Regression Analysis - Example with Solutions | M E 345, Study notes of Mechanical Engineering

Download Regression Analysis - Example with Solutions | M E 345 and more Study notes Mechanical Engineering in PDF only on Docsity! M E 345 Fall 2009 Professor John M. Cimbala Lecture 09 09/14/2009 Today, we will: • Finish reviewing the pdf module: Regression Analysis • Do some example problems – regression analysis • Review the pdf module: Outlier Points • Do some example problems – outlier points Example: Regression Analysis Given: Twenty data points of (x,y) pairs with lots of scatter (see Excel spreadsheet on website for the raw data). Data point x y 1 0 1.924 2 0.1 2.377 3 0.2 2.088 4 0.3 3.245 5 0.4 3.031 6 0.5 2.779 7 0.6 3.186 8 0.7 4.102 9 0.8 4.278 10 0.9 3.701 11 1 3.654 12 1.1 3.991 13 1.2 3.891 14 1.3 3.790 15 1.4 3.437 16 1.5 4.080 17 1.6 3.204 18 1.7 3.130 19 1.8 2.614 20 1.9 2.066 To do: Perform regression analysis – linear, quadratic, and cubic – and compare how the fitted curves fit to the data points. Solution: See Excel spreadsheet – I will show in class how to do the regression analysis in Excel. Example: Outliers – single set of data Given: Four data points are measured. Data point x 1 38 2 42 3 44 4 53 To do: Eliminate any “official” outliers, one at a time. Solution: Example: Outliers – single set of measurements Given: Janet takes 12 temperature measurements ranging from 23.0oC (lowest reading) to 25.7oC (highest reading). • The sample mean of all 12 readings is 24.88oC. • The sample standard deviation is 1.04oC. To do: Determine which, if any, of the extreme readings (lowest or highest) is an outlier. Solution: sample mean = 44.25 sample standard deviation =6.3443