Transformed Variables 1 Obs len sqrtlen per lenlen loglen logper 1 0.0254 0.15937 0.34000 0.00065 -3.67301 -1.07881 2 0.0508 0.22539 0.47333 0.00258 -2.97986 -0.74796 3 0.0762 0.27604 0.54667 0.00581 -2.57439 -0.60392 4 0.1016 0.31875 0.64000 0.01032 -2.28671 -0.44629 5 0.1270 0.35637 0.71667 0.01613 -2.06357 -0.33314 6 0.1524 0.39038 0.77667 0.02323 -1.88125 -0.25274 7 0.1778 0.42166 0.84000 0.03161 -1.72710 -0.17435 8 0.2032 0.45078 0.90000 0.04129 -1.59356 -0.10536 9 0.2286 0.47812 0.96667 0.05226 -1.47578 -0.03390 10 0.2540 0.50398 1.01667 0.06452 -1.37042 0.01653 11 0.2794 0.52858 1.06333 0.07806 -1.27511 0.06141 12 0.3048 0.55209 1.12000 0.09290 -1.18810 0.11333 13 0.3302 0.57463 1.15667 0.10903 -1.10806 0.14554 14 0.3556 0.59632 1.19667 0.12645 -1.03395 0.17954 15 0.3810 0.61725 1.24667 0.14516 -0.96496 0.22047 16 0.4064 0.63750 1.28333 0.16516 -0.90042 0.24946 17 0.4318 0.65711 1.30667 0.18645 -0.83979 0.26748 18 0.4572 0.67617 1.34667 0.20903 -0.78263 0.29763 19 0.4826 0.69469 1.39667 0.23290 -0.72857 0.33409 20 0.5080 0.71274 1.43333 0.25806 -0.67727 0.36000 Model 1: Simple Linear Regression 2 The REG Procedure Model: MODEL1 Dependent Variable: per Period of Pendulum (seconds) Number of Observations Read 20 Number of Observations Used 20 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 1.94274 1.94274 674.18 <.0001 Error 18 0.05187 0.00288 Corrected Total 19 1.99461 Root MSE 0.05368 R-Square 0.9740 Dependent Mean 0.98833 Adj R-Sq 0.9726 Coeff Var 5.43145 Parameter Estimates Parameter Standard Variable Label DF Estimate Error Intercept Intercept 1 0.42081 0.02494 len Length of Pendulum (meters) 1 2.12796 0.08195 Parameter Estimates Variable Label DF t Value Pr > |t| Intercept Intercept 1 16.88 <.0001 len Length of Pendulum (meters) 1 25.96 <.0001 Parameter Estimates Variable Label DF 95% Confidence Limits Intercept Intercept 1 0.36842 0.47320 len Length of Pendulum (meters) 1 1.95578 2.30014 Model 2: Quadratic Regression 3 The REG Procedure Model: MODEL1 Dependent Variable: per Period of Pendulum (seconds) Number of Observations Read 20 Number of Observations Used 20 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 1.99016 0.99508 3802.37 <.0001 Error 17 0.00445 0.00026170 Corrected Total 19 1.99461 Root MSE 0.01618 R-Square 0.9978 Dependent Mean 0.98833 Adj R-Sq 0.9975 Coeff Var 1.63681 Parameter Estimates Parameter Standard Variable Label DF Estimate Error Intercept Intercept 1 0.29426 0.01204 len Length of Pendulum (meters) 1 3.48676 0.10392 lenlen Len * Len 1 -2.54743 0.18924 Parameter Estimates Variable Label DF t Value Pr > |t| Intercept Intercept 1 24.45 <.0001 len Length of Pendulum (meters) 1 33.55 <.0001 lenlen Len * Len 1 -13.46 <.0001 Parameter Estimates Variable Label DF 95% Confidence Limits Intercept Intercept 1 0.26886 0.31965 len Length of Pendulum (meters) 1 3.26751 3.70601 lenlen Len * Len 1 -2.94670 -2.14816 Model 3: Transform x with Square Root 4 The REG Procedure Model: MODEL1 Dependent Variable: per Period of Pendulum (seconds) Number of Observations Read 20 Number of Observations Used 20 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 1.99330 1.99330 27276.9 <.0001 Error 18 0.00132 0.00007308 Corrected Total 19 1.99461 Root MSE 0.00855 R-Square 0.9993 Dependent Mean 0.98833 Adj R-Sq 0.9993 Coeff Var 0.86494 Parameter Estimates Parameter Standard Variable Label DF Estimate Error Intercept Intercept 1 0.01165 0.00621 sqrtlen Square Root of Period 1 1.98756 0.01203 Parameter Estimates Variable Label DF t Value Pr > |t| Intercept Intercept 1 1.87 0.0772 sqrtlen Square Root of Period 1 165.16 <.0001 Parameter Estimates Variable Label DF 95% Confidence Limits Intercept Intercept 1 -0.00141 0.02471 sqrtlen Square Root of Period 1 1.96228 2.01285 Model 4: Log-log transform 5 The REG Procedure Model: MODEL1 Dependent Variable: logper Log of Period Number of Observations Read 20 Number of Observations Used 20 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 2.96631 2.96631 14618.7 <.0001 Error 18 0.00365 0.00020291 Corrected Total 19 2.96996 Root MSE 0.01424 R-Square 0.9988 Dependent Mean -0.07655 Adj R-Sq 0.9987 Coeff Var -18.60855 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Intercept Intercept 1 0.68005 0.00702 96.85 loglen Log of Length 1 0.48618 0.00402 120.91 Parameter Estimates Variable Label DF Pr > |t| 95% Confidence Limits Intercept Intercept 1 <.0001 0.66530 0.69480 loglen Log of Length 1 <.0001 0.47773 0.49463