In Problems 5–8, determine whether the interaction plot suggests that significant interaction exists among the factors
Step 1 of 5) Whether the interaction plot suggests that significant interaction exists among the factors. Remember, the unexplained variation is found by summing the squares of the residuals. The sum of the squared residuals will never increase if more explanatory variables are added. The total variation is constant regardless of the number of explanatory variables. Therefore, the coefficient of determination, R2 , will never decrease with the addition of more explanatory variables; instead, it generally increases. So R2 can often be made as large as we like simply by adding more explanatory variables. To compensate for the ability to artificially inflate R2 by adding more explanatory variables, it is recommended that the adjusted R2 be used when working with leastsquares regression models with two or more explanatory variables. Definition The adjusted R2 , denoted Radj 2 or R2 , is the adjusted coefficient of determination. It modifies the value of R2 based on the sample size, n, and the number of explanatory variables, k. The formula for the adjusted R2 is In Other Words The value of R2 always increases by adding one more explanatory variable.