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.
To develop an estimated regression equation with caloric intake as the dependent variable and diet as the independent variable, you can follow these steps:
1. Assign categorical values to the diet categories: vegan = 0, vegetarian = 1, and keto = 2. This helps to convert the qualitative variable into a quantitative variable so that it can be used in the regression analysis.
2. Collect data on caloric intake and diet for a sample of individuals. For each person, record their caloric intake in one variable and their diet category in another variable.
3. Create indicator variables for the diet categories. This will help in building a regression model with multiple independent variables. In this case, you will need two indicator variables: one for vegetarian and another for keto. The reference category will be vegan, which does not require an indicator variable as it will be the baseline.
- Set the indicator variable for vegetarian to 1 if the person is vegetarian, and 0 otherwise.
- Set the indicator variable for keto to 1 if the person is on a keto diet, and 0 otherwise.
- Vegan will be the reference category and will have values of 0 for both indicator variables.
4. Run the regression analysis by including the caloric intake as the dependent variable and the diet category indicators (vegetarian and keto) as the independent variables. The regression equation will estimate the relationship between diet category and caloric intake.
The estimated regression equation might look like:
Caloric Intake = β0 + β1 * vegetarian + β2 * keto
Here, β0 represents the intercept (caloric intake for the vegan category), β1 represents the coefficient for the vegetarian indicator variable (impact on caloric intake for vegetarians compared to vegans), and β2 represents the coefficient for the keto indicator variable (impact on caloric intake for individuals on keto compared to vegans).
5. To test for multicollinearity, you can examine the correlation between the independent variables (vegetarian and keto). If the correlation is high (close to 1 or -1), it may indicate multicollinearity. In such cases, you may need to address the multicollinearity issue, such as by removing one of the highly correlated variables or employing techniques like ridge regression or principal component analysis (PCA).