Question

Method of Least Squares, Goodness of Fit Deepa Dalal opened a free-standing radiology clinic. She had anticipated that the costs for the radiological tests would be primarily fixed, but she found that costs increased with the number of tests performed. Costs for this service over the past nine months are as follows: Month January February March April May Radiology Tests 2,800 2,600 3,100 3,500 3,400 3,700 3,840 4,100 3,450 Total Cost $133,500 135,060 175,000 170,600 176,900 186,600 174,450 195,510 185,300 June July August September Required: + 1. Compute the cost formula for radiology services using the method of least squares. If required, round your answers to two decimal places. Yes 2. Using the formula computed in Requirement 1, what is the predlised cost of radiology services for October for 3,500 appointments? (Round the answer to the nearest dollar.)

Answer 1

Least Regression Analysis: Y 2,800 133,500 2,600 135,060 3,100 175,000 3,500 170,600 3,400 176,900 3,700 186,600 3,840 174,450 4,100 195,510 3,450 185,300 30,490 1,532,920 Regression equation is given by:- 7,840,000 6,760,000 9,610,000 12,250,000 11,560,000 13,690,000 14,745,600 16,810,000 11,902,500 105,168,100 xy 373,800,000 351,156,000 542,500,000 597,100,000 601,460,000 690,420,000 669,888,000 801,591,000 639,285,000 5,267,200,000 17,822,250,000 18,241,203,600 30,625,000,000 29,104,360,000 31,293,610,000 34,819,560,000 30,432,802,500 38,224,160,100 34,336,090,000 264,899,036,200 Y = a + bx 30,490 1,532,920 105,168,100 Exy 5,267,200,000 Calculating average variable cost per test: nExy - x. Sy n22 - 2x)" 9*5267200000 - 30490*1532920 9*105168100 - (30490 ) b = $ 39.48 Calculating approximate total fixed cost: Ey-bx b 1532920 - 39.48*30490 9 36,575 1 Cost function is given by:- y = 36575 + 39.48X 2 Cost of 3500 appointments Total Cost = 36575+ (39.48*3500) = 36575 + 138180 = $ 174,755

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