Question

2. Using the following data set find a prediction equation ( 9 = ax + b) relating the factor (x) and the response data (y). You can use Excel, Matlab, or similar software to help with the process. Comment on the predicted and adjusted R2 values of the resulting model. х у (y - ) (y-7) (ŷ - y) 100 100 100 100 200 200 200 200 500 500 500 500 16.7 12.2 8.4 6.6 15.3 10.7 10.3 21.1 45.6 43.9 47.7 43.2 SSE SST SSR

Answer 1

From the given data, the mean x and mean y are calculated. Using the linear regression model, the coefficients a and b for the best fit are determined. Once a and b are known, the y^ is determined and also the other as asked in the table. Finally SSE, SST and SSR are calculated.

22 X = 266.67 b= { (10-2) (y: Y 30950 ¿=1 => b 23.475 -> b = 0.08927 - 1 92 346666.67 (26. -57) ? az jabi bă = a = -0.3327.

2 a 4.595 (y-ý)² (y-g² groter 16.7 8.595 72 376 8.595 65.69 45.9 221.4144 100 12-2 12.996 127.13 221.4144 g = a at bu 100 8.4 0.038025 227.25 221.4144 100 6.6 8.595 32 376 2.595 32376 17.523 - 65 645 77.523 -65 645 3.980625 284.77 221-4144 y =(-0-3127) + (0.08927) " 200 153 4.9417 66.83 35.426 200 10.7 46.55 35.426 163.2 173.52 200 10.3 17-523 52.772 35.426 200 21.1 17.523 12.795 5.64 35.426 500 45.6 44.306 1-6744 489.52 433.93 43.9 44.306 500 0.1648 (117-18 433.93 44.306 11.52 47.7 Soo 433.93 586.85 44-306 433.93 43.2 1.223 389.0756 500 SST=2976.925 SSE=213.745 SSR = 2763-0816 - 7" (Peeniden Coffblend)