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Marketing research lacture 9

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  • 1. MARKETING - UTOPIA REGRESSION (IN BUSINESS RESEARCH)A regression is a statistical analysis assessing the association between twovariables. It is used to find the relationship between two variables.Usually, the investigator seeks to ascertain the casual effect of one variable uponanother-the effect of a price increase upon demand, for example, or the effect ofchanges in the money supply upon the inflation rate. Regression Equation =a+bxExample: A farmer wised to know how many Kg of Rice would result fromapplication of 20 pounds of Euria.The 20 pound of Euria is the X or value of the predictor variable. The predicted Kgof rice would be y or the predicted value of the criterion variable.Using the example we begun in correlation:Pounds of Euria (X) Kg of Rice (y) Table of Regression X (X- ) (X- )2 y (y- ) (y- )2 (X- ) (y- ) 10 -40 1600 30 -20 400 800 20 -30 900 40 -10 100 300 50 0 0 50 0 0 0 70 20 400 60 10 100 200100 50 2500 70 20 400 1000250 0 5400 250 0 1000 2300 =50 =50 www.marketingboys.tk
  • 2. MARKETING - UTOPIA Co-relation r= = = .99We calculate the components of the regression equation beginning with b. b= = = .43 Slope of regression numberThis gives us the slope of the regression line. For each 1.00 increment increase inx, we have a 0.43 increase in y. next, we calculate a. a = - b = 50 – (43)(50) = 28.5If we wish to know how much more rice to expect from a 35 pound application ofEuria, we calculate: = a+b (35) Y tau is the true value of x and y. = 28.5 + .43 (35) = 28.5 + 15.05 = 43.6 expected bushels of corn www.marketingboys.tk
  • 3. MARKETING - UTOPIA STANDARD ERROR The approximate value of the standard error of the estimate tells us the accuracyto expect from our prediction. The standard error for the estimate is calculated bythe following formula: – Syx = Total number of respondentThe formula may look formidable, but we already have calculated all of thecomponents except for sharing the :- STANDARD ERROR CALCULATIONSyx = = = = 2.6 Error in the regression Total number of respondentThis approximate value for the standard error of the estimate tells us the accuracyto expect from our prediction. Thus, for our prediction of 43.6 Kg from anapplication of 35 pounds of Euria, we can expect to predict a yield varying from 41to 46.2 Kg with approximately 68% accuracy, to predict a yield varying from 38.4 www.marketingboys.tk
  • 4. MARKETING - UTOPIAto 48.8 with approximately 95% accuracy, or to predict a yield varying from 35.8to 51.4 with 99% accuracy. www.marketingboys.tk