Example 1:Market Research The standard multiple linear regression model is inappropriate to model this data for the following reasons: 1.The model's predicted probabilities could fall outside the range 0 to 1. 2.The dependent variable is not normally distributed.In fact a binomial model would be more appropriate.For example,if a cell total is 11 then this variable can take on only 12 distinct values 0,1,2...11.Think of the response of the households in a cell being determined by independent flips of a coin with,say,heads representing adoption with the probability of heads varying between cells. 3.If we consider the normal distribution as an approximation for the binomial model, the variance of the dependent variable is not constant across all cells:it will be higher for cells where the probability of adoption,p,is near 0.5 than where it is near 0 or 1.It will also increase with the total number of households,n,falling in the cell.The variance equals n(p(1-p)). ATA 12 Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 12 Example 1:Market Research The standard multiple linear regression model is inappropriate to model this data for the following reasons:
Example 1:Market Research .The logistic regression model was developed to account for all these difficulties. 13 DATA Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 13 Example 1:Market Research The logistic regression model was developed to account for all these difficulties