Question 4. The local utility company hypothesizes that fuel consumption (natural gas) in their town would be affected by temperature and chill index. The following data was collected for 10 weeks during the winter.
Week Fuel Consumption Y(MMcf) Average Temp
X1 (0F) Chill Index
X2
1 160 30.0 18
2 130 28.0 15
3 135 32.5 25
4 120 39.0 20
5 105 41.0 10
6 75 51.0 16
7 110 40.5 5
8
9
10 100
100
95 50.5
45.0
48.0 0
10
8
Conduct a Multiple Regression among Fuel consumption (Y), temperature (X1), and chill index (X2). Solve using excel. What is the multiple regression equation- show all estimated coefficients in the equation? Interpret the coefficients and predict the fuel consumption when temperature is 45 degrees, and the chill index is
8. Are the coefficients of the multiple regression model statistically significant at alpha = 0.05 and 0.01? How do you know- discuss the test statistics used to determine the significance of overall explanatory power?
Discuss indicating the individual test statistics and p-values and their meaning in terms of statistical significance of individual coefficients.
What are R2, adjusted R2 and se? Interpret R2 and Adjusted R2 and compare these values. Discuss the ANOVA table and conclude about the overall statistical significance of the model. Plot the errors and comment on the plot.
What would be the estimated error when observed value of Fuel consumption is 75 units when Average Temp is 510 and Chill Index 16.
By looking at the overall explanatory power and the statistical significance of the individual slope coefficients, do you suspect Multicollinearity? Why or why not?