Questions -

Q1. Given the following model:

y_t = α + βx_t + u_t

After using White's test for heteroskedasticity, we get a statistic of 8.7, is there any evidence of heteroskedasticity?

We assume any heteroskedasticity follows the form below: E(u)_t² = σ²x_t

Show how you would remove the problem of heteroskedasticity and produce a constant variance error term.

Q2. Explain the relationship between the R² statistic and the RSS.

Q3. Why is the R² statistic not always appropriate in a multivariate regression with more than one explanatory variable? Is the adjusted R² statistic an improvement?

Q4. If we run a regression with 50 observations and 2 explanatory variables and produce an R² statistic of 0.36. Using a F-test, is the goodness of fit significant? In a study of the determinants of the demand for computers.

Q5. Is it preferable to have an econometric model that has as many explanatory variables as possible, or a smaller more parsimonious model? Explain some of these advantages and disadvantages.

y_t = α₀ + α₁x₁ + α₂p_t + α₃m_t + u_t

y_t - computer_demand

x_t - national_income

p_t - computer_price

m_t - marketing_expenditure

A firm then wanted to determine if the price of a computer and the amount spent on marketing were jointly significant determinants. They then estimated the above unrestricted model to produce a RSS of 0.96 and a restricted version of the model (without price or marketing variables) and produced a RSS of 0.98. If there are 120 observations for the tests, are the price of a computer and marketing expenditure jointly significant?