Question

provide a brief explanation for each chart below. Determine  whether a statistically reliable oil consumption model can be estimated based on the regression analysis charts below

Dupree Fuels Company is facing a difficult problem. Dupree sells heating oil to residential customers. Given the amount of competition in the industry, both from other home heating oil suppliers and from electric and natural gas utilities, the price of the oil supplied and the level of service are critical in determining a company’s success. Unlike electric and natural gas customers, 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. In fact, Dupree’s service pledge is, “50 free gallons on us if we let you run dry.” Beyond the cost of the oil, however, Dupree is concerned about the perceived reliability of his service if a customer is allowed to run out of oil. To estimate customer oil use, the home heating oil industry uses the concept of a degree-day, equal to the difference between the average daily temperature and 68 degrees 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 consumption 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. Dupree has used this scheme in the past but is disappointed with the results and the computational burdens it places on the company. First, the system requires that a consumption-per-degree-day figure be estimated for each customer to reflect that customer’s consumption habits, size of home, quality of home insulation, and family size. Because Dupree has more than 1500 customers, the computational burden of keeping track of all of these customers is enormous. Second, the system is crude and unreliable. The consumption per degree-day for each customer is computed by dividing the oil consumption during the preceding year by the degree-days during the preceding year. Customers have tended to use less fuel than estimated during the colder months and more fuel than estimated during the warmer months. This means that Dupree is making more deliveries than necessary during the colder months and customers are running out of oil during the warmer months. Dupree wants to develop a consumption estimation model that is practical and more reliable. The following data are available in the file

Variables Entered/Removeda
Model	Variables Entered	Variables Removed	Method
1	Number People, Home Index, Degree Days, Customerb	.	Enter
a. Dependent Variable: Oil Usage
b. All requested variables entered.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.889a	.790	.766	85.445
a. Predictors: (Constant), Number People, Home Index, Degree Days, Customer

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	962180.237	4	240545.059	32.948	.000b
	Residual	255527.663	35	7300.790
	Total	1217707.900	39
a. Dependent Variable: Oil Usage
b. Predictors: (Constant), Number People, Home Index, Degree Days, Customer

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	-261.897	77.152		-3.395	.002
	Customer	1.242	1.231	.082	1.010	.320
	Degree Days	.282	.037	.609	7.625	.000
	Home Index	89.407	9.921	.722	9.012	.000
	Number People	6.850	10.675	.051	.642	.525
a. Dependent Variable: Oil Usage

Answer 1

R-squared of the model = 0.790 Which represents that 79.0% of the varaibility in Oil usage has been explained by the predictor variables.

The ANOVA results shows that p-value =0 which is less than the level of significnce 0.05 hence we reject null hypothesis and conclude that there is significant linear relationship exists between the data.

The model is Oil Usage = -261.897 + 1.242 Coustmer + .282 Degree days + 89.407 Home index + 6.850 Number of people.

Here in this model we see that the variables Coustmer and Number of people are not statistically significant since its p-values are more than 0.05. Hence we can now remove this variables and rerun the regression analysis for better conclusion.