Regression Analysis of Coffee Cooling: Temperature vs Time - Prof. W. Robert Stephenson, Study notes of Statistics

Download Regression Analysis of Coffee Cooling: Temperature vs Time - Prof. W. Robert Stephenson and more Study notes Statistics in PDF only on Docsity! JMP Output for Cooling Coffee Time (min) Temp (F) 0 180.6 5 171.7 8 164.5 11 159.4 15 151.2 18 146.1 22 140.1 25 135.0 30 129.1 34 122.0 38 116.5 42 112.1 45 108.0 50 102.7 Simple Linear Regression of Temperature on Time 100 110 120 130 140 150 160 170 180 190 Te m p (F ) -10 0 10 20 30 40 50 60 Time (min) -5 -4 -3 -2 -1 0 1 2 3 4 5 R es id ua l -10 0 10 20 30 40 50 60 Time (min) Linear Fit Predicted Temp (F) = 176.68943 - 1.5587521*Time (min) Summary of Fit RSquare 0.991257 RSquare Adj 0.990528 Root Mean Square Error 2.410473 Mean of Response 138.5 Observations (or Sum Wgts) 14 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept 176.68943 1.219428 144.90 <.0001 Time (min) -1.558752 0.04226 -36.89 <.0001 1 Simple Linear Regression of Log(Temp) on Time 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 Lo g( Te m p) -10 0 10 20 30 40 50 60 Time (min) -0.010 -0.005 0.000 0.005 0.010 R es id ua l -10 0 10 20 30 40 50 60 Time (min) Linear Fit Predicted Log(Temp) = 5.194561 – 0.0113736*Time (min) Summary of Fit RSquare 0.999314 RSquare Adj 0.999257 Root Mean Square Error 0.004907 Mean of Response 4.915909 Observations (or Sum Wgts) 14 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 1 0.42086624 0.420866 17477.45 Error 12 0.00028897 0.000024 Prob > F C. Total 13 0.42115521 <.0001 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept 5.194561 0.002482 2092.5 <.0001 Time (min) -0.011374 0.000086 -132.2 <.0001 2