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I have created two Linear regression models on some social media data - one with outliers and one without outliers.

The one with outlier is giving below summary -

Residuals:
    Min      1Q  Median      3Q     Max 
-113420  -18903   -8995    1668 1039786 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       1.634e+05  6.311e+04   2.589  0.00997 ** 
Page.total.likes -9.758e-01  6.817e-01  -1.431  0.15311    
Category         -1.133e+04  4.406e+03  -2.571  0.01048 *  
Post.Month        1.430e+02  3.449e+03   0.041  0.96695    
Post.Weekday      1.746e+02  1.785e+03   0.098  0.92215    
Post.Hour        -7.046e+02  8.579e+02  -0.821  0.41194    
Paid              2.616e+03  8.164e+03   0.320  0.74885    
comment           7.068e+02  3.801e+02   1.859  0.06369 .  
like              1.285e+02  2.642e+01   4.864 1.64e-06 ***
share            -6.884e+02  2.459e+02  -2.800  0.00535 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74550 on 411 degrees of freedom
  (5 observations deleted due to missingness)
Multiple R-squared:  0.1789,    Adjusted R-squared:  0.1609 
F-statistic: 9.951 on 9 and 411 DF,  p-value: 7.437e-14

The one without outlier is giving below summary -

Residuals:
   Min     1Q Median     3Q    Max 
-62173 -12336  -6056   4175 220899 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       1.065e+04  2.532e+04   0.421  0.67428    
Page.total.likes  2.824e-01  2.721e-01   1.038  0.29993    
Category         -1.077e+04  1.783e+03  -6.038 3.55e-09 ***
Post.Month       -2.189e+03  1.366e+03  -1.603  0.10969    
Post.Weekday     -7.569e+02  7.056e+02  -1.073  0.28406    
Post.Hour        -1.375e+02  3.389e+02  -0.406  0.68507    
Paid              8.777e+03  3.239e+03   2.710  0.00703 ** 
comment          -8.732e+01  2.231e+02  -0.391  0.69571    
like              8.359e+01  1.101e+01   7.590 2.24e-13 ***
share             5.481e+00  1.187e+02   0.046  0.96320    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 29280 on 403 degrees of freedom
  (5 observations deleted due to missingness)
Multiple R-squared:  0.326, Adjusted R-squared:  0.311 
F-statistic: 21.66 on 9 and 403 DF,  p-value: < 2.2e-16

When I refer to estimate column for 'like', I see in the model with outliers each unit increase in like increments target by 128 units, where as same value is 84 in the model without ouliers.But the p-value for like in the 2nd model without outliers is way lesser than 1st model.So can we say the impact of 'like' co-efficient is lesser in the 2nd model? F-statistic and Adj. R square value is better in 2nd model.Certainly the model without outliers will give better response, but I am having this confusion over p-value in 'like'.

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  • $\begingroup$ You appear to have about 75,000 observations but less than 30,000 without "outliers." One can scarcely justify calling 60 percent of one's data "outlying!" $\endgroup$
    – whuber
    Apr 10, 2019 at 13:35
  • $\begingroup$ Actually some insignificant columns were deleted manually before finding outliers.Thats the reason for low no. of records.I am confused over 'like' value.It's estimate value is less in 2nd model but p-value(Pr) is better in 2nd model.So is it importance of 'like' is diminished in 2nd case? $\endgroup$
    – Ran
    Apr 10, 2019 at 16:37

1 Answer 1

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For both models, the p-values are very, very small. These mean that it's very unlikely that the effect of variable "like" is 0. The linearly-proportional effects of "like" on the response variable is lesser in the second model, where the response variable in the first model accounted for 128 unit changes in the response variable per one unit change in "like" and the second model accounted for 84 unit changes in the response variable per one unit change in "like". The data transform in the second model did indeed show a diminished effect, and in both models the effect of "like" is unlikely to be 0.

It's important to not interpret the p-value as a metric describing the strength of "like" on your response variable because is conveys not the strength, but the probability that you observed the relationship given that there's actually no relationship. HTH.

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