Question

(By Hand) For the dependent variable Y and the independent variables X1 and X2, the linear regression model is given by: Y=0.08059*X1-0.16109*X2+5.26570. Complete the following table:

Actual Y	X1	X2	Predicted Y	Prediction Error
6	6.8	4.7
3.1	5.3	5.5
5.8	4.5	6.2
4.5	8.8	7
4.5	6.8	6.1
3.7	8.5	5.1
5.4	8.9	4.8
5.1	6.9	5.4
5.8	9.3	5.9
5.7	8.4	5.4

Answer 1

For each of X1, X2 value ,

Predicted : Y = =0.08059*X1-0.16109*X2+5.26570.

And

Prediction error = Actual Y - Predicted Y

Actual Y	X1	X2	Predicted Y:	Predicted Y	Prediction Error	Prediction Error
6	6.8	4.7	=0.08059*6.8 - 0.16109*4.7 + 5.262570 = 5.056589	5.056589	= 6 - 5.056589 = 0.943411	0.943411
3.1	5.3	5.5	=0.08059*5.3 - 0.16109*5.5 + 5.262570 = 4.806832	4.806832	= 3.1 - 4.806832 = -1.706832	-1.706832
5.8	4.5	6.2	=0.08059*4.5 - 0.16109*6.2 + 5.262570 = 4.629597	4.629597	= 5.8 - 4.629597 = 1.170403	1.170403
4.5	8.8	7	=0.08059*8.8 - 0.16109*7 + 5.262570 = 4.847262	4.847262	= 4.5 - 4.847262 = -0.347262	-0.347262
4.5	6.8	6.1	=0.08059*6.8 - 0.16109*6.1 + 5.262570 = 4.831063	4.831063	= 4.5 - 4.831063 = -0.331063	-0.331063
3.7	8.5	5.1	=0.08059*8.5 - 0.16109*5.1 + 5.262570 = 5.129156	5.129156	= 3.7 - 5.129156 = -1.429156	-1.429156
5.4	8.9	4.8	=0.08059*8.9 - 0.16109*4.8 + 5.262570 = 5.209719	5.209719	= 5.4 - 5.209719 = 0.190281	0.190281
5.1	6.9	5.4	=0.08059*6.9 - 0.16109*5.4 + 5.262570 = 4.951885	4.951885	= 5.1 - 4.951885 = 0.148115	0.148115
5.8	9.3	5.9	=0.08059*9.3 - 0.16109*5.9 + 5.262570 = 5.064756	5.064756	= 5.8 - 5.064756 = 0.735244	0.735244
5.7	8.4	5.4	=0.08059*8.4 - 0.16109*5.4 + 5.262570 = 5.07277	5.07277	= 5.7 - 5.07277 = 0.62723	0.62723

Actual Y	X1	X2	Predicted Y	Prediction Error
6	6.8	4.7	5.056589	0.943411
3.1	5.3	5.5	4.806832	-1.706832
5.8	4.5	6.2	4.629597	1.170403
4.5	8.8	7	4.847262	-0.347262
4.5	6.8	6.1	4.831063	-0.331063
3.7	8.5	5.1	5.129156	-1.429156
5.4	8.9	4.8	5.209719	0.190281
5.1	6.9	5.4	4.951885	0.148115
5.8	9.3	5.9	5.064756	0.735244
5.7	8.4	5.4	5.07277	0.62723