I have a dataset of 100 observations and 5 numerical variables ($x\_1, x\_2, ..., x\_{5}$) which I used to generate a linear model which to predict some value $y$. I plugged in some values into the model and got a result for $\hat{y}$.

I would like to calculate a 95% confidence interval for this value.

Using Python I get the following model summary:

```
Adj. R-squared: 0.892
F-statistic:    27.63
Prop(F-stat):   2.45e-18

        coef   std err   t      P>|t|   [0.025    0.975]
const  -12.71  3.713    -3.424  0.001   -20.156  -5.268
x1       0.29  0.255     1.134  0.262   -0.222   -0.800
x2       0.17  0.031     5.283  0.000    0.103    0.228
x3       0.44  0.089     4.970  0.000    0.262    0.617
x4      -0.47  0.194    -2.414  0.019   -0.856   -0.079
x5       0.36  0.226     1.587  0.118   -0.094    0.811

```

I am aware that in order to calculate a 95% confidence interval for a simple linear regression the formula is $\hat{\beta} \pm t\_{0.95, f}\: \cdot \: \hat{\sigma}\_{B\_0}$ where $f$ is the degree of freedom and $\hat{\sigma}\_{B\_0}$ is the `std err`. But how do I calculate this for multiple linear regression?