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 + B3xw

lm(y ~ I(log(x)) + w)     yhat = B0 + B1log(x) + B2w
lm(y ~ I(log(x)) * w)      yhat = B0 + B1log(x) + B2w + B3log(x)w