learning R-understanding calculations for specific variable Clarify why the prediction for a female in the example below in related topics (taken from a question by @MsSnowy) do we use the new calculations and not the original lm:
fitted.model <- lm(spending ~ sex + status + income, data=spending), 
my results were as follows:
Coefficients:
                       Estimate  Std. Error t value   Pr(>|t|)    
(Intercept)    22.55565   17.19680   1.312   0.1968    
sex         **-22.11833**  8.21111  -2.694   0.0101 *  
status          0.05223    0.28111   0.186   0.8535    
income          4.96198    1.02539   4.839 1.79e-05 ***
verbal         -2.95949    2.17215  -1.362   0.1803 

Now, the new model is sex and all other predictors constant in lm model
mydata<-lm(spending ~ sex, data=spending)
was
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   29.775      5.498   5.415 2.28e-06 ***
**sex        **-25.909****    8.648  -2.996  0.00444 ** 

Question: Why isn't the prediction that females spend less than 22.118 (from the 1st lm) than males but rather the new lm coefficient value of less than -25.909? 
Someone please clarify because I would think its the first lm for prediction.
 A: Without the data it is hard to tell exactly, but it is most likely that there is some relationship between sex and at least one of the other 2 variables.
For example, if in the dataset females have a lower income on average then males then we would expect to see the above.  In the first model you are looking at the effect of sex above and beyond the effects of income and verbal.  In the second model you are looking only at sex, so any information that would have come from income gets merged into the sex effect.  The first model suggests that for male and female with the same income and verbal that the female will spend on average 22 less.  In the second model you don't include the information on income and verbal so we cannot compare a male and a female that are the same on income and verbal, just the average accross all males and females.  So the amount that females spend less than males includes the 22 from above, but also includes the lower spending due to lower income on average (or differences in verbal, but it is less clear what that measure is and likely differences).
The only time that two models with different sets of predictors will give the same estimates of the slopes are if the variables are perfectly orthogonal.
