Question

(a) Create a multiple linear regression model with 2 numeric variables and dummy variables for 3 categories (b) List out all of the assumptions for this regression model. (c) How can we test these assumptions? (d) If the model doesn't satisfy the model assumption, what else we can do to remedy the model? (e) Except these model assumptions, what else problems we may have when we solve a prac- tical problem? How to remedy when we have these problems? (f) In order to select the best model, what criterion we can use to do the selection? What else value can tell us the model fit is good?

question is about R

Answer 1

a. According to the problem, we have 2 numerical variabes and 1 dummy variable of 3 categories. Let us explain the same with example.

Let Y is the Final Test Score of a Student

X1 is the number of classes the student has attended in last semester

X2 is the Test Score of last semester

X3 is the categorical variable which assumes three values, Male, Female and Transgender

X3 = 0 if male

= 1 if female

= 2 if Transgender

So the regression equation will have the form

$Y = \alpha + \beta_1X_1 + \beta_2X_2 + \beta_3X_3$

b. The assumptions of this regression models are

(i) The dummy variables are categorical and can assume only 3 values

(ii) The variables numeric and categorical are independent of each other

(iii) The linear regression model fits the data and we have to check the extent of multicollinearity beween independent variables

c. We need to assess the extent the coefficients play role in predicting the value of Y

We need to check the collinearity between the independent variables

We need to check the goodness of fit of the regression equation

d. If we see the model can not predict the actual figures, we need to check the R value and may drop some variables which is loosely correlated with final value.

We may also try to fit regression equation of higher order (non-linear)

** Answered 4 parts **