Simple Regression in Minitab 1

Transcription

1 Simple Regressin in Minitab 1 Belw is a sample data set that we will be using fr tday s exercise. It lists the heights & weights fr 10 men and 12 wmen. Male Female Height (in) Weight (lb) Height (in) Weight (lb) Entering the data If yu haven t entered the data check the Minitab intrductry tutrial n the prper methd. When yu are finished yu shuld have 3 clumns in yur data view spreadsheet, a sample f which is shwn belw. Creating a scatterplt Befre any type f regressin analysis is begun a simple scatterplt f the data shuld be created. The reasning fr this is twfld. The first and mst imprtant is t verify the quality f yur data. Many times unusual pints and utliers can be identified easily n the plts. Additinally, we can check t see if the assumptins fr linear regressin seem valid mdel fr the data. If there appears t be curvature f the data r nn-hmgenus variance we might nt be able t use simple linear regressin. By clicking n the Graph and then Scatterplt buttn, the scatterplt windw will be pened. Chse the With Grups t graph males and females separately, and click k.

2 Simple Regressin in Minitab 2 We then enter the clumns int the apprpriate areas and the graph will appear in a new windw. It wuld als be beneficial t add a title t the graph. This can be dne by clicking n Labels in the Scatterplt-With Grups windw. As the default setting fr Minitab is t use clr and shapes t differentiate the grups [and mst prints are in black and white]. Yu shuld immediately edit the graph if yu have the same shape within the graph. T d this, duble click n the graph t bring it int edit mde. Click nce n a male symbl n the graph (all symbls will be highlighted). Click nce n a male symbl again (male symbls will be highlighted).duble click a male symbl and the prperties windw shuld appear. Chse a symbl and hit apply. The male symbl shuld change. Nw clse the windw and the graph is dne. [Nte if yu click a third time n a symbl befre duble clicking yu can change the symbl fr a single pint] Yu will nw be able t differentiate the grups if yu d a plt in black and white.

3 Simple Regressin in Minitab 3 (Nte: t change the title r labels just duble click the label and an edit windw will appear. The fnt, fnt size, clr, etc. can als be changed.) Seeing n prblems with the data we can nw run the regressin fr weight versus height. We select Stat-Regressin-Regressin frm the pull-dwn menu.

4 Simple Regressin in Minitab 4 Placing the variable we wuld like t predict, weight, in the dependent variable and the variable we will use fr predictin, height, in the independent variable, we hit OK. This part f the Minitab utput gives R 2, which indicates hw much f the variatin in the respnse variable Y, is explained by the fitted regressin line. We can see that there is a strng relatinship between the 2 variables (75% f the variatin in y is explained by the regressin line), indicating if I knw yur height I shuld be able t make sme predictin abut yur weight. S = R-Sq = 75.6% R-Sq(adj) = 74.3% The next part f the utput is the statistical analysis (ANOVA-analysis f variance) fr the regressin mdel. The ANOVA represents a hypthesis test with where the null hypthesis is H : 0 fr all i (i = 1 t k) i H : 0 fr at least 1 cefficient A i The ANOVA table uses an F-statistic t check the hypthesis. It similar t the Z & T tests, in that large values f F indicate a rare test scre (unusual data) under the null hypthesis and indicate that it is unlikely the null hypthesis is true. The significance level (r p-value) fr the test is less than 0.05, s we wuld reject the null hypthesis and cnclude that at least ne cefficient is nt zer (there is a significant linear relatinship between weight and height). Analysis f Variance Surce DF SS MS F P Regressin Residual Errr Ttal

5 Simple Regressin in Minitab 5 The cefficient table cntains the cefficients fr the least square (fitted) line and ther relative infrmatin abut the cefficients. In the clumn B, the cnstant represents the y-intercept and the Height represents ur slpe. Minitab als generates the regressin equatin autmatically. The regressin equatin is Weight = Height Predictr Cef SE Cef T P Cnstant Height A review f the table als indicates several ther statistical tests that Minitab is perfrming. Yu ll nte that Minitab tests bth f the cefficients t see if they are equal t zer with t-tests. We can see that bth f the cefficients are significantly different frm zer. H : 0 1 H : 1 0 H : 0 H : 0 A A Creating a fitted line plt After yu have created the scatterplt f the data, yu can add a regressin line. When the scatterplt is pen g t the pull-dwn menu Editr-Add-Regressin Fit

6 Simple Regressin in Minitab 6 This brings up the Add Regressin Fit windw. Under Mdel Order chse the Linear ptin (yu can leave the Fit intercept bx checked). Click OK. If yu wish it is als pssible t fit a line t each f the grups n a graph. The easiest way t d this is t make a new scatterplt by ging t the pull-dwn menu Graph-Scatterplt then chsing the With Regressin and Grups ptin. Fill in the X-variable, Y-variable, and Categrical variables the same way yu did befre fr making the first scatterplt. Creating cnfidence intervals n the regressin cefficients Cnduct the regressin as befre but select Stat-Regressin-General Regressin frm the pull-dwn menu. In the General Regressin windw select the Results buttn at the bttm. This will bring up the General Regressin-Results windw. Check the Display cnfidence intervals bx under the Cefficient table sectin. Click OK. Then run the test.

7 Simple Regressin in Minitab 7 The fllwing table will be created in yur utput: Cefficients Term Cef SE Cef T P 95% CI Cnstant ( , ) Height ( 5.590, 9.626) Creating fitted values with cnfidence & predictin intervals Cnduct the regressin as befre by selecting Stat-Regressin-Regressin frm the pulldwn menu. In the Regressin windw select the Optins buttn at the bttm. This will bring up the Regressin-Optins windw. Under Predictin intervals fr new bservatins: put the variable yu are interested in predicting. Then check the Cnfidence limits bx and click OK. Click OK t run the test, a new part f the utput will lk like the image belw, with CI and PI fr each bservatin given based n the variable yu were interested in.