In: Statistics and Probability
Briefly describe one way you could use each of the models in a research setting.
Simple linear regression : We know that Cigarette Smoking is injurious to health and it bring diseases like cancer,lung and heart diseases.If a person is a smoker and number of cigarette he smokes in a day over the years will be having the positive association with the age at which he gets his heart diseases like heart attack etc in future.Here number of average cigarettes smoked by the person in a day is called independent variable and the age at which he gets his first heart attack is called response variable.This data can be collected from the random sample of persons from different age groups and the simple linear regression model can be estimated using the simple linear equation where a is called Y-intercept and b is called slope of the linear regression line.
Multiple linear regression :Regression Model involving two or more independent variables are called multiple regression model.In the above example,we can add one or more categorical variable like whether the person is non-vegetarian or vegetarian and add other factors like his stress level,average sleeping hours and his daily exercise routines like cycling,yoga or walking etc in number of hours etc.Based on this data of different independent variables,suitable Multiple Regression Model can be predicted for heart related problems of people based on their life leading styles.The multiple regression model in this case will be
Y = b0 + b1X1 + b2X2 +b3X3 where X1,X2 and X3 are independent variables that are associated with response variable for early heart attack etc.
Multivariate Analysis of Variance (MANOVA) :This is a procedure in inferential statistics for Analysis Of Variance (ANOVA) with several dependent variables.Here ANOVA tests for the difference in means between two or more groups by comparing the significant difference of multivariate sample means.For example,we may conduct the experimental study for the effect of weight reduction exercise among two different groups of people like Men and Women etc.Here MANOVA could be used to test the hypothesis for two dependent variable for weight reduction exercise among Men and Women separately.Here we need to consider main effects of independent variables like dieting,type of food both quantity as well as quality on exercise treatment among these groups of Men and Women with their interaction among independent variables etc.