7. (13 pts) These data were obtained from a sample of counties in southwestern P

Question

7. (13 pts) These data were obtained from a sample of counties in southwestern Pennsylvania and indicate that number (in thousands) of tons of bituminous coal produced in each county and the number of employees working in coal production in each county Data No. of employees x Tonsy 110 227 731 1031 20 5410 5328 147 118 1162 103 729 8095 635 752 6157 Summary RSauare RSquare Adi Root Mean Square Error Mean of Response Observations (or Sum Wats) Source OF Mean Squar F Ratio Sum of Squares 1 68438806 4364108 68438806 94.0932 27351.32 Prob> F Model Error C. Total Term Intercept Employee 6.7034684 0.691068 772802914 .0001 Estimate Std Error tRatio Probe-It] 0.9446 9.70 0001* 33.35841 460.3583 0.07 a. (6pts) Fill in the 2 blacked out entries in the output table (2pts) Eind a quantity that measures the strength of the linear relationship between the two variables h. c. (3pts) Write down the fitted equation. d. (2pts) Predict the amount of coal produced for a county that has 500 employees

Explanation / Answer

a

The rsquare value is calculated as

SSmodel/SStotal = 68438806/72802914 = 0.9400

b

The rmse is calculated as
sqrt(ms error) = sqrt(727351.32) = 852.84

c

The fitted equation is written using the coefficients as

amount = -33.35 +6.703*Employee

d

here employee = 500
so the amount of coal produced is
amount = -33.35 +6.703*500 = 3318.15

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