(Each part is worth 5 points) A couple shopping for a diamond engagement ring is interested in the relationship between the price of the ring y (in dollars) and the size of the diamond x (in carats). A sample of n = 351 rings were evaluated and the following polynomial regression results of the data were reported. 3; hat = 522.7 + 23863 + 4498.22:2 SSResid= 12212.5 SSTotal = 13192.6753 a. Test the overall utility of this quadratic regression model, and show all six steps. Use a = .05. b. Given that 81,2 = 263.0 , test whether or not the 1:2 term is important (useful) in the aforementioned model. Use a = .05. c. Estimate the price for Debra's ring, which has a 2 carat diamond. d. Compute and interpret the value of R2 , the coefficient of multiple determination. e. Compute the value of the adjusted R2 statistic. Compare it to the value of R2 ? Why is it different? f. Calculate an estimate of the standard deviation of the residuals (i.e. calculate an estimate of Us ). [Upload a single .PDF or .DOCX file showing your BY HAND work and solution for this exercise.]