Firm-level sales are potentially affected by a number of factors including the expenditure on advertising and the size of a firm, its productivity as well as the capital intensity of its production technology. The objective of this project is to establish whether expenditure on advertising, size, productivity and capital intensity are determinants of firm sales in a cross-section of firms. The data below contains information, covering a sample of 55 firms, on firm sales (Sales), firm expenditure on advertising (Advert), a commonly used measure of firm size and in particular the number of employees of the firm (Empl), a measure of the productivity of the firm (Prod), as well as a measure of the capital intensity of the production technology used by the firm (Capit). Sales and expenditure on advertising are measured in million pounds while productivity is measured as the ratio of the value of sales to the value of inputs used and capital intensity is measured as the ratio between the capital stock of a firm (in million pounds) and the number of employees. Describe the data, using summary statistics and graphs, as appropriate. Calculate the pair-wise correlation coefficients between Sales and each of the other variables. Test the statistical significance of each correlation coefficient. Consider the two variables Empl and Prod. Compute the pairwise correlation of the two variables and test the significance of the correlation coefficient. Now group each of the two variables in 5 intervals (5 intervals of 11 observations each) and construct a contingency Table. Using the contingency Table perform a test for the presence of association between the two variables. Compare and discuss results from the contingency Table analysis with results from the correlation analysis. Consider again the two variables Empl and Prod and test the null hypothesis that the two variables have equal variance. Estimate a regression model of the form: Salesi =α + β1Adverti + β2Empli + β3Prodi + β4Capiti +ui where the i subscript corresponds to firm i. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. Interpret the R2 statistic from the regression and test whether it is statistically significant. .Re-estimate the model excluding the Capit variable and comment on any changes to the results and goodness of fit: Salesi =α + β1Adverti + β2Empli + β3Prodi +ui 8. Estimate a log-version of the regression model of the form: Log(Sales)i =α + β1Log(Advert)i + β2Log(Empl)i + β3Log(Prod)i +ui where the i subscript corresponds to firm i. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. Compare this model with the one estimated in point 7. What conclusions do you draw from your analysis? Everything is clear