Question

Consider the following data for a dependent variable y and two independent variables, x₁and x₂.

x 1	x 2	y
29	13	94
47	10	109
24	17	113
50	16	178
40	6	95
52	20	176
75	7	171
37	13	118
59	14	142
77	17	211

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.

ŷ =  +  x₁

Predict y if x₁= 35.

ŷ =

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

ŷ =  +  x₂

Predict y if x₂= 25.

ŷ =

c. Develop an estimated regression equation relating y to x₁and x₂.

ŷ =  +  x1 +  x2

Predict y if x₁= 35 and x₂= 25.

ŷ =

Answer 1

a)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	0.8107
R Square	0.6572
Adjusted R Square	0.6143
Standard Error	25.4010
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9894.4	9894.4	15.34	0.0044
Residual	8	5161.7	645.2
Total	9	15056.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	48.9812	24.7606	1.9782	0.0833	-8.1169	106.07926
X	1.8718	0.4780	3.9160	0.0044	0.7696	2.9741

Ŷ =   48.98 +   1.87 *x1

Predicted Y at X=   35   is                  
Ŷ =   48.98 +   1.87 *   35   =   114.50

b)

Regression Statistics
Multiple R	0.4588
R Square	0.2105
Adjusted R Square	0.1118
Standard Error	38.5461
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3169.7	3169.7	2.13	0.1823
Residual	8	11886.4	1485.8
Total	9	15056.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	85.5133	39.7013	2.1539	0.0634	-6.0380	177.06457
X	4.1494	2.8409	1.4606	0.1823	-2.4017	10.7005

Ŷ =   85.51 +   4.15 *x2

Predicted Y at X=   25   is                  
Ŷ =   85.51 +   4.15 *   25   =   189.25

c)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.955483
R Square	0.912948
Adjusted R Square	0.888076
Standard Error	13.68348
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	13745.44	6872.719	36.70587	0.000195
Residual	7	1310.663	187.2376
Total	9	15056.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-15.2058	19.44809	-0.78186	0.459918	-61.1932	30.78167	-61.1932	30.78167
x 1	1.938323	0.25791	7.515514	0.000136	1.328463	2.548182	1.328463	2.548182
x 2	4.58105	1.01012	4.535155	0.002683	2.192496	6.969603	2.192496	6.969603

ŷ = -15.21+ 1.94*x1 + 4.58 x2

if x₁= 35 and x₂= 25

ŷ = -15.21+ 1.94*35 + 4.58 *25 = 167.16(answer)