Q1. The following model was obtained by a researcher when investigating the response of demand of automobiles to prices for am period of 6 years.
Y = 5807 + 3.24X r^2 = 0.22
(0.45) (1.634)
The t values are provided in parenthesis.
a) Test the hypothesis that the intercept and the slope are equal to zero at the 5% level of significance. [6 marks]
b) Compute the elasticity of demand when the price is equal to 10 and comment on your results. [4 marks]
c) Interpret your r^2 and explain how it relates to the slope of the regression line. [4 marks]
d) Establish a 95% confidence interval for the population slope. [6 marks]
Q2. Consider the following data:
Y 15 10 14 8 3
X 1 2 3 4 5
a) Calculate the simple correlation coefficient and interpret your results. [5 marks]
b) Compute the rank correlation coefficient and interpret your results. [5 marks]
c) Compute the coefficient of determination for the relationship between Y and X and interpret your results. [3 marks]
d) Compute the adjusted R squared. [2 marks]
e) Test for the significance of the coefficient of determination in c) above assuming a 5% level of significance. [5 marks]
Q3. a) With the use of appropriate examples, explain what you understand by the term multicollinearity. [2 marks]
b) Discuss the main consequences of multicollinearity in an econometric relationship. [8 marks]
c) OLS estimators are BLUE with the use of appropriate examples, discuss clearly what you understand by this statement. [10 marks]
