Question

Consider the following estimated and true relationship between health (H) and hours of exercise (E):

Estimated: H_i = 20 + 10E_i - E_i²

True: H_i = β₁ + β₂E_i - β₃E_i² + e_i

a) Interpret the estimated equation, (not including elasticity)

b) Which parts of the true equation are observable and which are unobservable?

c) What is є_i and what 3 roles does it have? Give an example for each.

Answer 1

Solution:The above equation is a case of Multiple linear regression model with three variables. The intrepretation of the estimated equation goes like this :

1. The intercept coefficient of the regresson model is 20 which states that if the value of Ei variable is zero then the value of Hi will be 20.

2.If Ei2 is fixed, For a one unit change in Ei, on an average Hi will changes by 10 units.

3. If Ei is fixed , For a one unit change in Ei2 ,on an average Hi will change by 1 units.

B.) All the variables i.e independent variables Ei and Ei2 are all observable variables while ei is an unobservable variable.

C.) ei is the error term or the stochastic term which cannot be predicted easily. There are large number of factor which may be directly or indirectly affecting Hi.Apart from Ei and Ei2 the factors that are affecting Hi are considered under ei.In other words all those variations in Hi that cannot be explained by Ei's are considered under ei.

The role of ei are:

1. Many influences on Y are omitted from the model may be due to data insufficiency or non availability of data.All these defeciencies are to be considered under ei..

2. The underlying equation may be of different functional form due to which there may be variations in Y. These variations are considered under ei. For example, the underlying equation might be nonlinear in the variables for a linear regression.

4. All attempts to generalize human behavior must contain at least some amount of unpredictable or purely random variation. So we include ei term in our regression model.