using caloric intake as a dependent variable, and diet as independet variable, develop an estimated regression equation.
For this question diet has 3 categories- vegan vegatrian and keto. So my prof said we r testing for multicolinearity or something.
I am very confused.
To develop an estimated regression equation, also known as a multiple regression model, with caloric intake as the dependent variable and diet as the independent variable, you first need to convert the categorial variable "diet" into dummy variables.
Dummy variables represent categories as binary variables, with a value of 1 indicating that the observation belongs to a specific category and 0 indicating it does not. In this case, you would need two dummy variables since you have three categories: vegan, vegetarian, and keto.
Assuming you have a dataset with observations for caloric intake and diet, you can follow these steps to create the dummy variables:
1. Create two dummy variables: "dummy_vegan" and "dummy_vegetarian."
- Assign a value of 1 to "dummy_vegan" if the observation's diet is vegan; otherwise, assign 0.
- Assign a value of 1 to "dummy_vegetarian" if the observation's diet is vegetarian; otherwise, assign 0.
2. Drop one of the dummy variables to avoid multicollinearity.
- Since three dummy variables would lead to perfect multicollinearity (one variable can be perfectly predicted from the others), we need to drop one dummy variable as a reference category. In this case, you can drop the "dummy_vegan" variable, for example.
3. Perform the regression analysis.
- Use caloric intake as the dependent variable and include the remaining dummy variable ("dummy_vegetarian") as the independent variable in the regression model.
The estimated regression equation will provide the coefficients associated with each independent variable, including the one dummy variable representing the vegetarian diet. These coefficients will represent the mean differences in caloric intake between the reference category (keto) and the vegetarian category, while controlling for other factors in the model.
Keep in mind that regression analysis assumes certain conditions, such as linearity, independence of observations, and equal variance of errors. Additionally, the interpretation of the coefficients in the equation should consider the limitations of the data and the assumptions made during the analysis.