Introductory Applied Statistics for Engineers
Introductory Applied Statistics for Engineers STAT 324
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Mrs. Triston Collier
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 324 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/205089/stat-324-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
STAT 324224 DISCUSSION 7 Jan 28 2008 TA Meng Song O ice 1270 M807 1300 Universtiy Avenue Email songm statwiscedu 1 Linear Regression 11 simple linear regression The simple linear regression is given by yi 04 5 6i where 61 are indenpent and N07 02 Here x is called independenceor predictor7 y is called dependence or response The coef cients Oz and B can be estimated by the method of least square 12 general model of linear regression In most case7 we have many dependence variables7 such as temperature7 presure and so on The general linear model is Y o iX1 quot398p71Xp71 6 Suppose we have n observations then the the model can be writen as 1 oii i Mpil p11 Ei 77n If we introduce matrix notation7 Y1 1 11 1124 50 60 YZ 1 21 2124 51 61 Y X 7 6 yn 1 zn1 np71 61271 61271 Then the linear model can be writen as Y X6 E Here X is called designed matrix The Least Square estimator of is B XTX 1XTY 2 Linear Regression with R 21 steps 0 Plot the data xyplot to see whether there is a linear relationship You can add smoother to see the trend or add the the regression line 0 Look for transformation7 etc log Some time after the transformation7 the data is linear 0 Fit the model fm1lt lmy xdata 0 Check the result summaryfm17coeffm17modelmatrix7predict7 tted7resid7con nt 0 Residual Analysis Plot the residual versus tted value to see whether the assumption is satis ed 0 Statistical Inference t test7 F test 22 Examples