How detrend a line if i know the slope? [closed]

Question

I am using linear regression to get the slope of some data. If i know the slope how can i flatten the line so that it has no slope?

Answer 1

If you have the dataset $y_i = \beta x_i + \epsilon_i$ and you use linear regression to obtain the least square estimate $\hat{\beta}$, your fitted values are $\hat{y}_i = \hat{\beta}x_i$. Therefore, you detrend your dataset by calculating the difference $y_i - \hat{y}_i$.

Here an R example:

## generate a dataset and plot it
x = 1:20                 # predictor variable
y = 0.5*x + rnorm(length(x), 0,1) # response variable = slope + noise
plot(x,y)                # plot data

## now fit the data
df     = data.frame(x,y) # generate a dataframe
fit.lm = lm(y~x, df)     # linear regression
summary(fit.lm)          # display result of lin. reg. => get estimator of the slope

## Obtain the residual of the fit = retreaded data
yHat    = fitted(fit.lm) # get the fitted values
epsilon = y - yHat       # one way to obtain residuals

## There exists more direct ways to obtain the residual:
resid(fit.lm)            # second way to obtain residuals
fit.lm$residuals         # third way