Consider the following OLS estimation of a model to explain the stock prices of a FTSE100 company using 120 observations from 2012m1 to 2021m12, all variables are calculated at the end of month t: log(stock) 0.86 +0.54 log (profit,)-0.65 log (research,)-1.34 log (marketing,) (6.1) (1.12) (0.24) (0.30) (0.12) n=120, R² = 0.34, SSR-1.29, F16-3.89. where stock, is the stock price in GBP (British Sterling). profit, (the profit before tax in millions of GBP), research, (expenditure on research and development), and marketing, (expenditure on marketing) are measured in millions GBP. Standard errors are reported in parentheses, SSR is the Sum of Squared Residuals, and the F statistic for the significance of the regression is provided. (a) (5 marks) What is the interpretation of the coefficient on log (profit)? Is the sign of the coefficient as you would expect? Explain your answer. Would your interpretation change if the profit is now measured in thousands of GBP? Explain your answer. Hint: a million is thousand thousand. (b) (5 marks) Looking at the estimates, a colleague claims that the effect of marketing expenses is more than twice as large as the effect of research and development ex- penses on the stock price. Describe a suitable test to examine this claim Clearly specify the null and the alternative hypothesis and assumptions underlying your test. Indicate additional information, if necessary, to conduct such a test. (c) (5 marks) Another colleague gets hold of a variable small, which captures the monthly stock price of a small, random firm in Bulgaria from 2012m1 to 2021m12. Excited with the discovery, the colleague insists on including small, in the model. Discuss the statistical reasoning behind including additional variables in the model. What are the likely effects of the inclusion of small, on the properties of the OLS estimators of the parameters of the model? Explain your answers intuitively. Hints: The Bulgarian company is completely unrelated with the FTSE company in the model. (d) (5 marks) Your research manager believes that the stock price action of the FTSE100 company behaves differently after 2016m6. He claims that the coefficients of the regressors in (6.1) for the months after 2016m6 are different from the coefficients in (6.1) for the months in and before 2016m6. Discuss how you can test whether the manager is correct. Clearly specify the null and the alternative hypothesis. Indicate additional information, if necessary, to conduct such a test.