정리를 위한 블로그

> x <- c(1,2,3,4,5,6,7,8,9)

> y <- c(5,3,2,3,4,6,10,12,18)

> df1 <- data.frame(x,y)

> plot(df1)

> x2 <- x^2

> m <- lm(y~x, data=df1)

> m

Call:

lm(formula = y ~ x, data = df1)

Coefficients:

(Intercept)            x  

     -1.167        1.633  

> summary(m)

Call:

lm(formula = y ~ x, data = df1)

Residuals:

    Min      1Q  Median      3Q     Max 

-3.0000 -2.3667 -0.2667  0.9000  4.5333 

Coefficients:

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

(Intercept)  -1.1667     2.2296  -0.523  0.61694   

x             1.6333     0.3962   4.122  0.00445 **

---

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

Residual standard error: 3.069 on 7 degrees of freedom

Multiple R-squared:  0.7083, Adjusted R-squared:  0.6666 

F-statistic: 16.99 on 1 and 7 DF,  p-value: 0.004446

> 

> df2 <- cbind(x2,df1)

> lm(y~x+x2,data=df2)

Call:

lm(formula = y ~ x + x2, data = df2)

Coefficients:

(Intercept)            x           x2  

     7.1667      -2.9121       0.4545  

> summary(lm(y~x+x2,data=df2))

Call:

lm(formula = y ~ x + x2, data = df2)

Residuals:

    Min      1Q  Median      3Q     Max 

-0.9606 -0.1606  0.0303  0.2242  0.9455 

Coefficients:

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

(Intercept)  7.16667    0.78728   9.103 9.87e-05 ***

x           -2.91212    0.36149  -8.056 0.000196 ***

x2           0.45455    0.03526  12.893 1.34e-05 ***

---

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

Residual standard error: 0.6187 on 6 degrees of freedom

Multiple R-squared:  0.9898, Adjusted R-squared:  0.9864 

F-statistic: 292.2 on 2 and 6 DF,  p-value: 1.05e-06