# Data with two variables

### The Linear model for statistics

- If the relationship is linear, then a line of best fit is drawn on the graph. This line of best fit is called the linear model.
- The linear model can be written as:

\[ \hat{y} = b_{0} + b_{1}x \]

- This model is used to find the predicted \(\left(\hat{y}\right)\) value for any given value of the independent variable \((x)\).
- For the previous example the equation to the linear model is

\[ \hat{y} = -4.24 +1.04 x\]

- A predicted true speed can be calculated if the the speedometer reads \(90\) km/h.

\begin{eqnarray*}

\hat{y} &=& -4.24 +1.04 x \\

&=& -4.24 +1.04 \times 90 \\

&\approx & 93.6

\end{eqnarray*} Therefore, the predicted true speed is approximately \(93.6\) km/h.