Question

1. Explain the limitations of the linear regression model. [5 marks]
2. Using a sample of 1801 employees, the following earning equation has been estimated:   
   
                               (0.135)   (0.008)        (0.007)      (0.036)

Where:

Y is earnings, x₁ is education level,x₂ is experience and x₃ is female

The standard errors are the values in brackets.

R²=0.179

Required:

1. Interpret each of the coefficient estimates. [5 marks]
2. At 5% significance level, test the hypothesis that there is no difference in expected earnings between male and female employees. [5 marks]

Answer 1

(a) Linear regressions are sensitive to outliers.

It is easy to overfit your model such that your regression begins to model the random error (noise) in the data, rather than just the relationship between the variables.

Linear regressions are meant to describe linear relationships between variables. So, if there is a nonlinear relationship, then you will have a bad model.

(b) (i) For every addition in education level, the earnings will increase by 0.008.

For every addition in experience, the earnings will increase by 0.007.

For every female, the earnings will increase by 0.036.

(ii) The data is missing.