## Checking Multiple Regression Assumptions

## Relative Importance of Explanatory Variables

## Using Multiple Regression Model for Prediction

## Simple linear regression model

*Regression Statistics*
Multiple R
0.821384888
R Square
0.674673134
Adjusted R Square
0.672245321
Standard Error
1586.927704
Observations
136
ANOVA
* *
*df*
*SS*
*MS*
*F*
*Significance F*
Regression
1
7E+08
7E+08
277.8934
1.77E-34
Residual
134
3.37E+08
2518340
Total
135
1.04E+09
* *
*Coefficients*
*Standard Error*
*t Stat*
*P-value*
*Lower 95.0%*
*Upper 95.0%*
Intercept
798.7778605
173.5187
4.603411
9.54E-06
455.5881
1141.967622
New Capital Expenses
2.293338698
0.137572
16.67014
1.77E-34
2.021246
2.56543152

The coefficient for the new capital expenses [2.2933] implies that the value for the end of year inventory is expected to increase by 2.2933 as a result of a unit increase in new capital expenses. The P-value for this coefficient (1.77E-34 is less than significance level (5%) and hence we conclude that the coefficient is statistically significant.
#### Multiple linear regression model.

####

*Regression Statistics*
Multiple R
0.82948959
R Square
0.68805297
Adjusted R Square
0.68336204
Standard Error
1559.78299
Observations
136
ANOVA
* *
*df*
*SS*
*MS*
*F*
*Significance F*
Regression
2
713708763.6
3.57E+08
146.6772
2.27183E-34
Residual
133
323578756.1
2432923
Total
135
1037287520
* *
*Coefficients*
*Standard Error*
*t Stat*
*P-value*
*Lower 95%*
*Upper 95%*
Intercept
751.017158
171.7189238
4.373526
2.45E-05
411.3637782
1090.670538
Cost of Materials
0.03286509
0.013760177
2.388421
0.018326
0.005647998
0.06008219
New Capital Expenses
1.85477276
0.22803722
8.13364
2.58E-13
1.403723969
2.305821546

The coefficient for the new capital expenses [1.8548] in the multiple linear model implies that the value for the end of year inventory is expected to increase by 1.8548 as a result of a unit increase in new capital expenses when Cost of materials is controlled or held constant. The P-value for this coefficient (2.58E-13) is less than significance level (5%) and hence we conclude that the coefficient is statistically significant in the model.

##### Percent of change observed

$\%change= 100 - \frac{model2}{model1}*100$

$=100- \frac{1.8548}{2.2933}*100$

=100-80.9

=19.1%

Since the percentage is larger than 10%, then Cost of Materials is a confounding variable.

The larger the t-value, the larger the differences between the groups under consideration. From the table above, New Capital Expenses has a larger t score and hence it is most significant.

* *
*Coefficients*
*Standard Error*
*t Stat*
*P-value*
Intercept
751.017158
171.7189238
4.373526
2.45E-05
Cost of Materials
0.03286509
0.013760177
2.388421
0.018326
New Capital Expenses
1.85477276
0.22803722
8.13364
2.58E-13

##### Prediction

End of year inventory =751.017158+0.03286509*Cost of Materials+1.854772768New Capital Expenses
End of year inventory =751.017158+0.03286509*725+1.854772768*1369
End of year inventory=3314.028268