Quantitative Techniques in Regulation in Practice Laboratory 4

Quantitative Techniques for Regulation in Practice:

Laboratory 4: Multicollinearityand Electricity

Introduction

The purposeof this lab is to:

1. Remind you about eyeballing the data.

2. Introduce the idea of regression analysis for assessing comparative efficiency

3. Show the effect of collinearity on t and F statistics

4. See the effect of different equation specifications

The data

The data can be downloaded from the website as Lab4ElectricityDistributionpseudo-data2.xls.

Electricity distribution entails:

  • Transporting electricity from a grid supply point to the final consumer
  • Converting it in stages to the right voltage
  • Control of the distribution system.

Costs depend on, other things equal:

  • the maximum energy required (“peak load”) at each point on the system
  • the layout of the system –determined by the location and size of (current and past) customers

Nearby customers cost less than distant customers

Customers with large demands cost less per megawatt (or MWh) than small customers especially if they are on high voltage supplies.

The first Excel file

1. Look at the distribution of each of the variables. Do any of the variables have significant outliers? Look at the scatter diagram between overhead circuit length and the number of customers? Which companies would you want to ask particular questions about?

2. Which variables are particularly correlated with each other? Why do you suppose that underground cables are more correlated with customers than overhead cables?

3. From casual inspection of appropriate variables, is there any evidence of economies of scale?

Eviews

4. Get the file ready for reading into Eviews. How many variables are there?

5. Regress costs separately on:

a)Underground circuits

b)Number of customers

c)Total gigawatt hours

Note the t, F statistics and adjusted R2

6. Now regress all three together with costs as the dependent variable.

  1. Look at the t statistics and F test. Comment.
  1. Play around with the data, and see what your best model of the costs of electricity distribution would be for these data. Try quadratic functions, log-log, new variables including measures of density, etc. Why do you suppose area does not seem to matter in most formulations?
  1. Focus on a particular company. Does its residual change by much as you move from model to model?

The CityUniversity1

Quantitative Techniques in Regulation in Practice Laboratory 4

Lines / Transformers / Energy
Company i.d. / “Cost” / Customers ‘000 / Over / Under / Total / Number / Capacity / Low
voltage / High
Voltage / Total
Energy / Area
£million / head / ground
Company / Cost / Nocust / O/Hcirc / U/Gcirc / Totcirc / Transnum / Transcap / LVGwH / HVGwH / TotGwH / Area
1 / 176.0 / 3090 / 35,355 / 51,123 / 86,478 / 61,246 / 12,975 / 21,366 / 6,662 / 28,028 / 20300
2 / 134.9 / 2200 / 26,237 / 40,453 / 66,690 / 38,102 / 31,147 / 13,469 / 9,471 / 22,940 / 16000
3 / 122.7 / 1940 / 52 / 29,629 / 29,681 / 13,309 / 19,430 / 15,644 / 3,481 / 19,125 / 665
4 / 107.6 / 1320 / 21,179 / 22,630 / 43,809 / 40,635 / 16,536 / 8,604 / 4,310 / 12,914 / 12200
5 / 140.8 / 2160 / 27,302 / 36,566 / 63,868 / 47,742 / 24,765 / 13,505 / 8,655 / 22,160 / 13300
6 / 100.3 / 1430 / 17,306 / 23,033 / 40,339 / 22,598 / 12,474 / 8,435 / 3,348 / 11,783 / 14400
7 / 129.7 / 2130 / 15,653 / 43,592 / 59,245 / 31,160 / 29,879 / 13,248 / 7,118 / 20,366 / 12500
8 / 137.2 / 1950 / 12,166 / 31,205 / 43,371 / 30,975 / 23,838 / 13,548 / 2,985 / 16,533 / 8200
9 / 157.5 / 2530 / 28,917 / 42,031 / 70,948 / 52,026 / 37,746 / 17,850 / 6,506 / 24,356 / 16900
10 / 88.5 / 940 / 18,788 / 12,883 / 31,671 / 38,697 / 11,534 / 5,547 / 2,068 / 7,615 / 11800
11 / 115.6 / 1270 / 29,018 / 17,890 / 46,908 / 48,309 / 19,272 / 9,123 / 2,732 / 11,855 / 14400
12 / 126.6 / 2000 / 15,233 / 37,480 / 52,713 / 30,773 / 30,955 / 11,946 / 7,743 / 19,689 / 10700
13 / 63.2 / 600 / 32,808 / 11,923 / 44,731 / 46,252 / 9,884 / 5,829 / 1,355 / 7,184 / 54390
14 / 111.6 / 1750 / 24,405 / 37,174 / 61,579 / 38,220 / 22,552 / 14,343 / 4,791 / 19,134 / 22950
15 / 90.3 / 644 / 29,670 / 9,959 / 39,629 / 63,342 / 9,961 / 4,897 / 1,632 / 6529 / 14122

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