Question

if we make a linear regression model and we got low r² we look to the casewise daignostic information of the set of points that having st. deviation for example 2 and more, and we have the folloing information case number, std.residual, dependent value, predicted value and risudual. which case number delete first to got a max.r² regression model

look to image

Casewise Diagnosticsa,

N/ Std. Residual /RT /Predicted Value/ Residual

8 2.445 .86000 .5123167 .34768325

14 2.211 .88000 .5655977 .31440228

53 -2.129 .21000 .5127622 -.30276217

96 2.237 .91300 .5948380 .31816197

126 2.151 .81000 .5041431 .30585693

134 2.174 .80600 .4968071 .30919294

155 -2.028 .24700 .5354094 -.28840936

188 -2.005 .24700 .5321719 -.28517186

228 -2.058 .24200 .5347141 -.29271412

236 -2.057 .21000 .5025825 -.29258252

244 -2.023 .21200 .4997483 -.28774833

246 2.102 .83600 .5371107 .29888933

259 2.375 .85600 .5182902 .33770981

271 2.399 .91100 .5697906 .34120940

305 -2.034 .28000 .5692569 -.28925695

320 2.275 .94600 .6224150 .32358496

326 2.130 .84200 .5391055 .30289446

393 2.152 .87000 .5639231 .30607686

400 2.337 .87300 .5407160 .33228400

401 -2.038 .27700 .5668742 -.28987422

516 2.330 .91300 .5815944 .33140562

543 2.218 .80600 .4905374 .31546256

544 2.086 .80600 .5093900 .29661003

642 2.028 .77300 .4846380 .28836200

650 2.078 .88500 .5895640 .29543602

673 2.268 .88000 .5575039 .32249609

694 2.242 .87600 .5572246 .31877543

696 2.085 .87700 .5804693 .29653065

763 2.275 .80700 .4834668 .32353318

765 -2.044 .31700 .6077117 -.29071171

775 2.328 .88000 .5488906 .33110944

798 2.397 .84000 .4990831 .34091690

a Dependent Variable: RT

b Linear Regression through the Origin

question can we use b and remove constant from the eq. to have good r^2 explain please

Answer 1

casewise results give the cases which are 2 or more standard deviations away from the mean. so these cn be treated as outliers. clearly such residuals will lower the R^2 value. So we should remove these cases and rerun the model for a better R^2

besides the number of such cases seem to be less than 5% so we need not worry about data loss

rember just remve the row number given by N in the above table

Regression through orgin makes sense only when we can see that y=0 when x=0 makes sense for the data at hand. It may increase or decrease the r^2 depending on the data. For example if you were predicitng stopping distance of a car which speed. if spped is 0 stopping distnace should be zero.

In this case, we should run a lm test to compare models with and without intercept. Just a casewise regression would not work