(Prediction Intervals "without" `predict`)

how to write a function named `calc_pred_int` that performs calculates prediction intervals:

$$

\hat{y}(x) \pm t_{\alpha/2, n - 2} \cdot s_e\sqrt{1 + \frac{1}{n}+\frac{(x-\bar{x})^2}{S_{xx}}}.

$$

for the linear model

$$

Y_i = \beta_0 + \beta_1 x_i + \epsilon_i.

$$

**(a)** with this function. You may use the `predict()` function, but you may **not** supply a value for the `level` argument of `predict()`. (You can certainly use `predict()` any way you would like in order to check your work.)

The function should take three inputs:

- `model`, a model object that is the result of fitting the SLR model with `lm()`

- `newdata`, a data frame with a single observation (row)

- This data frame will need to have a variable (column) with the same name as the data used to fit `model`.

- `level`, the level (0.90, 0.95, etc) for the interval with a default value of `0.95`

The function should return a named vector with three elements:

- `estimate`, the midpoint of the interval

- `lower`, the lower bound of the interval

- `upper`, the upper bound of the interval