Please pay attention to the words in bold. There are 6660 observations of data on houses sold from 1999-2002 in Stockton California in the file "hedonic1.xls". Use the data of 2001 and 2002 only to estimate the next linear model and answer the associated questions below. SPB1B2 SFLA + u, (1) where u is an error term. Note that the sub-index i of each variable has been suppressed in the above equation. SP = Selling Price, which is a function of SFLA (size of living area in square feet). Questions: (20 marks in total) 1. (a). Consider the data from from both years 2001 and 2002, and generate the descriptive statistics for SP and SFLA (i.e., 2 VARIABLES IN TOTAL), and report them in a table. (2 points 1 point for each variable) - (b). Using the data from both years 2001 and 2002, plot SP (y-axis) against SFLA (x- axis). Do you observe any pattern? (2 points 1.5 points for the plot, and 0.5 point for the comment) 2. Estimate the model (1) for the houses sold in Stockton California. (a). Write down the estimated model (including estimates of the coefficients and the associated standard deviations), and comment on the estimation result using Goodness of 1 points for reporting the results properly, and 1 point for commenting on Goodness of fit correctly) fit. (2 points (b). Plot the estimated error terms, and calculate the mean squared errors (i.e., A ). (2 points 1 point for plotting, and 1 point formean squared errors) 3. At the 5% significance level, test if SFLA has POSITIVE impacts on SP. Keep two decimals for the calculation involved. (4 points) 4. The model (1) can be written in a sample version as follows: Yi = 1 + 2xi2 = x +ui, where i = 1,..., N, = (, 2), xi = (Xi1, Xi2) = (1, SFLA,), and the definition of y; should be obvious. Further define X = (x1,...,xN) in case one may need this notation to answer the following questions. (a). To obtain the OLS estimate of of (2), we need to minimize an objective function. Please write down the correct function form of the objective function. (1 point) (b). Describe the basic assumptions of the classic linear regression models using the nota- tions of (2). (2 points) (c). Provided that these assumptions hold, what conclusions can you make about the OLS estimator? (1 points) 5. Provide detailed steps to prove that by minimizing the objective function in question (4), your OLS estimate has the form B = (XTX)-XTY, where X is defined in question (4), (y1,..., YN) T. We assume that XTX is invertible. (4 points) and Y =