Question

I NEED THE ANSWER OF PART (F) (G) (H) (I), THANKS

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:

cons 6o + 61size; E Where: cons is annual electricity consumption measured in megawatt hours for store i; size; is the size of store i measured in square meter; ε¡ is the disturbance term; and 60 and 61 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 Coefficients Standard Error t Stat 860.2 0.672 P-value 0.0003 0.0000 Intercept 210.0 size 7.305 (a) What does the regression estimate for B1 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 B1 provided in Table 1? Test the null hypothesis that ß1-0 against the alternative that ß1#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 (%) 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 B1 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 B1 reported in Table 1?

Answer 1

ANSWER:

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: cons 6o + 61size; E Where: cons is annual electricity consumption measured in megawatt hours for store i; size; is the size of store i measured in square meter; ε¡ is the disturbance term; and 60 and 61 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 Coefficients Standard Error t Stat 860.2 0.672 P-value 0.0003 0.0000 Intercept 210.0 size 7.305 (a) What does the regression estimate for B1 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 B1 provided in Table 1? Test the null hypothesis that ß1-0 against the alternative that ß1#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 (%) 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 B1 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 B1 reported.

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  (a) The regressi on estimate for 0.672 This is sample covari ance between consumption and size Coefficient of Intercept 860.2 Stan dard error of Intercept 210.0 Coefficient of Size 0.672 (b) The t Stat (A)- an dard eror (BStat of Size 7.305 4 0.09199 (c) The regression estimate for 0.672 Therefore, for every unit electricity consumption the store size will increases by 0.672 times The test statistic for t Stat is, 7.305, and the p - value is 0.0000 Decision rule P- value approach: We reject our null hypothesis, Ho , when p-value α Let the level of significance will be, -0.05 Here, the p-value 0.0000, this is smaller than the significance level at 0.05 Thus, we reject our null hypothesis, H0 Therefore, there is sufficient evi dence that there is significant effect exists between Consumption and store size, at 5% level of significance

  

  we know that a 100 (1-α) % confidence interval for the slope of the true regression line, A is defined as wheres n- 2 From the above output wehave = 0.672 and s = 0.09 199 Therefore the 90% confidence interval for the slope of the true regression line, A is defined as At 0.10/230-2 = 0.672±t005 ,28 (0.09199) =0.672 ±2.0484(0.09199) = 0.67 2 ± 0.1 8844 (0.48356 0.86044)

• e ) p value in simple terms means the evidence that the data suggests in favor of the null hypothesis.

  p values are usuallu used in conjunction with hypothesis test

  here in this case of intercept , it means

  H0 : The intercept is not significant

  H1 : The intercept is significant

  so at an alpha =0.05 , we can say that the test is significant and hence intercept is significant , as p value 0.003 is less than 0.05

  

  e) Thep - value is the probability of finding the observed, or more extreme, results when the null hypothesis (Ho) of a study question is true. f) The forecast for the electricity consumption of such a store For X 2200 The adequate regression analyis is, 860.2+0.672X 860.2+0.672 (2200) - 2338.6

• g) It means that the B1 coefficient is significant in explaining the model variation

  h) as the R2 value is 0.809 , it means that the model is able to explain 81% of the variability , also both the variables are signifcant as the p value is less than 0.05 , so overall the model quality is good enough