We use Regression analysis to create models which describe the effect of variation in predictor variables on the response variable. Sometimes, if we have a categorical variable with values like Yes/No or Male/Female etc. The simple regression analysis gives multiple results for each value of the categorical variable. In such scenario, we can study the effect of the categorical variable by using it along with the predictor variable and comparing the regression lines for each level of the categorical variable. Such an analysis is termed as Analysis of Covariance also called as ANCOVA. Example Consider the R built in data set mtcars. In it we observer that the field “am” represents the type of transmission (auto or manual). It is a categorical variable with values 0 and 1. The miles per gallon value(mpg) of a car can also depend on it besides the value of horse power(“hp”). We study the effect of the value of “am” on the regression between “mpg” and “hp”. It is done by using the aov() function followed by the anova() function to compare the multiple regressions. Input Data Create a data frame containing the fields “mpg”, “hp” and “am” from the data set mtcars. Here we take “mpg” as the response variable, “hp” as the predictor variable and “am” as the categorical variable. When we execute the above code, it produces the following result − Explore our latest online courses and learn new skills at your own pace. Enroll and become a certified expert to boost your career. ANCOVA Analysis We create a regression model taking “hp” as the predictor variable and “mpg” as the response variable taking into account the interaction between “am” and “hp”. Model with interaction between categorical variable and predictor variable When we execute the above code, it produces the following result − This result shows that both horse power and transmission type has significant effect on miles per gallon as the p value in both cases is less than 0.05. But the interaction between these two variables is not significant as the p-value is more than 0.05. Model without interaction between categorical variable and predictor variable When we execute the above code, it produces the following result − This result shows that both horse power and transmission type has significant effect on miles per gallon as the p value in both cases is less than 0.05. Comparing Two Models Now we can compare the two models to conclude if the interaction of the variables is truly in-significant. For this we use the anova() function. When we execute the above code, it produces the following result − As the p-value is greater than 0.05 we conclude that the interaction between horse power and transmission type is not significant. So the mileage per gallon will depend in a similar manner on the horse power of the car in both auto and manual transmission mode.

Poisson Regression involves regression models in which the response variable is in the form of counts and not fractional numbers. For example, the count of number of births or number of wins in a football match series. Also the values of the response variables follow a Poisson distribution. The general mathematical equation for Poisson regression is − Following is the description of the parameters used − The function used to create the Poisson regression model is the glm() function. Syntax The basic syntax for glm() function in Poisson regression is − Following is the description of the parameters used in above functions − Example We have the in-built data set “warpbreaks” which describes the effect of wool type (A or B) and tension (low, medium or high) on the number of warp breaks per loom. Let’s consider “breaks” as the response variable which is a count of number of breaks. The wool “type” and “tension” are taken as predictor variables. Input Data When we execute the above code, it produces the following result − Create Regression Model When we execute the above code, it produces the following result − In the summary we look for the p-value in the last column to be less than 0.05 to consider an impact of the predictor variable on the response variable. As seen the wooltype B having tension type M and H have impact on the count of breaks.