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 and C3 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 Y b0 b1 X where b0 0 833 and b1 0 667 is printed out This is followed by a short table that repeats in the Coef column the coefficients b0 and b1 The quantities in the Stdev column are the two standard deviations sb0 and sb1 In the t ratio column are the two ratios t t b1 0 which are used to test sb1 H10 0 0 H11 0 0 and b0 0 and sb0 H 20 1 0 Finally in H 21 1 0 the 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 b0 and thus say that the intercept is not significant Similarly since the second p value is below the significance level we reject the null hypothesis for b1 and say that the slope is significant s is the standard error se which is used in computing t tests and confidence intervals R sq is of course R 2 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 hypothesis tested 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 Y predicted by the equation Y b0 b1 X 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 and predicted values plotted on the same axes and thus enables us to connect the predicted points to show the regression line compared to the actual points The actual commands used here which produce a color plot are explained in the MINITAB Handbook under High Resolution Graphics 252regrex1 9 20 99 Minitab Output Worksheet size 100000 cells MTB Retrieve C MINITAB FAMDAT MTW Retrieving worksheet from file C MINITAB FAMDAT MTW Worksheet was saved on 4 1 1998 MTB print y x Data Display Row Y X 1 2 3 4 5 6 7 8 9 10 0 2 1 3 1 3 4 2 1 2 0 1 2 1 0 3 4 2 2 1 MTB plot y x 4 Y 3 2 1 0 0 1 2 X 3 4 252regrex1 9 20 99 MTB regress y on 1 x resid pred Regression Analysis The regression equation is Y 0 833 0 667 X Predictor Constant X Coef 0 8333 0 6667 s 0 9014 Stdev 0 4751 0 2375 R sq 49 6 t ratio 1 75 2 81 p 0 117 0 023 R sq adj 43 3 Analysis of Variance SOURCE Regression Error Total DF 1 8 9 SS 6 4000 6 5000 12 9000 MS 6 4000 0 8125 F 7 88 p 0 023 MTB print y x resid pred Data Display Row Y X RESID PRED 1 2 3 4 5 6 7 8 9 10 0 2 1 3 1 3 4 2 1 2 0 1 2 1 0 3 4 2 2 1 1 08786 0 59300 1 37281 1 77900 0 21757 0 21155 0 78446 0 19612 1 37281 0 59300 0 83333 1 50000 2 16667 1 50000 0 83333 2 83333 3 50000 2 16667 2 16667 1 50000 MTB plot pred x PRED 3 2 1 0 1 2 X 3 4 252regrex1 9 20 99 MTB SUBC SUBC SUBC SUBC plot y x pred x symbol type 3 1 color 8 9 overlay 4 Y 3 2 1 0 0 1 2 X MTB stop 3 4
View Full Document
Unlocking...