5 A simple linear regression model relating investment y by

5. A simple linear regression model relating investment (y) by companies to bank lending interest rate (x) is stated as follows: a. What are the intercept and slope for the relationship between investment and bank lending interest rate stated above? What sign would you expect for the slope in the relationship for investment and bank lending interest rate? Please explain your reasoning. [3 points] b. What is the role of the error term in the simple linear regression model like the one stated above? Please state at least two examples of the factors that you think belong in the error term of the simple linear regression model stated above briefly justifying each example. [3 points] c. Please explain how you would estimate the relationship between investment and interest rate specified above. [Note: you do not need to write any formulas as an answer to this question. Just explain what you will need and the reasoning behind the method you would use to estimate the relationship]. [3 points] d. For what purpose could you use the estimated simple linear regression model for investment and interest rate? Why could the simple linear regression model stated above be inadequate for the purpose?

Solution

a.) For the linear regression model,

Y = a + bX

The intercept a will be the original amount of investment and the slope b will be the increase in interest for every unit of time.

The slope will have a positive sign because longer the period of investment more will be the interest.

b.) The error will be due to changes in the interest rate during the time of investment.

c.) You will need the amount of investments and the different rates of interest for different time periods.

d.) We could use the simple regression when we are investing a particular amount for a certain specified time with known interest rate.

This would be inadequate if you decide to invest a certain amount at a varied interest rate for a period of time