This function performs the univariate linear
regression y ~ x separately for each column x of X. Each regression
is implemented using `.lm.fit()`

. The estimated effect size
and stardard error for each variable are outputted.

```
univariate_regression(
X,
y,
Z = NULL,
center = TRUE,
scale = FALSE,
return_residuals = FALSE
)
```

## Arguments

- X
n by p matrix of regressors.

- y
n-vector of response variables.

- Z
Optional n by k matrix of covariates to be included in all
regresions. If Z is not `NULL`

, the linear effects of
covariates are removed from y first, and the resulting residuals
are used in place of y.

- center
If `center = TRUE`

, center X, y and Z.

- scale
If `scale = TRUE`

, scale X, y and Z.

- return_residuals
Whether or not to output the residuals if Z
is not `NULL`

.

## Value

A list with two vectors containing the least-squares
estimates of the coefficients (`betahat`

) and their standard
errors (`sebetahat`

). Optionally, and only when a matrix of
covariates `Z`

is provided, a third vector `residuals`

containing the residuals is returned.

## Examples

```
set.seed(1)
n = 1000
p = 1000
beta = rep(0,p)
beta[1:4] = 1
X = matrix(rnorm(n*p),nrow = n,ncol = p)
X = scale(X,center = TRUE,scale = TRUE)
y = drop(X %*% beta + rnorm(n))
res = univariate_regression(X,y)
plot(res$betahat/res$sebetahat)
```