## Related questions with answers

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

Solution

VerifiedThe 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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