Determine the regression equatoin for this multiple regression model. Also calcu
ID: 2906606 • Letter: D
Question
Determine the regression equatoin for this multiple regression model. Also calculate the adjusted R squared and P value.
Pedictor Variables/Data Length (inches) Braking (ft from 60 mph) Engine Displacement (liters) GHG 154 133 1.6 6.6 167 132 1.6 6.1 177 136 1.8 6.3 177 138 2 6.6 179 137 2 6.4 188 135 2 8.0 177 126 2 7.7 191 136 2.3 8.0 194 140 2.4 7.7 189 137 2.4 7.3 180 135 2.5 8.3 190 136 2.5 7.1 180 140 2.5 8.0 200 131 2.7 8.7 193 134 3.3 8.7 191 128 3.5 8.3 197 139 3.5 8.0 208 145 4.6 10.2 203 143 4.6 10.2 212 140 4.6 9.6 215 143 4.6 9.6Explanation / Answer
Using Excel we get following output
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.911590634
R Square
0.830997484
Adjusted R Square
0.801173511
Standard Error
0.54976783
Observations
21
ANOVA
df
SS
MS
F
Significance F
Regression
3
25.2647
8.421566
27.86341
8.65122E-07
Residual
17
5.138159
0.302245
Total
20
30.40286
Coefficients
Standard Error
t Stat
P-value
Intercept
5.359938521
4.559404882
1.175579
0.255965
Length (inches)
0.018520385
0.016658021
1.1118
0.281701
Braking (ft from 60 mph)
-0.02522475
0.031380555
-0.80383
0.43259
Engine Displacement (liters)
0.910291795
0.244316648
3.725869
0.001681
Using minitab we get following output:
Regression Analysis: GHG versus Length (inches), Braking (ft from, Engine Displacem
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 25.2647 8.4216 27.86 0.000
Length (inches) 1 0.3736 0.3736 1.24 0.282
Braking (ft from 60 mph) 1 0.1953 0.1953 0.65 0.433
Engine Displacement (liters) 1 4.1958 4.1958 13.88 0.002
Error 17 5.1382 0.3022
Total 20 30.4029
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.549768 83.10% 80.12% 74.04%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 5.36 4.56 1.18 0.256
Length (inches) 0.0185 0.0167 1.11 0.282 4.04
Braking (ft from 60 mph) -0.0252 0.0314 -0.80 0.433 1.50
Engine Displacement (liters) 0.910 0.244 3.73 0.002 4.24
Regression Equation
GHG = 5.36 + 0.0185 Length (inches) - 0.0252 Braking (ft from 60 mph)
+ 0.910 Engine Displacement (liters)
Using above result from minitab and excel we get
Multiple regression model is given by,
GHG = 5.36 + 0.0185 Length (inches) - 0.0252 Braking (ft from 60 mph)
+ 0.910 Engine Displacement (liters) (Rounded value)
OR
GHG = 5.35994 + 0.018520385 Length (inches)-0.02522475 Braking (ft from 60 mph)
+ 0.910291795 Engine Displacement (liters)
Adujested R_Sq is
R-sq(adj)= 80.12%
P value is given by
P-value
Rounded P-value
Intercept
0.255965414
0.256
Length (inches)
0.281700818
0.282
Braking (ft from 60 mph)
0.432590092
0.433
Engine Displacement (liters)
0.001680723
0.002
Steps involve in minitab
Copy data > Stat >Regression > Regression > Fit Regression model > Select Response variable (GHG), Select predictor variable one by one (Length,Braking,Engine Displacement)>ok.
IN Excel
Copy data > Data> Data Analysis > Regression > select Response Range (GHG), select all predictor (Length,Braking,Engine Displacement) >ok
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.911590634
R Square
0.830997484
Adjusted R Square
0.801173511
Standard Error
0.54976783
Observations
21
ANOVA
df
SS
MS
F
Significance F
Regression
3
25.2647
8.421566
27.86341
8.65122E-07
Residual
17
5.138159
0.302245
Total
20
30.40286
Coefficients
Standard Error
t Stat
P-value
Intercept
5.359938521
4.559404882
1.175579
0.255965
Length (inches)
0.018520385
0.016658021
1.1118
0.281701
Braking (ft from 60 mph)
-0.02522475
0.031380555
-0.80383
0.43259
Engine Displacement (liters)
0.910291795
0.244316648
3.725869
0.001681
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