859	2.589404946
x1	4.028824834	0.08407101	47.92169	0.000435	3.667096472	4.390553196
x2	-2.859201774	0.094524793	-30.2482	0.001091	-3.26590913	-2.452494417

So from the above output

The equation is  y^= (1.8902 ) + ( 4.0288 ) x1 + ( - 2.8592 ) x2