Nolan Banks is an auditor for the Public Service Commission for thestate of Georgia. The PublicService Commission is a governmentagency responsible for ensuring that utility companies throughoutthe state manage their operations efficiently so that they canprovide quality services to the public at fair prices. Georgia isthe largest state east of the Mississippi River, and variouscommunities and regions throughout the state have differentcompanies that provide water, power, and phone service. Thesecompanies have a monopoly in the areas they serve and, therefore,could take unfair advantage of the public. One of nolan's jobs itto visit the companies and audit their financial records to detectwhether or not any abuse is occuring. A major problem Nolan facesin his job is determining whether the expenses reported by theutility companies are reasonable. For example, when he reviews afinancial report for a local phone company, he might see cable linemaintenance costs of $1,345,948, and he needs to determine if thisamount is responsible. This determination is complicated by thefact that the companies differ in size - so he cannot compare thecosts of one company directly to another. Similarly, he cannot comeup with a simple ratioo to determine costs (such as 2% for theratio of line maintenance costs to total revenue) because a singleratio might not be appropriate for companies of differentsizes.

To help solve this problem, Nolan wants you to build a regressionmodel to estimate what level of line maintenance expense would beexpected for companies of different sizes. One measure of size fora phone company is the number of customers it has. Nolan collectedthe data in the file PhoneService.xlsx representing the numeber ofcustomers and line maintenance of 12 companies he audited in thepast year and determined being run in a reasonably efficientmanner.

What level of line maintenance expense would be expected for aphone company with 75,000 cutomers according to this new estimatedregression function? Show how you arrive at the value.

(Y=b₀+b₁x₁+b₂x^2/1)

X	Y	XY	X sq	Forecast Y
Customers (in 1000s)	Line Maint. Expense(in $1000s)
25.3	484.6	12260.38	640.09	413.00
36.4	672.3	24471.72	1324.96	579.80
37.9	839.4	31813.26	1436.41	602.30
45.9	694.9	31895.91	2106.81	722.50
53.4	836.4	44663.76	2851.56	835.10
66.8	681.9	45550.92	4462.24	1036.40
78.4	1,037.0	81300.8	6146.56	1210.60
82.6	1,095.6	90496.56	6822.76	1273.70
93.8	1,563.1	146618.78	8798.44	1441.90
97.5	1,377.9	134345.25	9506.25	1497.50
105.7	1,711.7	180926.69	11172.49	1620.70
124.3	2,138.6	265827.98	15450.49	1900.00