Question

Please, I need a two-page report interpreting the regression results for the management of Cool Stuff.

Answer 1

Using Minitab

Regression Analysis: Y versus X1, X2, X3, X4

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 4 8718.02 2179.51 129.74 0.000
X1 1 759.83 759.83 45.23 0.000
X2 1 12.22 12.22 0.73 0.404
X3 1 1064.15 1064.15 63.35 0.000
X4 1 260.74 260.74 15.52 0.001
Error 20 335.98 16.80
Total 24 9054.00

Model Summary

S R-sq R-sq(adj) R-sq(pred)
4.09864 96.29% 95.55% 94.27%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -124.38 9.94 -12.51 0.000
X1 0.2957 0.0440 6.73 0.000 1.14
X2 0.0483 0.0566 0.85 0.404 1.37
X3 1.306 0.164 7.96 0.000 3.02
X4 0.520 0.132 3.94 0.001 2.83

Regression Equation

Y = -124.38 + 0.2957 X1 + 0.0483 X2 + 1.306 X3 + 0.520 X4

This is regression model Which is used for prediction for value of Y .

just put the value of X1 , X2 , X3 and X4 in Regression equation then you get value of Y .

R-square =96.29%

Determination of variation which used for deciding model is best or not you can see here R-square is 96.29% which very strong that indicates model is very powerfull .

plot of Regression analysis

Assumption of Regression Analysis

Assumption of Regression Analysis

1) Normalility

using above first plot we say that data follow normal distribution this is one of the assumption of regression analysis

2) Constant variance

Using Second plot you can see the plot show random pattern thats why the assumption of constant variance and independence is satisfied .

3) linear relationship

You can see above plot there is linear relationship between Response(Y) and regressor (X1 , X2, X3 and X4)

that's why the main assumption of regression satisfied .