Question

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow: Month Machine Hours Electricity Costs January 3,000 $ 18,650 February 3,400 $ 21,500 March 2,400 $ 13,750 April 3,600 $ 23,500 May 4,300 $ 28,500 June 3,800 $ 22,500 July 4,600 $ 25,000 August 4,000 $ 23,000 September 2,500 $ 16,000 October 4,200 $ 26,500 November 5,600 $ 31,500 December 5,200 $ 28,000 Summary Output Regression Statistics Multiple R 0.952 R Square 0.906 Adjusted R2 0.897 Standard Error 1,676.51 Observations 12.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3,639.33 2,048.60 1.78 0.11 (925.25) 8,203.90 Machine Hours 5.04 0.51 9.83 0.00 3.89 6.18 Based on the results of the regression analysis, the estimate of electricity costs in a month with 2,700 machine hours would be: (Round to the nearest whole dollar. Your answer may be different by a few dollars due to rounding of the regression coefficients. Choose the answer closest to your calculation.)

Answer 1

we have given output of the regression model : y on x

here y is dependent variable is : Electicity cost and

x is independent variable is : month hours

Based on the results of the regression analysis, the estimate of electricity costs in a month with 2,700 machine hours would be:

yhat = bo + b1* x

here bo is intercept is : 3639.33

and slope is = 5.04

yhat = 3639.33 + ( 5.04* x)

ie Electricity cost = 3639.33 + ( 5.04* month hours)

we have to estimate y when x is 2700

yhat = 3639.33 + ( 5.04* 2700)

yhat = 17247.33

that is approximately $ 17247 electricity cost .

check output :