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* I WILL PAY FOR THIS HW* Keep Answers as brief as possible. Include key Stata output with answers. You need files AED KNEEREPLACE.DTA, ass4s18sim.do, oecdhealth2008.dta at Smartsite. 1. R-squared Suppose regression of y on an intercept and x with 50 observations yields total sum of squares 100 and explained sum of squares 36. (a) What is R2? (b) What is the correlation coefficient between y and x? (c) What is the standard error of the residual? 2. Use dataset AED KNEEREPLACE.DTA. The data are 2011 data from 170 New York hospitals for knee replacement surgeries. For each hospital variable discharges is the number of knee replacements, variable medcost is the median cost to the hospital of these knee replacements, and variable medcharge is the median charge by the hospital for knee replacements. Note that the hospital charge is the initial price that the hospital charges, but the hospital usually receives less than this after negotiating with the patient or the patient's insurance company (a) Provide a scatterplot of medcharge against medcost, along with fitted regression line. (b) Regress medcharge against medcost. Provide an interpretation of the slope coefficient. (c) Calculate the residuals from this regression. (Hint: Create a variable equal to yi = b1 − b2xi. Alternatively after command regress give command predict uhat, resid). (d) Do the residuals sum over observations to zero? Comment. (e) Given these residuals, calculate the standard error of the regression. (f) Given these residuals, calculate the sum of squared residuals and compare this to the regression output. (g) Calculate the total sum of squares. (Hint: The sample variance of yi equals 1 n (yi − y ̄)2.) n−1 (h) Given your preceding answers, calculate R2 and compare to the regression output. 3. Continue with the same data as in question 2. (a) Create the z-scores for medcharge and medcost. (Recall: zi = (yi − y ̄)/sy ). i=1 (b) Regress the z-score for medcharge against the z-score for medcost. Provide an interpretation of the slope coefficient. (c) Compare the slope coefficient in part (b) to the correlation coefficient between medcharge and medcost. (d) Regress medcharge against just an intercept. (In Stata simply regress medcharge). (e) Compare your results in part (d) to the sample mean of medcharge and its standard error. (f) Do reverse regression of medcost against medcharge. Compare the slope coefficient and R2 with that from regression of medcharge against medcost. Comment.

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