Compass Maritime Services
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Based on the regression below, there appears to be a positive linear relationship between Profit and RD after the Risk of the project has been controlled. The estimated coefficient for RD from the regression is 4.51 and the confidence interval is (4.18, 4.84). This suggests that there is an increase in Profit of 4.51 units for every 1 unit increase in RD. The plot, Profit vs RD, also indicates there is a positive linear relationship.
The residuals vs fitted values plot appears to have a parabolic relationship as shown below.
This violates multiple regression assumptions. The additive errors are not:
Normally distributed
Independent from each other
Having constant variance
Plotting the Residuals vs Risk & RD clearly shows the violation in b) is related to RD. The Residual vs RD plot has the same parabolic relationship similar to b).
One suggestion for eliminating this violation is to take RD2, then re-run the regression with Risk, RD, and RD2. After re-running the regression and plotting the Residuals vs Fitted Values, the violation in b) is eliminated as shown in the plot below (i.e. there is constant variance between the residuals and fitted values).
The new model suggests that Profit goes up 23.3 units for every 1 unit of Risk and Profit goes up 1 unit for every 1 unit of RD.
The estimated value for the demand elasticity for orange juice is ϒ = -1.752. By taking the ln(Sales) and ln(Price) and running a regression I got the following formula:
ln(Sales) = 4.812 – 1.752*ln(Price)
Thus, when price goes up 1 unit, sales go down 1.752 units.
If the unit cost c = $1, the price that maximizes profits for the convenience store is $2.35. I arrived at this price by running a regression of ln(Sales) on ln(Price) which output the formula defined in a). I then generated a list of prices ranging from $1.00 to $3.50 in $0.05 increments. Using these prices and the formula in a), I was able to solve for Sales. I then found overall Profit by using the following formula:
Profit = (Price-Cost)*Sales
The graph of Total Profit vs Price is shown below. This graph shows that at a Price of $2.35, 27.5 units are sold for a Profit of $37.13.