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I construct a liner model.But the results are either diffetent or same when the model be complicated or easy repectively. Is there someone know the reason?

This is the different results.

> lm_all <- lm(mtci_ac~sd_height+density+ORA+dry_weight+northess,data=at_growth)
> summary(lm_all)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.480e-01  3.984e-02   6.225 1.33e-07 ***
sd_height    1.106e-02  1.045e-02   1.058    0.295    
density      1.006e-01  1.481e-01   0.679    0.501    
ORA         -3.397e-04  1.361e-03  -0.250    0.804    
dry_weight   5.045e-06  1.636e-05   0.308    0.759    
northess     5.077e-03  3.203e-02   0.159    0.875    
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> anova(lm_all)
Analysis of Variance Table

Response: mtci_ac
           Df  Sum Sq   Mean Sq F value  Pr(>F)  
sd_height   1 0.02525 0.0252488  3.3059 0.07555 .
density     1 0.00469 0.0046852  0.6135 0.43750  
ORA         1 0.00006 0.0000560  0.0073 0.93214  
dry_weight  1 0.00074 0.0007426  0.0972 0.75659  
northess    1 0.00019 0.0001919  0.0251 0.87475  
Residuals  46 0.35132 0.0076374                  
---

This is the same results.

> lm_all <- lm(mtci_ac~sd_height,data=at_growth)
> anova(lm_all)
Analysis of Variance Table

Response: mtci_ac
          Df  Sum Sq   Mean Sq F value  Pr(>F)  
sd_height  1 0.02525 0.0252488  3.5363 0.06587 .
Residuals 50 0.35700 0.0071399                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(lm_all)

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.261539   0.019209   13.62   <2e-16 ***
sd_height   0.013703   0.007287    1.88   0.0659 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


ChuDingjin
  • 11
  • 3
  • By "same result", I assume you mean the p-values are identical. This happens in the *simple* linear regression case, basically because the F-value is then the square of the t-value, and 2*p(t>x) = p(F>x^2), for a t(n) and a F(1,n) distribution. More information about this for instance [here](https://online.stat.psu.edu/stat462/node/77/), see 3.5-3.7 for the simple regression and 5.5-5.7 for the multiple regression. –  Oct 13 '22 at 08:04

0 Answers0