Describe the set of assumptions underlying the mathematical regression model in terms of the error term.
Explain why the above assumptions are necessary.
Explain what is meant by the residual standard error, how it is calculated, and why it is a useful measure.
Explain, using a graph, what it means if in the 2-variable regression model the estimator of B2 is biased.
Explain, using a graph, what it means if in the 2-variable regression model the estimator of B2 is unbiased but inefficient.
Explain what is meant by the coefficient of determination and how it is related to the F-statistic.
2. The following data relates to the demand for a homogeneous product sold by seven firms:
Sales (units) 112 120 120 192 104 72 176
Price ($) 26 24 22 20 23 25 21
Estimate the linear relationship between price and sales.
Does price significantly affect sales?
Forecast sales next month, with 95% confidence limits, for a firm charging a price of $24; state any assumptions that you need to make.
3.
a) Explain what is meant by an ANOVA table and its purpose.
b) Using the data in the previous question, construct an ANOVA table and interpret it.
c) Explain in general terms how the addition of another explanatory variable would affect the ANOVA table.
4. The following regression results have been obtained for aggregate final energy demand in 7 OECD countries (US, UK, Canada, Germany, France, Italy and Japan) for the period 1960-82, using annual data:
lnQ = 1.594 + 0.9972lnY – 0.3315lnP
t 17.17 52.09 13.61
R2 = 0.994
F = 1688
Where
Q = measure of energy consumption in BTU
Y = aggregate real GDP in $
P = real energy price in $
Comment on the goodness of fit of the model and the overall significance of the explanatory variables.
Explain whether the signs of the coefficients of the variables are what you would expect.
Interpret the coefficients of the variables.
Comment on the significance of the variables.
Is demand elastic or inelastic? Is the result what you would expect?
5. Explain why multiple regression analysis is superior to simple regression analysis, giving two examples