Consider the following models and their R^2 values: State how one computes R^2 f
ID: 3180062 • Letter: C
Question
Consider the following models and their R^2 values: State how one computes R^2 for a model. If needed you can use the generic names: mod for a model and data for a dataset. What is the smallest possible R^2 value for Model 4? Justify your response and explain what must be true about X_1, X_2, X_3 for Model 4 to achieve this minimum R^2 value. What is the largest possible R^2 value for Model 4? Justify your response and explain what must be true about X_1, X_2, X_3 for Model 4 to achieve this maximum R^2 value. Your friend tells you that "Model 1 must have a lower R^2 than Model 4." Do you agree? Why or why not?Explanation / Answer
(a) R2=1-RSS/TSS, RSS=regression/model sum of squrare and TSS=total sum of square.
it is explained variation by the model
(b) in model 4, there are two independent variable X2 and X3. so minimum sum of square will be maximum of (X2, X3).
so minimum R2 will be 0.65
(c) largest R2 will be sum of R2 of X2 and X3 i.e.0.65+0.17=0.82. Maximum R2 will be 1 if X1,X2,X3 are in model 4.
(d) Agree, model 1 has only one indpendent variable and model 4 have two inpedependent varaiable, because addition of indpendent variable increase the R2