Figure 1 : Multiple linear regression output
| SUMMARY OUTPUT | ||||||||
|
Regression Statistics |
||||||||
| Multiple R |
0.9882 |
|||||||
| R Square |
0.9766 |
|||||||
| Adjusted R Square |
0.9722 |
|||||||
| Standard Error |
0.7634 |
|||||||
| Observations |
20 |
|||||||
| ANOVA | ||||||||
|
df |
SS |
MS |
F |
Significance F |
||||
| Regression |
3 |
388.40 |
129.47 |
222.13 |
0.00 |
|||
| Residual |
16 |
9.33 |
0.58 |
|||||
| Total |
19 |
397.72 |
||||||
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
| Intercept |
11.2424 |
1.04 |
10.80 |
0.00 |
9.04 |
13.45 |
9.04 |
13.45 |
| Prep |
0.0608 |
0.08 |
0.80 |
0.43 |
-0.10 |
0.22 |
-0.10 |
0.22 |
| Delivery |
-0.0085 |
0.02 |
-0.53 |
0.60 |
-0.04 |
0.03 |
-0.04 |
0.03 |
| Distance |
1.0266 |
0.06 |
16.15 |
0.00 |
0.89 |
1.16 |
0.89 |
1.16 |
The regression equation is Cost = 11.2424 + 0.0608 (Prep) – 0.0085 (Delivery) + 1.0266 (Distance) (Figure 1).
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A slope of 0.0608 implies that a unit change in preparation time increases the cost by 0.0608, while all the other variables remain constant. The slope associated with delivery is -0.0085, meaning that a unit increase in delivery causes a 0.0085 decrease in cost while the other factors remain constant. The slope related to distance is 1.0266, meaning that a unit change in distance increases costs by 1.0266 while all the other factors remain constant. The y-intercept, 11.24, refers to the costs when preparation, delivery, and distance are equal to zero. It is possible to test the independent variables' significance in the multiple regression model using a t-test. A variable is considered significant if the p-value < level of significance, 0.05 (Camm et al., 2018). Preparation (t=0.80, p-value = 0.43) and delivery (t= -0.53, p-value =0.60) are insignificant because the p-value > 0.05. On the other hand, distance (t=16.15, p-value=0.00) is significant because the p-value < 0.05. The variance of a significant independent variable has a reasonable effect on the dependent variable's variance (Zikmund et al., 2013). Contrary, the variance of an insignificant independent variable does not have any reasonable effect on the dependent variable's variance (Camm et al., 2018). Variance in minutes to prepare and deliver therefore has a negligible impact on the cost variance, but distance has a reasonable impact on the cost variance.
The r-squared for the multiple linear regression model is 0.9766, meaning that the independent variables' variance explains 97.66% of the variance in cost. Based on the F-test (F=222.13, p-value= 0.00), we can conclude that the multiple linear regression's predictive power is significant.
The regression equation is: Cost = 11.2424 + 0.0608 (Prep) – 0.0085 (Delivery) + 1.0266 (Distance).
Substitute the variables:
Preparation = 10 minutes
Delivery = 30 minutes
Distance = 14 miles
Cost = 11.2424 + 0.0608 (10) – 0.0085 (30) + 1.0266 (14) = 25.9664
The delivery cost for a kit that takes 10 minutes to prepare, 30 minutes to deliver, and a distance of 14 miles is 25.9664.
References
Camm, J. D., Cochran, J. J., Fry, M. J., Ohlmann, J. W., and Anderson, D. R. (2018). Essentials of business analytics. Cengage Learning.
Zikmund, W. G., Carr, J. C., & Griffin, M. (2013). Business Research Methods. Cengage Learning
