Question

A.(4) Obtain the ANOVA table that decomposes the regression sum of squares into extra sums of squares associated with X2 and with X1, given X2.
B.(6) Test whether X1 can be dropped from the regression model given thatX2 is retained. Use the F* test statistic and level of significance 0.05. State the alternatives, decision rules, and conclusion. What is the p-value of the test?
C.(5) Obtain and present the standardized regression coefficients. What do these indicate about the relative contributions of the two predictors?

Data:

Y	X1	X2
64	4	2
73	4	4
61	4	2
76	4	4
72	6	2
80	6	4
71	6	2
83	6	4
83	8	2
89	8	4
86	8	2
93	8	4
88	10	2
95	10	4
94	10	2
100	10	4

Answer 1

The solution in details given below.

A)

solution

General Linear Model: Y versus X1, X2

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
X1	1	1566.45	1566.45	215.95	0.000
X2	1	306.25	306.25	42.22	0.000
Error	13	94.30	7.25
Lack-of-Fit	5	37.30	7.46	1.05	0.453
Pure Error	8	57.00	7.13
Total	15	1967.00

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.69330	95.21%	94.47%	92.46%

B)

solution: x1 can dropped from the regression model given that x2 is retained

Ho: The variable is in not significance at 5% of l.o.s

H1: The variable is significance at 5% of l.o.s

General Linear Model: Y versus X2

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
X2	1	306.3	306.3	2.58	0.130
Error	14	1660.8	118.6
Total	15	1967.0

From the above table we can say that F-stat=2.58 F-tab=0.1305344 (Formula in excel FDIST(2.58,1,14))

The p-value =0.130 and alpha value=0.05 p-value is greater than alpha value then Accept Ho (null hypothesis)

Conclusion:

Then we can say that the x2 variable is not much significance at 5% of level of significance.

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
10.8915	15.57%	9.54%	0.00%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	68.63	8.61	7.97	0.000
X2	4.38	2.72	1.61	0.130	1.00

Regression Equation

Y

=

68.63 + 4.38 X2

c)

solution:

Standardize Regression coeffiecient

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	37.65	3.00	12.57	0.000
X1	4.425	0.301	14.70	0.000	1.00
X2	4.375	0.673	6.50	0.000	1.00

Regression Equation

Y

=

37.65 + 4.425 X1 + 4.375 X2

Standardize Residual plot