In: Statistics and Probability
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 |
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