For questions 1 – 3 use the following information: For a multiple linear regress
ID: 3183145 • Letter: F
Question
For questions 1 – 3 use the following information: For a multiple linear regression analysis there are 3 independent variables (X1, X2, X3), and a sample size of n = 30. Find degrees of freedom for error and regression for the following models:
First order linear model:
Df for Error = _________
Df for Regression = ________
Complete second order model:
Df for Error = _________
Df for Regression = ________
Complete second order model with all interaction:
Df for Error = _________
Df for Regression = _________
For questions 4 – 8 use the following information: A multiple regression analysis with n = 20 was done to fit the model: Y = 0 + 1X1 + 2X2 + 3X12 + 4X22 + 5X1X2 +
Finish filling out the ANOVA table given below. (Round your answers to two decimal places where necessary.)
Source
Df
SS
MS
F
Regression
4.8
Error
3.2
Total
19
What is the value of S for the above model? (Round your answer to two decimal places.)
Calculate adj R2. (Enter your solution in decimal representation, not percentages, and round to two decimal places.)
What are the null and alternative hypothesis used to test if the model is useful?
H0: 1 = 2 = 3 = 0 vs. Ha: at least one 0
H0: 1 = 2 =…= 5 = 0 vs. Ha: at least one 0
H0: 0 = 0 vs. Ha: 0 0
H0: 3 = 5 = 0 vs. Ha: at least one 0
What critical value from the F-table would be used in an Analysis of Variance F test?
Source
Df
SS
MS
F
Regression
4.8
Error
3.2
Total
19
Explanation / Answer
n=30, total df=30-1=29
First order linear model: y=0 +1*X1 +2*X2+ 3 *X3
Df for Error =total df - Df for Regression=29-3=26
Df for Regression =4-1=3
Complete second order model:y=0 +1*X1 +2*X2+ 3 *X3+11*X12 +22*X22+ 33 *X32
Df for Error =total df - Df for Regression=29-6=23
Df for Regression =7-1=6
Complete second order model with all interaction:
:y=0 +1*X1 +2*X2+ 3 *X3+11*X12 +22*X22+ 33 *X32+12*X1*X2 +23*X2*X3+ 13 *X1*X3
Df for Error =total df - Df for Regression=29-9=20
Df for Regression =10-1=9
here regression df=5, so error df=19-5=14
error SS=MS*error df=3.2*14=44.8
regression MS=F*error(MS)=3.2*4.8=15.36
regression SS=(regression MS)*(regression df)=15.36*5=76.8
total SS=regression SS + error SS=76.8+44.8=121.6
R2=regression SS/total SS=76.8/121.6= 0.6316
right choice is H0: 1 = 2 =…= 5 = 0 vs. Ha: at least one 0
at 5% ,critical F(0.05,5,14)=2.96
Source Df SS MS F Regression 5 76.8 15.36 4.8 Error 14 44.8 3.2 Total 19 121.6Related Questions
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