# Solutions

Here are answers and solutions to selected exercises.

````{solution} exercise:ols_example_1
:label: solution:ols_example_1
:class: dropdown

We have the following design matrix

$$
\dmat = \left[
    \begin{array}{cc}
        1 & -2 \\
        1 & 1
    \end{array}
\right],
$$

which in the present case yields the parameter values

$$
\pars^{*} = \dmat^{-1}\data = [1,2]^T.
$$
````

````{solution} exercise:ols_example_3
:label: solution:ols_example_3
:class: dropdown

For the warmup case we have fitted a straight line through two data points, which is always possible, and we cannot determine the sample variance. This will be even more clear when we come to [](sec:BayesianLinearRegression).

````