Question

n for the state of Georgia. The PublicService Commission is a government agency responsible for ensuring that utility companies throughout the state manage their operations efficiently so that they can provide quality services to the public at fair prices. Georgia is the largest state east of the Mississippi River, and various communities and regions throughout the state have different companies that provide water, power, and phone service. These companies have a monopoly in the areas they serve and, therefore, could take unfair advantage of the public. One of nolan's jobs it to visit the companies and audit their financial records to detect whether or not any abuse is occuring. A major problem Nolan faces in his job is determining whether the expenses reported by the utility companies are reasonable. For example, when he reviews a financial report for a local phone company, he might see cable line maintenance costs of $1,345,948, and he needs to determine if this amount is responsible. This determination is complicated by the fact that the companies differ in size - so he cannot compare the costs of one company directly to another. Similarly, he cannot come up with a simple ratioo to determine costs (such as 2% for the ratio of line maintenance costs to total revenue) because a single ratio might not be appropriate for companies of different sizes.

To help solve this problem, Nolan wants you to build a regression model to estimate what level of line maintenance expense would be expected for companies of different sizes. One measure of size for a phone company is the number of customers it has. Nolan collected the data in the file PhoneService.xlsx representing the numeber of customers and line maintenance of 12 companies he audited in the past year and determined being run in a reasonably efficient manner.

What level of line maintenance expense would be expected for a phone company with 75,000 cutomers according to this new estimated regression 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

Answer 1

Quadratic equation represent the relationship between x and y is

y = 0.1543x² - 7.3922x + 707.47

For company with 75000 customers, x=75

y = 0.1543*75² - 7.3922*75 + 707.47 = 1,020.99

Therefore, level of line maint. expenses for the company would be = 1,020.99 ($1000s)