6. The University of Arizona surveyed a large number of households. One purpose of the survey was to determine if annual household income could be predicted from size of family home.

The graph of Annual household income, $y$, versus Size of family home, $x$, is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{4ecf99c5-c4b3-41b7-a8df-a7c2ca7fcd6a-5_616_1257_566_365}
\begin{enumerate}[label=(\alph*)]
\item State the limitations of using the regression line above with reference to the scatter diagram.

The data for size of family homes between 2000 and 3000 square feet are shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{4ecf99c5-c4b3-41b7-a8df-a7c2ca7fcd6a-5_652_1244_1516_360}

Summary statistics for these data are as follows.

$$\begin{array} { r c c } 
\sum x = 93160 & \sum y = 3907142 & n = 37 \\
S _ { x x } = 2869673.03 & S _ { y y } = 44312797167 & S _ { x y } = 348512820 \cdot 6
\end{array}$$
\item Calculate the equation of the least squares regression line to predict Annual household income from Size of family home for these data.
\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 2 2019 Q6 [6]}}