BA222_ProblemSet3

a. What is the median value of height in the sample? b. Estimate the average earnings for workers whose height is at most 67 inches. Then, estimate the average earnings for workers whose height is greater than 67 inches. Based on your calculations, what do you think is the relation between height and earnings? Use the results to estimate how earnings change by each additional inch? c. Construct a scatterplot of annual earnings (Earnings) on height (Height). Notice that the points on the plot fall along horizontal lines. (There are only 23 distinct values of Earnings). Why? Is there an alternative way of displaying the relation between the two variables that is more appropriate to determine if the two variables are related? If yes, produce the appropriate type of graph. d. Run a regression of Earnings on Height . What is the estimated slope? Interpret the value of the slope and compare it to your answer in part b. e. Use the estimated regression in part d to predict the earnings for a worker that is 65 inches tall. f. What problems may you encounter if you try to use the model to predict the earnings of extremely tall/ short individuals? Explain. g. Estimate the model only using data for females, and then using data only for males. Do you observe any difference in the estimated coefficients? Why that may be the case? Problem 1.3 Use the HousePrices.csv database to answer the following questions: a. Represent graphically the relation ship between price and lot size. Describe the statistical relation ship between the variables. If necessary, compute the correlation coefficient. b. Estimate a univariate regression model using price as the dependent variable and lot size as the independent variable. Display the results in a table. c. Interpret the intercept, slope, R-Squared and the statistical significance of the beta coefficients. d. What is the average house price for a house with lot size of 3,600 SQF versus a house with a lot size of 6,360 SQF? e. Are there other factors that may be omitted from the regression but are related to price? Explain. f. Represent graphically the regression line of your estimation for part (b). Part 2. Multivariate Regressions Use the HousePrices.csv database to answer the following questions: a. Estimate the following multivariate regression models.