Page 348 - Applied Statistics with R

348 CHAPTER 14. TRANSFORMATIONS

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quad_fit = lm(y ~ x + I(x^2), data = quad_data)
summary(quad_fit)

##
## Call:
## lm(formula = y ~ x + I(x^2), data = quad_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.4167 -3.0581 0.2297 3.1024 12.1256
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.0649 0.9577 3.200 0.0016 **
## x -0.5108 0.8637 -0.591 0.5549
## I(x^2) 5.0740 0.1667 30.433 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.531 on 197 degrees of freedom
## Multiple R-squared: 0.9853, Adjusted R-squared: 0.9852
## F-statistic: 6608 on 2 and 197 DF, p-value: < 2.2e-16

plot(y ~ x, data = quad_data, col = "grey", pch = 20, cex = 1.5,
main = "Simulated Quadratic Data")
curve(quad_fit$coef[1] + quad_fit$coef[2] * x + quad_fit$coef[3] * x ^ 2,
from = -5, to = 30, add = TRUE, col = "darkorange", lwd = 2)