Question

The Municipality of a city wants to estimate the daily expenditure of the fuel consumption for city’s garbage removal.

The city contains a business part and a residential part. City officers believe that, the amount of the fuel Y (in thousands of liters) depends on the weight of the garbage (in Tons) in the two parts of city x1 and x2. A random sample is collected for six days and the data was as follows:

                    y           x1             x2

1.4	255	2500
0.9	178	2250
1.8	263	2900
0.7	127	1800
2.6	305	3200
1.2	164	2400
2.1	245	2700
1.1	146	2050
2.8	287	2850
1.6	189	2600
1.7	211	2300
0.5	123	1700

a)     Fit a regression model and write the regression equation

b)    Is the model valid?

c)     Which independent variables are linearly related to Y?

d)    What are the assumptions for the regression model?

e)     How is the fit of the model?

f)     For a given day, if the weight of the garbage from the two parts of the city are 300 and 2500 tons

respectively, predict the amount of fuel that will be consumed on that day. Predict with 95% the fuel consumption for that day?

             Your Case Study must contain each of the following:

1.     Write an introduction about the problem. This introduction must contain what needs to be done, and the steps you need take in doing this problem,

2.     Conduct an analysis about your findings,

3.     Write the conclusion about your findings.

Answer 1

SOLUTION

Running the above example in R we get;

a)Regression equation:y=-1.2973450+(0.0061661)x1+(0.0006358)x2

b)Yes the model is valid because we are accessing the impact of garbage from the two cities(x1 and x2) on fuel.

c)Both weight of garbage from city 1 (x1) and weight of garbage from city 2 (x2) is linearly dependent of amount of fuel with correlations 0.908243 and 0.8980353 respectively.

d)Assumption of regression model

1. Linear relationship between dependent variable y and independent variables x1 and x2
2. Multivariate normality :the independent variables follow normal distribution
3. No or little multicollinearity: There is no multicollinearity between independent variables
4. No auto-correlation: the value of y(x+1) is independent from the value of y(x).
5. Homoscedasticity: The error terms(residuals)are independent.