Use the following Excel regression output to answer the next 5 questions. The ou

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Use the following Excel regression output to answer the next 5 questions. The output shows the result of running a regression relating costs to production volume. Fill in the highlighted cells first. SUMMARY OUTPUT Regression Statistics Multiple R 0.9877 R Square Adjusted R Square 0.9695 Standard Error Observations 6 ANOVA df SS MS F Signif F Regression 1 160.071587 2.25E-04 Residual 184775.04 Total 5 7579083.33 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 617.662 428.31 1.442 0.2227 -571.51 1806.84 X Variable 1 8.755 0.0002 6) The percentage of the variations in cost explained by production volume is: A 97.6% B 93.0% C 90.3% D 87.7% 7) The predicted total cost when production volume is 1,000 is, A 8,581 B 8,827 C 9,373 D 9,670 8) Given that the sum of the squared deviations of production volume is 96,470.83, the standard error of the slope coefficient is A 1.280 B 1.084 C 0.888 D 0.692 9) The lower end of the 95% confidence interval for the slope coefficient is A 5.16 B 6.83 C 8.98 D 9.49 10) The value of the t Stat for the slope coefficient is A 12.65 B 10.17 C 7.69 D 5.21 Use the following Excel regression output to answer the next 5 questions. The output shows the result of running a regression relating costs to production volume. Fill in the highlighted cells first. SUMMARY OUTPUT Regression Statistics Multiple R 0.9877 R Square Adjusted R Square 0.9695 Standard Error Observations 6 ANOVA df SS MS F Signif F Regression 1 160.071587 2.25E-04 Residual 184775.04 Total 5 7579083.33 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 617.662 428.31 1.442 0.2227 -571.51 1806.84 X Variable 1 8.755 0.0002 6) The percentage of the variations in cost explained by production volume is: A 97.6% B 93.0% C 90.3% D 87.7% 7) The predicted total cost when production volume is 1,000 is, A 8,581 B 8,827 C 9,373 D 9,670 8) Given that the sum of the squared deviations of production volume is 96,470.83, the standard error of the slope coefficient is A 1.280 B 1.084 C 0.888 D 0.692 9) The lower end of the 95% confidence interval for the slope coefficient is A 5.16 B 6.83 C 8.98 D 9.49 10) The value of the t Stat for the slope coefficient is A 12.65 B 10.17 C 7.69 D 5.21

Explanation / Answer

6)The percentage of the variations in cost explained by production volume is given by R2

R2 = square of Multiple R = (0.9877)2 =0.9755 = 97.6%

Ans) A 97.6

7) The equation is: Cost = 617.662 + 8.755*Volume
For volume = 1000,
Cost = 617.662 + 8.755*1000 = 9373

Ans) C 9,373

8) SE of the slope = sqrt [ ?(yi - ?i)2 / (n - 2) ] / sqrt [ ?(xi - x)2 ]

From the output we have ?(yi - ?i)2 = SS Residual = 184775.04

And given squared deviations of production volume =?(xi - x)2 = 96,470.83

n = 6

Std Error = sqrt [ 184775.04 / (6 - 2) ] / sqrt [ 96470.83 ] = 0.6919 = 0.692

Ans) D 0.692

9) The lower end confidence interval = sample statistic - margin of error

Sample Statistic = slope coefficient = 8.755

Critical value for t at 95% confidence and Degrees of Freedom n -2 ( 6 - 2 =4) is

Std error = 0.692

Margin of Error = Critical value for t*Std Error = 2.776 * 0.692 = 1.92

The lower end confidence interval = sample statistic - margin of error = 8.755 - 1.92 = 6.83

Ans) B 6.83

10) t stat = coefficient of slope/std error = 8.755/0.692 = 12.651

Ans) A 12.65

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