Please answer and explain For the data given below, assume a model of the form:
ID: 3200912 • Letter: P
Question
Please answer and explain
For the data given below, assume a model of the form:
E(y) = 0 + 1x1 + 2x2
A. Determine the least-squares multiple regression line.
B. What is the estimate of the standard deviation of the random error component () for this model and data?
C. Find and interpret a 95% confidence interval for 2.
D. Test the overall adequacy of the model using alpha = 0.05.
E. Predict, with 95% confidence, y for x1 = 3 and x2=10.
Y X1 X2 0 9.0 45.0 1 15.0 57.0 0 10.0 45.0 2 16.0 51.0 4 10.0 65.0 4 20.0 88.0 1 11.0 44.0 4 20.0 87.0 3 15.0 89.0 0 15.0 59.0 2 8.0 66.0 1 13.0 65.0 4 18.0 56.0 1 10.0 47.0 0 8.0 66.0 1 10.0 41.0 3 16.0 56.0 0 11.0 37.0 1 19.0 45.0 4 12.0 58.0 4 11.0 47.0 0 19 64 2 15 97 3 15 55 1 20 51 0 6 61 3 15 69 3 19 79 2 14 71 2 13 62 3 17 87 2 20 54 2 11 43 3 20 92 4 20 83 4 20 94 3 9 60 1 8 56 2 16 88 0 10 62Explanation / Answer
A)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
b0=Ey-b1Ex/n
Calculating that we get the value -1.24+0.09X1+0.03X2- Multiple regression line.
Detailed output given below:-
B)
Estimate of the standard deviation of the random error component () for this model and data is MSE which is 1.5189=1.52 approx.
C)
Lower limit as seen from the table is 0.0037 and upper limit is 0.0583.
D)
F-Score is 7.83 and is greater than significant F i.e. 0.0014 and hence reject the null hypothesis.
E)
-1.24+0.09X1+0.03X2
Substituting values for X1 and X2 we get
-1.24+0.09(3)+0.03(10)=-1.24+0.27+0.3=-0.67
SUMMARY OUTPUT Regression Statistics Multiple R 0.545436182 R Square 0.297500629 Adjusted R Square 0.25952769 Standard Error 1.232443735 Observations 40 ANOVA df SS MS F Significance F Regression 2 23.80005028 11.90002514 7.834543134 0.001455291 Residual 37 56.19994972 1.51891756 Total 39 80 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.243310021 0.842642904 -1.475488626 0.148541077 -2.950666722 0.464046681 -2.950666722 0.464046681 X1 0.090067685 0.052662508 1.710280959 0.095588224 -0.016636692 0.196772062 -0.016636692 0.196772062 X2 0.031052017 0.013484557 2.302783579 0.027014927 0.003729709 0.058374325 0.003729709 0.058374325B)
Estimate of the standard deviation of the random error component () for this model and data is MSE which is 1.5189=1.52 approx.
C)
Lower limit as seen from the table is 0.0037 and upper limit is 0.0583.
D)
F-Score is 7.83 and is greater than significant F i.e. 0.0014 and hence reject the null hypothesis.
E)
-1.24+0.09X1+0.03X2
Substituting values for X1 and X2 we get
-1.24+0.09(3)+0.03(10)=-1.24+0.27+0.3=-0.67