SmithFuel sells heating oil to residential customers and would like to build a model to predict its customer's oil consumption.

Oil customers are exposed to the risk of running out of fuel. Home heating oil suppliers therefore have to guarantee that the customer's oil tank will not be allowed to run dry. Home heating oil industry try uses the concept of a degree-day, equal to the difference between the average daily temperature and 68 degree Fahrenheit. So if the average temperature on a given day is 50, the degree-days for that day will be 18. If the degree-day calculation results in a negative number, the degree-day number is recorded as 0.

By keeping track of the number of degree-days since the customer's last oil fill, knowing the size of the customer's oil tank, and estimating the customer's oil consumptions as a function of the number of degree-days, the oil supplier can estimate when the customer is getting low on fuel and then resupply the customer. However, SmithFuel has more than 2000 customers and computational burden of keeping track of all of these customers is enormous.

SmithFuel wants to develop a consumption estimation model that is practical and reliable.

The file 'Oil usage.xlsx Download Oil usage.xlsxDownload Oil usage.xlsx' contains recent oil usage of 40 customers recent with the following variables:

OilUsage: The oil consumption amounts in gallons for 40 customers.

DegreeDays: The number of degree-days since the last oil fill for 40 customers.

HomeFactor: An assessment of the home type of each of the 40 customers (levels={1,2,3,4,5}).

NumberPeople: The number of people residing in the home of each of the 40 customers.

Use StatTools to conduct the statistical analysis asked below. For questions that ask for an oil usage (or change in oil usage), use two decimal places in your final numerical answer.

Part A - Linear Regression

Create a regression model for OilUsage using all three variables (Degree Days, Home Factor, Number People) as the independent variables. Let us call this Model A. Also, create the scatter plot of fit vs. OilUsage and the residual plot when you generate the regression output.

1. Include the StatTools regression output as Exhibit A. Copy and paste the regression output, and the plots. Write out the estimated regression equation (copy and paste the equation from StatTools report).

2. Provide an economic interpretation of the coefficient of NumberPeople.

Model B - Adding Categorical Variables

Model A treats the HomeFactor variable as a numerical variable. Build a model, which treats the HomeFactor variable as a categorical variable. Let us refer to this model as Model B. Create the scatter plot of fit vs. OilUsage and the residual plot.

1. Include the StatTools regression output as Exhibit B. Copy and paste the regression output, and the plots. Write out the estimated regression equation (copy and paste the equation from StatTools report).

2. Provide an economic interpretation of the coefficient of (HomeFactor level = 5).

3. According to Model B estimated above, by how much higher/lower is the average oil consumption of customers in HomeFactor level 2 compared to the average oil consumption of customers in HomeFactor level 4, when DegreeDays and NumberPeople remain the same?

4. Provide an economic interpretation of the coefficient of DegreeDays.

5. Compare the performance of two models (Model A and Model B). Explain why or why not use dummies for HomeFactor instead of the variable itself?

Part C - Adding Interactions

Next, suppose it is conjectured that the DegreeDays varies by HomeFactor. To account for this conjecture, we augment Model B with interaction terms between DegreeDays and HomeFactor. Let us call this model Model C. Create the scatter plot of fit vs. OilUsage and the residual plot.

1. Include the StatTools regression output as Exhibit C. Copy and paste the regression output, and the plots. Write out the estimated regression equation (copy and paste the equation from StatTools report).

2. According to Model C estimated above, by how much higher/lower is the average oil consumption of customers in HomeFactor level 2 compared to the average oil consumption of customers in HomeFactor level 4 when DegreeDays = 1000 and NumberPeople is the same?

3. Estimate the oil consumption of a customer with DegreeDays =380, NumberPeople =4, HomeFactor = 1

LINK to oil data: https://docs.google.com/spreadsheets/d/1L80oLdLZ7r9OnCJPMoi08j6Gi_gHRMR-/edit?usp=share_link&ouid=110469295481558893940&rtpof=true&sd=true