Consider the following data for the average cost of various fuels and electricit

Question

Consider the following data for the average cost of various fuels and electricity for a twelve year period. The data measure the following: Your model will attempt to predict residential electricity costs using the cost of the other fuels. State whether you would expect a positive or negative relationship between electricity costs and each of the independent variables and explain why. Use EXCEL, to create a correlation using all independent variables provided. Discuss all aspects of the correlation matrix, as it compares to your expectations in nd what it tells you about the potential results of a regression analysis. Use EXCEL to run a multiple regression to estimate electricity costs using all independent variables provided. Test if the overall regression is significant at the 5% level. Test for the significance of each slope coefficient at the 5% level. (Incorporate all tests into ONE five step answer as in the slides.) Based on your correlation matrix and the results of your regression do you suspect multicollinearity If yes, which independent variable (s) to you think could be responsible Explain how you test for multicollinearity but do not test. How could you rerun the regression taking into account the issues in the first regression Which variable or variables would you keep as an explanatory variable (s), and why

Explanation / Answer

a)

Expect a positive relation between electricity and the given fuels as they act as a source of power generation: complementary relationship exits. When cost of fuels rises, cost of electricity increases

b)

The correlation coefficient matrix is shown below:

Column 1

Column 2

Column 3

Column 4

Column 1

1

Column 2

0.96411

1

Column 3

0.680018

0.715173

1

Column 4

0.497928

0.570268

0.471422

1

An investigation in the matrix suggests that the cost of natural gas is highly correlated with cost of producing electricity (0.94) when it is the only fuel available. But as other fuels are available, the cost decreases.

c)

Regression analysis results in:

d)

Analyse the following table:

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1.93

0.54

3.56

0.01

0.68

3.19

0.68

3.19

X Variable 1

1.05

0.15

7.20

0.00

0.71

1.38

0.71

1.38

X Variable 2

-0.04

0.62

-0.07

0.94

-1.47

1.38

-1.47

1.38

X Variable 3

-0.73

1.08

-0.68

0.52

-3.21

1.75

-3.21

1.75

If the absolute value of the t-statistic is greater than or equal to 2, then the corresponding parameter estimate is statistically different from zero. Given the values of t-statistic for intercept and cost of natural gas, the absolute values of t-statistic for intercept and natural gas are greater than 2.

Hence the estimated coefficient of the intercept and natural gas are statistically different from zero.

The F-statistic has a value of 37.5 which is high enough. The significance value for this regression is 0.00. This implies that there is 0 percent chance that the estimated regression model fits the data purely by accident. The regression is thus highly significant.

Column 1

Column 2

Column 3

Column 4

Column 1

1

Column 2

0.96411

1

Column 3

0.680018

0.715173

1

Column 4

0.497928

0.570268

0.471422

1

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.