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I am trying to understand the significance of the intercept in my model. The model was created using

lm.fit <-lm(target ~ .,train)

and the intercept figures were

                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)              -1.783e+02  8.587e+01  -2.076  0.03809 *

Then the model was pruned using

sw.fit = step(lm.fit,trace=0,k=log(nrow(train)),direction="both")

and the intercept figures became

                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)              16.196874   0.282901  57.253  < 2e-16 ***

I understand that in writing out the new formula I would have something like

y = 16.20 + the rest

which is easier to think about than the previous

y = -178 + the rest

It seems as if my accuracy has gone up ( the better P value) but the Std.Error has gone from approx 85 to 0.28 and the T value has gone from approx -2 to 57

I understand that the T value is the estimate divided by the standard error. Thus a smaller standard error causes a larger T-value. I read that

the standard error of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation

Why does the pruning decrease the standard error of the intercept?

Kirsten
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  • https://stats.stackexchange.com/questions/18208/how-to-interpret-coefficient-standard-errors-in-linear-regression/18213#18213 – Kirsten Nov 13 '20 at 18:10
  • https://stats.stackexchange.com/questions/344006/understanding-t-test-for-linear-regression – Kirsten Nov 13 '20 at 19:44
  • https://www.khanacademy.org/math/ap-statistics/tests-significance-ap/one-sample-t-test-mean/v/calculating-p-value-from-t-statistic – Kirsten Nov 13 '20 at 19:51
  • like high Z values, high T values indicate increased certainty. ( i.e we look up Z tables and T tables) – Kirsten Nov 13 '20 at 20:47

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