Problem
Assume that the given $x$-value comes from within the range of sample data. (In other words, there will be no extrapolation.) Round your answers to 3 places after the decimal point, if necessary. (a) Suppose a sample of 12 pairs of sample data result in a test statistic of $r=0.831$ and the regression equation $\hat{y}=7.1-7.1 x$. Additionally, $\bar{y}=61.1$ for this data. What is the best predicted value of $y$ for $x=22$ ?
Solution
Step 1 ：Given the regression equation \(\hat{y}=7.1-7.1 x\), we can find the best predicted value of \(y\) for a given \(x\) by substituting the \(x\) value into the equation.
Step 2 ：Substitute \(x=22\) into the equation to get \(\hat{y}=7.1-7.1 \times 22\).
Step 3 ：Solving the equation gives \(\hat{y}=-149.1\).
Step 4 ：\(\boxed{-149.1}\) is the best predicted value of \(y\) for \(x=22\).
