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I have full model summary:

lm(formula = Swir2ref ~ x1 + y1 + x2 + y2)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0219319 -0.0061738 -0.0000579  0.0060872  0.0197778 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    

(Intercept)  0.637722   0.029059  21.946  < 2e-16 ***

x1           0.040600   0.004534   8.954 5.24e-13 ***

y1          -0.012630   0.032577  -0.388  0.69950    

x2          -4.438403   1.642197  -2.703  0.00874 ** 

y2          -1.502393   0.724077  -2.075  0.04190 *  
---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.009531 on 66 degrees of freedom
Multiple R-squared:  0.579, Adjusted R-squared:  0.5535 
F-statistic: 22.69 on 4 and 66 DF,  p-value: 8.043e-12

I have summary of interaction model:

    lm(formula = Swir2ref ~ x1 + y1 + x2 + y2 + x1 * y1)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0199133 -0.0059021 -0.0008173  0.0061518  0.0204091 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.72335    0.05054  14.313  < 2e-16 ***
x1           0.19106    0.07361   2.596  0.01166 *  
y1          -0.25164    0.12098  -2.080  0.04146 *  
x2          -4.52826    1.60445  -2.822  0.00632 ** 
y2          -1.47253    0.70732  -2.082  0.04130 *  
x1:y1       -0.41058    0.20050  -2.048  0.04462 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.009309 on 65 degrees of freedom
Multiple R-squared:  0.6045,    Adjusted R-squared:  0.5741 
F-statistic: 19.87 on 5 and 65 DF,  p-value: 5.767e-12

My question is in the full model there is y2 is insignificant, but for the interaction model it is significant. What would be the reason? Help will be appreciated. Thank you!

ychaulagain
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  • Do you mean y1? Because y2 looks to be significant in both models... – Pyll Sep 11 '17 at 17:03
  • yes, I am sorry. It should be y1. –  Sep 11 '17 at 17:04
  • This is not a programming question. If you need help with the interpretation of statistical models, you should be asking such questions over at [stats.se], not Stack Overflow. – MrFlick Sep 11 '17 at 17:31

1 Answers1

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I started typing a response, but @Glen_b said it really well...

https://stats.stackexchange.com/questions/160026/why-does-an-insignificant-regressor-become-significant-if-i-add-some-significant

There are two main reasons this can happen.

Adding a significant regressor - whether related to dummies or not - reduces the mean square residual. By reducing estimate of error variance, other regressors may become more significant even if the parameter estimate hardly changes, by reducing the denominator of their t-statistic (equivalently, their partial F). This one needn't involve any dependence between regressors at all.

Adding a regressor can also change the numerator of the t-statistic, by changing the parameter estimate, due to dependence between regressors, which can move coefficients either toward or away from zero; it will also alter the denominator (so it's not as simple as just considering the numerator). Sometimes the overall effect can be to make a previously insignificant regressor significant.

Pyll
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