(Simple Linear Regression) Thirty (n 30) College graduates who have recently ent
ID: 3264434 • Letter: #
Question
(Simple Linear Regression) Thirty (n 30) College graduates who have recently entered the job market. For each student, the CGPA (cumulative grade-point average X) and SAL (Starting Annual Salary in thousands dollars Y) were recorded, as shown in the following table. Reference Kleinbaum, D., Kupper, L., Nizam, A., and Rosenberg, E. (2013) Applied Regression Analysis and Other Multivariable Methods. Cengage Learning SAL 10.455 9.680 7.300 9.388 12.496 26.974 22.361 18.031 23.658 40.237 39.806 22.414 2.58 6.656 5.336 09.307 93.702 53.290 88.135 156.150 139.523 85.082 2.47 6.350 10.368 22 812 .905 11.812 9.224 11.725 11.320 12.000 12.500 13.310 12.105 6 3.37 2.43 11.357 8,880 12.603 13.250 13.838 128.142 144.000 156.250 177.156 146.531 31.470 35.760 44.375 48.448 45.031 3.888 132.756 64.000 157.452 59.290 100.561 173.607 175.693 169.104 64.000 67.634 115.563 136.166 151.832 121.044 113.764 117.484 15 27 62001.83177, 8.000 12.548 18.400 35.511 18.249 25.271 42.427 47.055 46.164 19.760 20.313 29.885 32.440 36.720 28.385 27.518 27.965 2.83 2.37 2.52 17 8,009 10.028 13.176 13.255 6.350 10.368 12.603 12.603 20 3.55 13.006.101 24 24713.00412 25 278 ,123D 6656 113 21 2.47 2.47 8.000 8.224 10.750 11.669 12.322 11.002 10.666 10-839 6.101 7.728 27 28 2.98 2.58 8.880 6.656 6.656 30 sum 85.15 322.22 247.515 3573.136 935.738Explanation / Answer
Solution
Sxx = [1,n](xi2/n) – (Xbar)2 = (247.515/30) – (2.8383)2 = 0.19455
Syy = [1,n](yi2/n) – (Ybar)2 = (3573.136/30) – (10.7407)2 = 3.7419
Sxy = [1,n](xi.yi/n) – (Xbar x Ybar) = (935.738/30) – (2.8383 x 10.7407) = 0.70594
Regression equation: y = + x
Least squares estimates of and : b = Sxy/Sxx = 3.629 and a = Ybar – b.Xbar = 0.442.
Thus the estimated value of y = ycap = 0.442 + 3.629x.
For the first student, x = 2.58 and so the estimated value of y for this student
= 0.442 + (3.629 x 2.58) = 9.803. ANSWER 1
Actual value of y for the first student is 10.455.
Hence residual = 10.455 – 9.803 = 0.652 ANSWER 2
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