Regressions-Statistik

[BenediktXVI]

Hi,

könntest Du offen legen wie Du gerechnet hast?

Gruß,

el_horst

ungefähr so:

Now you are ready to rerun the regression analysis with the corrected data. Simply repeat the menu selection you made earlier; the Regression dialog box and Graphs subdialog box contain the same settings as before. You are ready to go!

1 First, close all the graphs that you created before correcting the data. Choose Window > Close All Graphs. Click OK.

2 Choose Stat > Regression > Regression. Click OK.

Tip
To reset a dialog box to its defaults, press [F3].


As before, Minitab displays the text output in the Session window, and displays each of the three graphs in its own Graph window. First, look at the Session window output.

Regression Analysis: Weight versus D2H



The regression equation is

Weight = 0.0200 + 0.00829 D2H



Predictor Coef SE Coef T P

Constant 0.01999 0.01365 1.46 0.160

D2H 0.0082897 0.0002390 34.68 0.000



S = 0.0387993 R-Sq = 98.5% R-Sq(adj) = 98.4%



Analysis of Variance



Source DF SS MS F P

Regression 1 1.8108 1.8108 1202.88 0.000

Residual Error 18 0.0271 0.0015

Total 19 1.8379



Unusual Observations



Obs D2H Weight Fit SE Fit Residual St Resid

12 126 1.11000 1.06491 0.02142 0.04509 1.39 X

17 107 0.79000 0.90858 0.01740 -0.11858 -3.42R



R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.


If you have a good model and have satisfied all the statistical assumptions, then you can measure the diameter and height of any poplar in this population and be able to predict its weight without actually weighing it.

From the regression output, you see a high t-ratio and a low p-value for D2H in the table of coefficients, indicating strong evidence of a relationship between D2H and Weight. The large F-statistic and low p-value in the analysis of variance table quantify this relationship in a different way. The R2 and adjusted R2 values of greater than 98% further reinforce the assertion that there is a strong linear relationship between D2H and Weight.

Before making a final conclusion, however, you decide to look at the plots: Normal Probability Plot of the Residuals, Histogram of the Residuals, and Residuals Versus D2H.








You notice from the Residuals Versus D2H plot that the variance does not appear to be constant - an important assumption for a regression model to meet. The variance becomes larger as D2H increases. In the interest of time, you can continue with this session, but this nonconstant variance is something you should examine more closely.