Regessão: Estudando os coeficientes não padronizados e padronizados

 setwd("~/Dropbox/R Stat")

Análise de regressão simples

# Abrir banco de dados
load("senna.RData")
# Análise da correlação simples entre Notas e Auto gestão
fit <- lm( m_notas~F1.Cons, data=sennav1)
summary(fit)

Call:
lm(formula = m_notas ~ F1.Cons, data = sennav1)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.6174 -0.6358  0.0137  0.6415  3.4231 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   4.9825     0.5480   9.092 4.49e-13 ***
F1.Cons       0.6682     0.1519   4.400 4.27e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.044 on 63 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.235, Adjusted R-squared:  0.2229 
F-statistic: 19.36 on 1 and 63 DF,  p-value: 4.267e-05

library(sjPlot)
sjt.lm(fit, show.std = TRUE)

sjt.lm(fit, show.std = TRUE)$knitr

Análise de regressão simples padronizando o preditor X, depois Y

library(psych)
describe(sennav1[ , c("m_notas", "F1.Cons")])

        vars  n mean   sd median trimmed  mad  min  max range  skew kurtosis   se
m_notas    1 65 7.33 1.18   7.33    7.33 1.27 4.67 9.88  5.21  0.00    -0.66 0.15
F1.Cons    2 66 3.50 0.85   3.36    3.51 0.86 1.22 5.00  3.78 -0.17    -0.27 0.11

# Cria novas variáveis mudando a métrica original para para M=0 e DP=1 (escore z)
sennav1$m_notasz <- scale(sennav1$m_notas)
sennav1$F1.Consz <- scale(sennav1$F1.Cons)
describe(sennav1[ , c("m_notasz", "F1.Consz")])

         vars  n mean sd median trimmed  mad   min  max range  skew kurtosis   se
m_notasz    1 65    0  1   0.01    0.00 1.07 -2.24 2.15  4.40  0.00    -0.66 0.12
F1.Consz    2 66    0  1  -0.16    0.02 1.01 -2.67 1.76  4.43 -0.17    -0.27 0.12

plot(sennav1$F1.Consz, sennav1$F1.Cons)
# Regressão com a  X padronizado. 
fit2 <- lm( m_notas ~ F1.Consz , data=sennav1)
sjt.lm(fit2, show.std =  TRUE)
summary(fit2)

Call:
lm(formula = m_notas ~ F1.Consz, data = sennav1)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.6174 -0.6358  0.0137  0.6415  3.4231 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   7.3218     0.1295   56.54  < 2e-16 ***
F1.Consz      0.5704     0.1297    4.40 4.27e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.044 on 63 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.235, Adjusted R-squared:  0.2229 
F-statistic: 19.36 on 1 and 63 DF,  p-value: 4.267e-05

# Regressão com a  X e Y padronizado. Note os parâmetros B e Std B 
fit3 <- lm( m_notasz ~ F1.Consz , data=sennav1)
sjt.lm(fit3, show.std =  TRUE)
summary(fit3)

Call:
lm(formula = m_notasz ~ F1.Consz, data = sennav1)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.20991 -0.53682  0.01157  0.54162  2.89017 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.002901   0.109343  -0.027    0.979    
F1.Consz     0.481638   0.109472   4.400 4.27e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8815 on 63 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.235, Adjusted R-squared:  0.2229 
F-statistic: 19.36 on 1 and 63 DF,  p-value: 4.267e-05

		m_notas
		B	CI	std. Beta	CI	p
(Intercept)		7.32	7.06 – 7.58			<.001
F1.Consz		0.57	0.31 – 0.83	0.48	0.27 – 0.70	<.001
Observations		65
R2 / adj. R2		.235 / .223

		B	CI	std. Beta	CI	p
(Intercept)		-0.00	-0.22 – 0.22			.979
F1.Consz		0.48	0.26 – 0.70	0.48	0.27 – 0.70	<.001
Observations		65
R2 / adj. R2		.235 / .223