252DoReg 4/23/07Doing a RegressionAssume that your dependent variable (‘response’ in Minitab talk) is in c1 and your independent variables (‘predictors’ in Minitab) are in c2, c3 and c4. You can always refer to them by their names if the columns are labeled.The basic commands for a regression with 3 independent variables are Regress c1 3 c2 c3 c4Stepwise c2 c1 c2 c3 BReg c1 c2 c3 c4The stepwise and BReg commands are usful when you have a large number of independent variables and want to remove the least useful.There are examples of commands like this in problems like 14.35, written up in pages like pp 9-11 etc. in 252SolnK1. It is often easier to use the pull-down menus in Minitab. In the examples below I ran data from your disk provided with the text after downloading it with the labels provided by the data set. To run ‘regress,’ I used the ‘stat’ pull-down menu and picked ‘regression’ twice. The only option I picked was Variance Inflation Factor. In the example below, the dependent variable (Sales) was in C2 and the independent variables (DistCost and Orders) in C1 and C3. ————— 4/19/2004 4:53:41 PM ————————————————————Welcome to Minitab, press F1 for help.252cp403 4/19/04 MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\Warecost.MTW". #I used a pull-down menu and ‘open a new worksheet’Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\Warecost.MTW# Worksheet was saved on Tue Dec 02 2003Results for: Warecost.MTWMTB > Regress c2 2 c1 c3;SUBC> Constant; #Don’t bother with this option – it is put in automatically.SUBC> VIF; # This is the Variance inflation factor. For interpretation, see the text or the #outline.SUBC> Brief 2. #This is a default value too. You can play around with brief 3, these control #the amount of detail in the output and can be used to give you predicted #values for Y .Regression Analysis: Sales versus DistCost, OrdersThe regression equation isSales = 65.6 + 4.32 DistCost + 0.0188 OrdersPredictor Coef SE Coef T P VIFConstant 65.64 57.51 1.14 0.267DistCost 4.323 1.865 2.32 0.031 6.4Orders 0.01884 0.03272 0.58 0.571 6.4S = 45.66 R-Sq = 71.4% R-Sq(adj) = 68.6% #Note that only the coeff of DistCost is#significant.Analysis of VarianceSource DF SS MS F P1252DoReg 4/23/07Regression 2 109116 54558 26.17 0.000Residual Error 21 43776 2085Total 23 152892Source DF Seq SSDistCost 1 108425Orders 1 691Unusual ObservationsObs DistCost Sales Fit SE Fit Residual St Resid 14 72.3 328.00 461.65 9.37 -133.65 -2.99R R denotes an observation with a large standardized residualHere I repeated the analysis using the ‘stat’ pull-down menu, picked ‘regression’ and then ‘stepwise.’ The subcommands were all generated by Minitab and would be what would have been used if I had just put in the first line as a command.MTB > Stepwise c2 c1 c3;SUBC> AEnter 0.15;SUBC> ARemove 0.15;SUBC> Constant.Stepwise Regression: Sales versus DistCost, Orders Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15 Response is Sales on 2 predictors, with N = 24 Step 1Constant 78.09DistCost 5.31 # The computer came up with ‘Sales’ = 78.09 + 5.31’DistCost’ and quit. It #decided that ‘Orders’ had very weak explanatory power.T-Value 7.32P-Value 0.000S 45.0R-Sq 70.92R-Sq(adj) 69.59C-p 1.3 More? (Yes, No, Subcommand, or Help)SUBC> y No variables entered or removed
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