Question

Use the following data to develop a multiple regression model to predict from and . Discuss the output, including comments about the overall strength of the model, the significance of the regression coefficients, and other indicators of model fit. y x1 x2 198 29 1.64 214 71 2.81 211 54 2.22 219 73 2.70 184 67 1.57 167 32 1.63 201 47 1.99 204 43 2.14 190 60 2.04 222 32 2.93 197 34 2.15 Appendix A Statistical Tables *(Round your answer to two decimal places.) **(Round your answer to 4 decimal places.) ***(Round your answer to 3 decimal places.) The regression equation is: *+( **) +( ***) * with *** * with * * with ** *** *** Adjusted ***

Answer 1

Sol:

Install anaysis tool pack in excel and then

Go to data >dataanalysis>Regression

Select X

select Y

click ok

You will get below output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.855239
R Square	0.731433
Adjusted R Square	0.664292
Standard Error	9.400891
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1925.532	962.7658	10.89388	0.005202
Residual	8	707.014	88.37674
Total	10	2632.545
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	137.268	14.77854	9.28833	1.47E-05	103.1886	171.3474
x1	0.002515	0.18628	0.0135	0.98956	-0.42705	0.432078
x2	29.2061	6.533584	4.47015	0.002083	14.13963	44.27257

The regression equation is

y^=137.27+0.0025x1+29.206x2

F=

10.89 with p=0.005

t x1=

0.01 with p=0.99

tx2 =

4.47 with p=0.0021

S=9.401

R² =0.731

ad j R ² =0.664

From F output

p<0.05 model is significant

for X1 p=0.99,p>0.05 X1 is not significant variable

for X2 p=0.002,p<0.05 X2 is significant variable.