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Question

# Calculate and plot the residuals and predicted values of y for Exercise 16.5.

Solution

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The goal of this task is to compute the residuals and we have to also determine the predicted values of $y$. To solve this task we will use the values that are given to us in the Problem $5$.

In this task, we will use some values ​​that we have already calculated in the Problem $5$ so that we do not have to calculate again. It will be the following data:

\begin{align*} n&=9,\\ \sum_{i=1}^nx_i&= 805,\\ \sum_{i=1}^ny_i&= 211,447\\ \sum_{i=1}^nx_i^2&=65,239, \\ \sum_{i=1}^ny_i^2&=5,569,844,521\\ s_{xy}&=73,396.389\\ s_x^2&= 48.5\\ s_y^2&=122,095,682.23\\ \=x&=80.5\\ \=y&=21,144.7. \end{align*}

And we can also use a regression line that we have already determined then:

\begin{align*} \^y=-100,678.37+1,513.33x. \end{align*}

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