Question

Consider the following data for a dependent variable y and two independent variables, x1 and x2.

x1	x2	y
29	13	94
46	10	109
24	17	112
50	17	178
40	6	94
52	19	176
75	8	171
36	13	118
60	13	143
76	17	212

Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.

a. Develop an estimated regression equation relating y to x1 .

y = __ + __ x1

Predict y if x1 = 45

y=___

  

b. Develop an estimated regression equation relating y to x2.

      

Predict y if x2 = 25

y = __.

  

c. Develop an estimated regression equation relating y to x1 and x2.

y = ___ + ___x1 + ___x2   

Predict y if x1=45 and x2=25 .

y = ___

Answer 1

( a )

Using Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.812209997
R Square	0.659685079
Adjusted R Square	0.617145714
Standard Error	25.55354199
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10126.23193	10126.23	15.50764	0.00430814
Residual	8	5223.868066	652.9835
Total	9	15350.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	48.21953469	24.83565128	1.941545	0.088136	-9.0515798	105.490649
x1	1.895091502	0.481235166	3.937974	0.004308	0.78536122	3.00482178

from the above output

y = 48.22 + 1.90 x1

if x1 = 45

y = 48.22 + 1.90 ( 45 )

= 133.72

( b )

Using Excel we get output as

Regression Statistics
Multiple R	0.502203567
R Square	0.252208422
Adjusted R Square	0.158734475
Standard Error	37.87920851
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3871.424503	3871.425	2.698168	0.13908867
Residual	8	11478.6755	1434.834
Total	9	15350.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	76.49006623	40.8842998	1.870891	0.098272	-17.789298	170.769431
x2	4.82781457	2.939111618	1.64261	0.139089	-1.949789	11.6054181

from the above output

y = 76.49 + 4.83 x2

if x2 = 25

y = 76.49 + 4.83 ( 25 )

= 197.24

( c )

Using Excel we get output as

Regression Statistics
Multiple R	0.972662657
R Square	0.946072645
Adjusted R Square	0.930664829
Standard Error	10.87454629
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	14522.3097	7261.155	61.40213	3.6419E-05
Residual	7	827.7902994	118.2558
Total	9	15350.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-22.69958904	15.71624081	-1.44434	0.191871	-59.862593	14.4634151
x1	1.94512482	0.204958423	9.490339	3.02E-05	1.46047516	2.42977448
x2	5.148684046	0.844451487	6.097075	0.000492	3.15187358	7.14549451

from the above output

y = -22.70 + 1.95 x1 + 5.15 x2

= -22 70 + 1.95 ( 45 ) + 5.15 ( 25 )

= 193.8