Regression Analysis

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Regression Analysis

Basic Concepts & Methodology

1. Introduction

Regression analysis is by far the most popular technique in business and economics for seeking to explain variations in some quantity in terms of variations in other quantities, or to develop forecasts of the future based on data from the past. For example, suppose we are interested in the monthly sales of retail outlets across the UK. An initial data analysis would summarise the variability in terms of a mean and standard deviation, but the variation from outlet to outlet could be very large for a variety of reasons. The size of the local market, the size of the shop, the level of competition, the level of advertising, etc.. would all influence the sales volume from outlet to outlet. This is where regression analysis can be useful. A regression analysis would seek to model the influence of these factors on the level of sales. In statistical terms we would be seeking to regress the variation in sales ⎯ the dependent variable ⎯ upon several explanatory variables such as advertising, size, etc.. From a forecasting point of view we can use regression analysis to develop predictions. If we were asked to make a forecast for the monthly sales of a proposed new outlet in, say, Oxford, we can simply compute the average outlet sales and put this forward as our prediction ⎯ i.e. ignoring specific characteristics of the Oxford market or the shop in question such as its size ⎯ or we can base our prediction on issues like: How large is the Oxford market? How large is the shop being proposed? What is the outlet’s monthly promotional budget? and adjust our forecast based on the answers to the above questions, so that we can make a more informative prediction along the lines of: "For a market of 150,000, an outlet of 1,200 sq.ft., and an average monthly advertising budget of £2,000, we would predict monthly sales to be £50,000.” This estimate will, in general, be much more accurate than a simple average of all...