Question

Problem 3 You are given the following data: 510 15 20 25 30 35 40 45 50 Y 17 24 31 33 37 37 40 40 42 41 a. Use linear regression to fit a straight line, a parabola, and a cubic function to the data b. Plot the data and the different curves on the same plot c. What are the errors associated with the derived parameters for the different curves? d. Which curve best aligns with the given data? Why? e. For the curve of your choice in d) interpolate Y, for the following X values: 12, 27, and 46 f. What are the errors associated with the interpolated values?

Answer 1

LINEAR Calculated y Error 23.07272727 5.072727273 10 24 25.54545455 1.545454545 15 28.01818182 2.981818182 20 30.49090909 37 32.96363636 4.036363636 37 30 35.43636364 1.563636364 35 40 37.90909091 2.090909091 40 40.38181818 3.818181818.10 42 45 42.85454545 8.545454545 10 10 45.32727273 4.327272727 y = 4.945454545-10-1 x + 20.6 Residual Sum of Squares: rss 97.16363636 Coefficient of Determination: R2 .8384

PARABOLIC Calculated y Error 17 18.25454545 1.254545455 10 24 6.060606061.102 23.93939394 15 31 28.82121212 2.178787879 20 32.9 0.1 25 37 8.242424242.10 36.17575758 30 37 38.64848485 1.648484848 40.31818182 3.181818182 10 40 40 41.18484848 1.184848485 45 42 7.515151515 10 41.24848485 10. 50 40.50909091 4.909090909 10 1 y =-1.606060606-10-2x2 + 1.377878788 x + 11.76666667 Residual Sum of Squares: rss 12.04242424 Coefficient of Determination: R2- .9799

CUBIC Calculated y Error 17 17.15804196 0.158041958 10 24.3048951 3.048951049-101 15 29.73496503 1.265034965 20 7.093240093 10 33.70932401 37 36.48904429 0.510955711 30 37 38.33519814 1.335198135 39.50885781 4.911421911 10- 40 40.27109557 2.71095571 1.10% 45 42 40.88298368 1.117016317 41.60559441 10. 50 6.055944056 10- y = 3.48096348 1-10-4 x3-4.477855478-10-2 x2 + 2.04013209 x + 8.033333333 Residual Sum of Squares: rss 6.194405594 Coefficient of Determination: R2 .9897

SINCE VALUE OF THE CUBIC IS THE GREATEST, THE CUBIC CURVE IS THE BEST BIT