Calculate the value of a dependent variable given the following values of X1= 100, X2= 17, X3= 34, X4= 12 X4 34 56 74 Option X1 12 45 23 9.0 4.7 9.0 7.0 4.2 6.2 5.0 6.0 7.6 X2 100 50 100 100 50 80 75 65 90 90 4 4 12 56 89 12 67 23 47 34 4 9 10 17 57
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Expert Answer
Option Y X1 X2 X3 X4
1 9.00 12 100 4 34
2 4.70 45 50 3 56
3 9.00 23 100 4 74
4 7.00 14 100 2 8
5 4.20 56 50 2 12
6 6.20 89 80 2 2
7 5.00 12 75 3 34
8 6.00 67 65 4 7
9 7.60 23 90 3 17
10 7.10 47 90 2 57
Using Multiple linear regression we need to find the equation
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.966018268
R Square 0.933191293
Adjusted R Square 0.879744328
Standard Error 0.582295069
Observations 10
ANOVA
df SS MS F Significance F
Regression 4 23.68066 5.920166 17.46014 0.003845
Residual 5 1.695338 0.339068
Total 9 25.376
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -2.339985294 1.401437 -1.6697 0.155846 -5.94249 1.262524
X1 0.012612394 0.00926 1.361961 0.23136 -0.01119 0.036417
X2 0.079305539 0.011604 6.834378 0.001023 0.049477 0.109134
X3 0.636629894 0.241122 2.640283 0.045961 0.016807 1.256453
X4 0.007971912 0.008566 0.930651 0.39475 -0.01405 0.029991
So the equation will be
Y = -2.3399 + 0.0126*X1 + 0.0793*X2 +0.6366*X3
OR
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