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Question

# Refer to Exercise 16.2. Calculate the residuals and the predicted values of y.

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 data that are given to us in the Problem $2.$

In this task, we will use some values ​​that we have already calculated in the Problem $2$ so that we do not have to calculate again. It will be the following data:

\begin{align*} n&=12,\\ \sum_{i=1}^nx_i&=615,\\ \sum_{i=1}^ny_i&=144.9,\\ \sum_{i=1}^nx_i y_i&=7882.2,\\ \sum_{i=1}^nx_i^2&=39561,\\ \sum_{i=1}^ny_i^2&=1795.77,\\ s_{xy}&=41.461,\\ s_x^2&=731.114,\\ s_y^2&=4.19,\\ \=x&=51.25,\\ \=y&=12.075. \end{align*}

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

\begin{align*} \^y=9.154+0.057x. \end{align*}

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