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Introduction
Management of a soft-drink company wants to develop a method for assigning delivery costs to customers. The company selected 20 customers from their sales territory and delivery time in minutes and the number of cases delivered were recorded in a data set. I will develop a regression model to help assign delivery costs by calculating unloading time based on the number of cases delivered to the customer.
As one can interpret from the graph above, the higher number of cases of soft-drinks results in a longer delivery time. This is a positive relation
Regression Analysis: Delivery Time versus Number of cases
The regression equation is
Delivery Time = 24.8 + 0.140 Number of cases
Predictor Coef SE Coef T P
Constant 24.835 1.054 23.56 0.000
Number of cases 0.140026 0.005627 24.88 0.000
S = 1.98650 R-Sq = 97.2% R-Sq(adj) = 97.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 2443.5 2443.5 619.20 0.000
Residual Error 18 71.0 3.9
Total 19 2514.5
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI 1 52.840 0.475 (51.841, 53.839) (48.548, 57.131)
Values of Predictors for New Observations
Number
New Obs of cases 1 200
Regression Equation
The regression equation is
Delivery Time = 24.8 + 0.140 Number of cases 24.8 is (the y intercept of the estimated regression line) 24.8 is the average estimated amount of delivery time when number of cases is 0.
0.140 is ( the slope of the estimated regression line) As number of cases increases by 1 then the average amount of delivery time should increase by .140.
Coefficient of Determination The coefficient of determination is R-Sq = 97.2%. This tells us that 97.2% of the delivery time is being explained by variation in number of cases delivered.
Delivery time of 200 cases
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI 1 52.840 0.475 (51.841, 53.839) (48.548, 57.131)
Values of Predictors for New Observations
Number
New Obs of cases 1 200
The result of delivery 200 cases of soft drink is a delivery time of 52.840. We can also be confident that the delivery time will be between 51.841 and 53.839.
500 cases?
We should not use this model to predict the delivery time for a customer receiving 500 cases because 500 is outside the range of our data set.
Hypothesis Testing
The null hypothesis tested is
H0: There is no significant linear correlation between delivery time and the number of cases delivered. (ρ = 0)
The alternative hypothesis is
