Question

Nolan Banks is an auditor for the Public Service Commission 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.

In your spreadsheet, calculate the estimated line maintenance expense that would be predicted by the quadratic regression function for each company in the sample. Plot these values on your graph (connected with a line) along with the original data and the original regression line.

(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

Solution-

In order to do quadratic regression in excel, you have to calculate X^2 values side by side to X values and then enter both the columns in the X column value in the regression field as shown below-

We get the following result from Regression-

From this output, we get the equation (looking at the value of Coefficients) as follows-

Y = 0.154 X^2 - 7.39 X + 707.4747

If you put X = 75, you get Y = 1019.475

However If we use linear regression, the equation fits better than quadratic equation.

Linear regression equation comes out to be-

y = 14.94x + 11.793

For x = 75, Y comes out to be 1132.29 which is more accurate.