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 Radiology Tests Total Cost

January $2,800$ $$133,500$

February $2,600135,060$

March $3,100175,000$

April $3,500170,600$

May $3,400176,900$

June $3,700186,600$

July $3,840174,450$

August $4,100195,510$

September $3,450185,300$

Required:

$1.$ Compute the cost formula for radiology services using the method of least squares. If required, round your answers to two decimal places.

Y $=$ $fill in the blank $1$

$+$ $fill in the blank $2$

X

$2.$ Using the formula computed in Requirement $1,$ what is the predicted cost of radiology services for October for $3,500$ appointments? $($Round the answer to the nearest dollar.$)$