Differences in means: In dummy variable regression we compared one mean to a base level mean. If all the variables are qualitative, the Tukey HSD method allows you to find confidence intervals on every combination of differences in means with 95% confidence indicating that in 95% of all experiments that all the intervals will be correct. Example: Two-Factor Results From Tukey's confidence interval, the difference in means between each of the six combinations require 15 combinations. I have listed three of these and their interpretations: Difference Lower Upper A 1 - B 2 4.9 7.9 B 2 - A 2 -2.4 0.7 B 2 - C 1 2.9 6 : With 95% confidence we can say that all students who use … Textbook A and Software 1 have average grades between 4.9 and 7.9 points higher than those you use Textbook B with Software 2. Textbook B and Software 2 have average grades between 2.4 points lower up to 0.7 points higher than those you use Textbook A with Software 2. Textbook B and Software 2 have average grades between 2.9 and 6 points higher than you use Textbook C with Software 1. 4.2 A mixture of qualitative and quantitative independent variables with each quantitative variables represented by one variable and each qualitative variable with c levels represented by c-1 dummy variables. The models used can be either first order or include all possible interactions. II. Qualitative Dependent Variable We will restrict our discussion to qualitative dependent variables that only have two levels pass-fail, product A or B, candidate A or B, etc.). We cannot use a dummy variable, Dy, with least squares regression for this since according to our notes the mean of a dummy variable is p and the variance of a dummy variable is p(1-p). Thus the variance of Dy would not be constant but depend on the mean. In fact we switch from least squares to another estimation procedure called maximum likelihood. In maximum likelihood the probability functions of each observation are multiplied together and then
Differences in means: In dummy variable regression we compared one mean to a base level mean. If all the variables are qualitative, the Tukey HSD method allows you to find confidence intervals on every combination of differences in means with 95% confidence indicating that in 95% of all experiments that all the intervals will be correct. Example: Two-Factor Results From Tukey's confidence interval, the difference in means between each of the six combinations require 15 combinations. I have listed three of these and their interpretations: Difference Lower Upper A 1 - B 2 4.9 7.9 B 2 - A 2 -2.4 0.7 B 2 - C 1 2.9 6 : With 95% confidence we can say that all students who use … Textbook A and Software 1 have average grades between 4.9 and 7.9 points higher than those you use Textbook B with Software 2. Textbook B and Software 2 have average grades between 2.4 points lower up to 0.7 points higher than those you use Textbook A with Software 2. Textbook B and Software 2 have average grades between 2.9 and 6 points higher than you use Textbook C with Software 1. 4.2 A mixture of qualitative and quantitative independent variables with each quantitative variables represented by one variable and each qualitative variable with c levels represented by c-1 dummy variables. The models used can be either first order or include all possible interactions. II. Qualitative Dependent Variable We will restrict our discussion to qualitative dependent variables that only have two levels pass-fail, product A or B, candidate A or B, etc.). We cannot use a dummy variable, Dy, with least squares regression for this since according to our notes the mean of a dummy variable is p and the variance of a dummy variable is p(1-p). Thus the variance of Dy would not be constant but depend on the mean. In fact we switch from least squares to another estimation procedure called maximum likelihood. In maximum likelihood the probability functions of each observation are multiplied together and then
dummyvariables.docx