Question

The Australian Government’s Energy Efficiency Opportunities program encourages large energy using businesses to improve their energy efficiency. It does this by requiring businesses to identify, evaluate and report publicly on cost effective energy savings opportunities. As part of the process of identifying factors impacting on electricity consumption, a large super market chain took a sample of 30 stores and investigated the relationship between electricity consumption and store size. Consider the simple regression model: consi = β0 + β1sizei +εi

Where: consi is annual electricity consumption measured in megawatt hours for store i; sizei is the size of store i measured in square meter; εi is the disturbance term; and β0 and β1 are unknown parameters. The regression model was estimated by ordinary least squares and an extract of the resultant EXCEL output is reproduced below:

Table 1: EXCEL output for the simple linear regression of consumption on size Regression Statistics R Square Standard Error Observations 0.809 329.2 30 P-value 0.0003 0.0000 Coefficients Standard Error t Stat 210.0 860.2 0.672 Intercept size 7.305

(a) What does the regression estimate for β1 provided in Table 1 imply about the sample covariance between consumption and size? Is this result what you would expect? Why?

(b) The t Stat for the estimated intercept (A) and the Standard Error for the estimated coefficient for size (B) are missing. Determine their values.

(c) How would you interpret the regression estimate for β1 provided in Table 1? Test the null hypothesis that β1=0 against the alternative that β1≠0 using the results of the EXCEL output, explain your answer and be specific of any assumption made.

(d) Construct a 90% confidence interval for the coefficient on size (β1) and interpret the result.

(e) Explain the meaning of ‘P-value” in the output and interpret the calculated “P-value” reported for the intercept.

(f) Consider a store that is 2200 square meters which is the sample average. What is the forecast for the electricity consumption of such a store?

(g) What does it mean to say the least square estimate of β1 is unbiased?

(h) Briefly comment on the quality of the fit.

(i) Give an example of another variable that might impact on store electricity consumption and hence should be in the regression model. Does the existence of such variables have implications for the ordinary least square estimate of β1 reported in Table 1?

Answer 1

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