Question

1. Explain any two diagnostics of the ordinary least squares estimator

2. Mention the circumstance under which Durbin Watson and Dickey fuller tests would yield invalid results.

3. What are the consequences of under fitting a model?

Answer 1

1 OLS is used for estimating unknown parameters in an regression model Geometrically, this is the sum of squared distances parellel to the axis of dependent variable The OLS method provides minimum variance mean unbiased estimation. i. Principal of Unbiasedness Suppose population size is 100 We use Sample size is 10 to test the Apha (a) and Beta (b) As the no.trial increase with samples size of 10, the mean of all Alpha and Beta becomes to equal to or close to the actual Alpha or Beta of the population as whole. So the ii. Minimum Variance This property makes it the best method to for estimating Aplha and Beta. Varinace is the measure of how far the Apha and Beta are from their mean. An estimator that has a lower variance is one whose individual data points are those that are closer to the mean. The OLS gives the minimum Variance. 2 The Data must satisfy the condition of conintegration that is if there exists a stationary linear combination of nonstationary random variables, the variables combined are said to be cointegrated In case of DW test, when large deendent variables are included in the explanatory variables, then it is inappropriate to use this test. 3 When a statistical model cannot adequately capture the underlying structure of the data, Underfitting of model occurs. The problem of Underfitting appears with the polynomial degree. An underfit model will be less flexible and cannot account for the data. An underfit model has low variance and high biasness. The model does not depend on training data and makes strong assumptions about the data and fails to learn the relationship between and dependent (Y) variable and (X) independent Variable