Question

The multiple regressions serve to explain the behavior of one variable (dependent variable) though a set of some explanatory variables for which we can find a logical/theoretically founded relationship with the dependent variable.

Please discuss three business situations (either real or a business situation) with proposed set of 5 explanatory variable. Could you define the expected sign (positive or negative) of these selected explanatory variables?

As e have discussed the usage of the dummy variables propose at least in one of the three cases you discuss previously one or two dummy variables you think are good explanatory variables for the case you are discussing.

Answer 1

The linear regression consists of the dependent variable and the independent variables.

The dependent variable is denoted by Y and the independent variables are denoted by different X_I's.

The examples of multiple regression are:

1) The selling price of the house can depend on the desirability of the location, the number of bedrooms, the number of bathrooms, the years house was built and the square foot of the house.

2) The height of the child depends on the height of the mother, the height of the father, nutrition, environmental factors and the other factors such as if the family is dwarf.

3) Salary of an individual depends on the age, gender, educational attainment, nature of the job and the hours spent on the job.

Here, in this example, the gender is a dummy variable with male and female and the educational attainment can be further classified as below graduation and above graduation and nature of job is also a categorical variable.

4) The levels of the cholesterol level is determined by the age, gender, race of an individual, frequency of going out to the restaurant and the food items ordered in the restaurant.

Here, the gender and the race is a dummy variable.

5) Selection of a car depends on the brand of the car, the model of the car, average kilometer per litre of fuel, the number of seating capacity, the price of the car and many more variables.

Here, the number of cateogrical variables is 2. That is, the model of the car and the brand of the car.

These are the few examples of the multiple regression with the independent variables as the continuous variables or the dummy variables.