Linear Regression with R

Linear Regression:

Yi = beta0 + beta1Xi + ei

lm(y~x, tab)   #y dependent variable, x regressor
coef(lm(y~x, tab))  #estract the coefficient beta0 and beta1
summary(lm(y~x, tab))   #detailed summary

To print only a parameter:

summary(lm(y~x, tabella))$sigma   #only residual sd

To plot the regression line (g is a pre builded graph):

g + geom.smooth(method="lm", formula=y~x)   #formula is optional (y~x is the default)

I() if I want to use a function:

lm(y~I(x-mean(x)), data=tab))

beta1 (slope) unchanged (y increase for each increase of x)
beta0 (intercept) became y expected for each average value of x

To predict using the regression line:

Predict(lm(y~x, tab), newdata=data.frame(x=z))   #z is a vector with x values

Residuals:

resid(lm(y~x, tab))

Without "newdata" it uses the lm parameters, so it calculates residuals for each x and y

SUMMARY LM FUNCTION

model <- lm(y ~ 1) Intercept only (no slope coefficient)
model <- lm(y ~ x - 1) Slope only (no intercept coefficient)
model <- lm(y ~ x) Intercept & slope (x is not a factor)
model <- lm(y ~ w) Intercepts only (w is a factor)
model <- lm(y ~ x + w) Intercepts & slope against confounding x & w
model <- lm(y ~ x * w) Intercepts & slopes against interacting x & w

lm(y ~ 1) yhat = B0
lm(y ~ x - 1) yhat = B1x
lm(y ~ x) yhat = B0 + B1x
lm(y ~ w) yhat = B0 + B2w
lm(y ~ x + w) yhat = B0 + B1x + B2w
lm(y ~ x \ w) yhat = B0 + B1x + B2w + B3x\w

lm(y ~ I(log(x)) + w) yhat = B0 + B1log(x) + B2w
lm(y ~ I(log(x)) * w) yhat = B0 + B1log(x) + B2w + B3*log(x)*w