Run the regression until you have removed the “non-significant” ? coefficients.
ID: 3055090 • Letter: R
Question
Run the regression until you have removed the “non-significant” ? coefficients. What is the final regression model?
What percent of the initial variability in Job Income is explained by the regression equation?
From the final regression model what is my expected income if I am a female with a 3.0 GPA with SAT score of 2000 and an IQ = 130?
How much more money would I make if I had a 150 IQ?
Male(O) Female College GPA Job Income (in 000s) SAT Score x4 110 160 140 120 125 120 110 130 120 160 110 100 Which individual coefficient would I remove from the model first? 60 69 62 59 58 73 85 1300 1700 1400 2000 2400 2200 2300 1700 1200 1500 2300 1500 4 3.9 2.2 4 2.9 3.8 89 95 93 76 0 0 0 0 0 0 4 3.7 1. 2. Oun the regression until you have removed the "non-significant" B coefficients. What is the final regression model? What percent of the initial variability in Job Income is explained by the regression equation? From the final regression model what is my expected income if I am a female with a 3.0 GPA with SAT score of 2000 and an IQ-130? How much more money would I make if I had a 150 IQ? 3. 4. 5.Explanation / Answer
Here dependent variable is job income and there are four independent variables which are college gpa, SAT score, IQ and gender.
This is the problem of multiple regression.
Assume alpha = level of significance = 0.05
Which individual coefficient would I remove from the model first?
Here we have to do regression.
We can do regression in excel.
steps :
ENTER data into excel sheet --> Data --> Data analysis --> regression --> ok --> Input Y range : select y range --> Input X range : Select all the x variables together --> Labels --> Output range : select one empty cell --> ok
We can remove the variable from the model which p-value is greator than alpha.
WE can see that x2 and x3 have p-value 0.1839 and 0.6417 respectively.
So x2 and x3 we will remove from the model.
Run the regression until you have removed the “non-significant” ? coefficients.
Now we have to do regression without taking x2 and x3.
After doing this regression we will get the regression equation as,
y = 66.60 + 6.52*x1 - 23.84*x4
ANd also we can see that all the variablesare significant which can included into the model.
What is the final regression model?
The final regression equation will be :
y = 66.60 + 6.52*x1 - 23.84*x4
What percent of the initial variability in Job Income is explained by the regression equation?
We have to take R2 from the first model.
R2 = 0.9603 = 96.03%
It can expresses the proportion of variation in y which is explained by variation in independent variables.
From the final regression model what is my expected income if I am a female with a 3.0 GPA with SAT score of 2000 and an IQ = 130?
Now we have to predict y when x1 = 3.0, x2 = 2000, x3 = 130 and x4 = 1
This also we can find using regression equation.
The regression equation is,
y = 56.39 + 6.30*x1 + 0.00*x2 + 0.04*x3 - 24.43*x4
y = 56.39 + 6.30*3.0 + 0.00*2000 + 0.04*130 - 24.43*1 = 111.86
SUMMARY OUTPUT Regression Statistics Multiple R 0.979968 R Square 0.960337 Adjusted R Square 0.937672 Standard Error 3.502404 Observations 12 ANOVA df SS MS F Significance F Regression 4 2079.049 519.7622 42.37135 5.42E-05 Residual 7 85.86783 12.26683 Total 11 2164.917 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 56.38506 9.358431 6.025054 0.0005 34.25588 78.51423 34.25588 78.51423 x1 6.304294 1.676187 3.761092 0.0071 2.340741 10.26785 2.340741 10.26785 x2 0.003766 0.002554 1.474463 0.1839 -0.00227 0.009805 -0.00227 0.009805 x3 0.035404 0.07283 0.486115 0.6417 -0.13681 0.20762 -0.13681 0.20762 x4 -24.4308 2.131434 -11.4621 0.0000 -29.4708 -19.3908 -29.4708 -19.3908Related Questions
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