Nolan Banks is an auditor for the Public Service Commission for the state of Geo

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.

Use regression to estimate to estimate the parameters for the following quadratic equation for the data:

Y = b0 + b1X1 + b2X2/1

To do this, you must insert a new column in your spreadsheet next to the original X values. In this new column, calculate the values X2/1. What is the new estimated regression equation for this model and interpret the value for R2 obtained using the equation above and what is the value for the adjusted-R2 statistic? What does the statistic tell you?

Customers (in 1000s) Line Maint. Expense (in $1000s) 25.3 484.6 36.4 672.3 37.9 839.4 45.9 694.9 53.4 836.4 66.8 681.9 78.4 1,037.0 82.6 1,095.6 93.8 1,563.1 97.5 1,377.9 105.7 1,711.7 124.3 2,138.6

Explanation / Answer

The calculations are done through excel

Steps

Here intercept gives you the b0 value and the two coefficients of X1 and X12 tells you the value of b1 and b2

so the equation will be

Y = 707.47+(-7.39)X1+0.154X12

R square value = 0.9416

Adjusted R square = 0.92

The statistic tells us that when the customer no increases the value of maintenance cost should decrease as there is a negative coefficient for X1 and when we take a square of customer number the coefficient is little positive i.e. 0.15

So it shows us that with the increase of consumers the maintenance cost should decrease

R square tells us that how close the data are fitted to the regression line or what percentage of data shows the variability of our predictor. The high value of Rsquare tells that the data is well fitted.

Customers (in 1000s)(X1) (X1)^2 Line Maint. Expense (in $1000s) 25.3 640.09 484.6 36.4 1324.96 672.3 37.9 1436.41 839.4 45.9 2106.81 694.9 53.4 2851.56 836.4 66.8 4462.24 681.9 78.4 6146.56 1,037.00 82.6 6822.76 1,095.60 93.8 8798.44 1,563.10 97.5 9506.25 1,377.90 105.7 11172.49 1,711.70 124.3 15450.49 2,138.60

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