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252regrex1 9/20/99 MINITAB EXAMPLE Simple Regression Explanation: The data set has already been prepared and stored as famdat.mtw. Column 1 (C1) is labeled ‘Y’, C2 is labeled ‘X’, C3 is labeled ‘RESID’ and C4 is labeled ‘PRED’. C1 and C2 contain the data andC3 and C4 are blank. The data set is retrieved, plotted, and printed out. Then the command for simple regression is given. In the command, the words ‘on 1’ indicate that there is only one independent variable. The equation of the regression line (XbbY10, where 833.00b and667.01b) is printed out. This is followed by a short table that repeats in the ‘Coef’ column the coefficients 0b and 1b. The quantities in the ‘Stdev’ column are the two standard deviations 0bs and 1bs. In the ‘t-ratio’ column, are the two ratios 000bsbt and101bsbt, which are used to test 0:0:011010HH and 0:0:121120HH. Finally, inthe ‘p’ column are the p-values for the two null hypotheses. If we assume that 05., since the first p-value is 0.117, which is above the significance level, we do not reject the null hypothesis for 0b, and thus say that the intercept is not significant. Similarly, since thesecond p-value is below the significance level, we reject the null hypothesis for 1b and say that the slope is significant. ’s’ is the standard error es, which is used in computing t-tests and confidence intervals. ‘R-sq’ is, of course, 2R. An analysis of variance table now appears. Note that the value of F that is shown is the square of the t-ratio used to test the hypothesis that the slope is zero, and that the p-values are the same. This is because the hypothesis that the slope is zero and the hypothesistested by the analysis of variance are equivalent in simple regression.A printout of the original data follows with two new columns added. The column labeled ‘RESID’ seems to be a standardized residual, and can be ignored. The column labeled ‘PRED’ is the value of Y (Yˆ) predicted by the equation XbbY10, using the values of ‘X’ . The next graph shows the values of ‘PRED’ plotted against ‘X’. These are the regression line. The final graph shows both the actual andpredicted values plotted on the same axes, and thus enables us to connect the predicted points to show the regression line compared to theactual points. The actual commands used here, which produce a color plot, are explained in the MINITAB Handbook under “High Resolution Graphics.”252regrex1 9/20/99Minitab Output:Worksheet size: 100000 cellsMTB > Retrieve 'C:\MINITAB\FAMDAT.MTW'.Retrieving worksheet from file: C:\MINITAB\FAMDAT.MTWWorksheet was saved on 4/ 1/1998MTB > print 'y''x'Data Display Row Y X 1 0 0 2 2 1 3 1 2 4 3 1 5 1 0 6 3 3 7 4 4 8 2 2 9 1 2 10 2 1MTB > plot 'y'*'x'0 1 2 3 401234XY252regrex1 9/20/99MTB > regress 'y' on 1 'x' 'resid''pred'Regression AnalysisThe regression equation isY = 0.833 + 0.667 XPredictor Coef Stdev t-ratio pConstant 0.8333 0.4751 1.75 0.117X 0.6667 0.2375 2.81 0.023s = 0.9014 R-sq = 49.6% R-sq(adj) = 43.3%Analysis of VarianceSOURCE DF SS MS F pRegression 1 6.4000 6.4000 7.88 0.023Error 8 6.5000 0.8125Total 9 12.9000MTB > print 'y''x''resid''pred'Data Display Row Y X RESID PRED 1 0 0 -1.08786 0.83333 2 2 1 0.59300 1.50000 3 1 2 -1.37281 2.16667 4 3 1 1.77900 1.50000 5 1 0 0.21757 0.83333 6 3 3 0.21155 2.83333 7 4 4 0.78446 3.50000 8 2 2 -0.19612 2.16667 9 1 2 -1.37281 2.16667 10 2 1 0.59300 1.50000MTB > plot 'pred'*'x'0 1 2 3 4123XPRED252regrex1 9/20/99MTB > plot 'y'*'x' 'pred'*'x';SUBC> symbol;SUBC> type 3 1;SUBC> color 8 9;SUBC> overlay.MTB > stop0 1 2 3


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WCU ECO 252 - Simple Regression

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