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`Applied Linear Statistical ModelsDiagnostic Methods - F Tests for Lack of Fit Dr. DH JonesExample: Bank DataX is the minimal deposit to receive gift, Y the number of new savings accounts opened. Each case represents the experience at unique bank branches. Scatter plot of data clearly shows that the simple linear model does not fit the data. Note the replications at most of the X's.ScatterplotANOVA TableANOVA aModel 1Regression Residual TotalSum of Squares 5141.34 14741.6 19882.9df 1 9 10Mean Square 5141.34 1637.95F 3.139Sig. .110ba. Dependent Variable: ACCOUNTS b. Independent Variables: (Constant), DEPOSITFormula for SSE with ReplicationsYij represents the ith case of the jth replication group  SSE =   Yij - Yij()2Note: Fitted values of the same jth replication group are all the sameComponents of the Sum of Squares for Error  Yij - Yij = Yij - Y j + Y j - Yij  (Y(ij - Yij) =   (Y2) ()- Yjij) +   (Y2j - Yij)2SSE = SSPE + SSLF n - 2 = ( n - c) + ( c - 2)Note: The Sum of Squares for Pure Error SSPE is also called the &quot;Within Groups Sum of Squares.&quot; Note: The Sum of Squares for Lack of Fit SSLF is also called the &quot;Sum of Squares Deviation from Linearity.&quot;Example: Box Plot of Bank Data Residuals from Fitted Line with Group Means.Expected Values of Mean SquaresE{ MSPE} =  2 E{ MSLF } =  2 + n j µ j - 0 + 1 X jc-2[ ()]2Example: Bank Data ANOVA TableANOVA TableACCOUNTS * DEPOSITBetween Groups(Combined) Linearity Deviation from LinearitySum of Squares 18734.9 5141.34 13593.6 1148.00 19882.9df 5 1 4 5 10Mean Square 3746.98 5141.34 3398.39 229.600F 16.320 22.393 14.801Sig. .004 .005 .006Within Groups Total`

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Applied Linear Statistical Models

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