Chapter F, Problem 1CP

$\begin{array}{|cc|}\hline \text{Zestimate(\$}\text{thousands)}& \text{Selling}\text{Price(\$}\text{thousands)}\\ 291.5& 268\\ 320& 305\\ 371.5& 375\\ 303.5& 283\\ 351.5& 350\\ 314& 275\\ 332.5& 356\\ 295& 300\\ 313& 285\\ 368& 385\\ \hline\end{array}$

The graph below, called a scatter diagram, shows the points $\left(291.5,268\right),\left(320,305\right),\mathrm{...},\left(368,385\right)$ in a Cartesian plane.

From the graph, it appears that the data follow a linear relation.

Imagine drawing a line through the data that appears to fit the data well. Do you believe the slope of the line would be positive, negative, or close to zero? Why?

To determine

The slope of the line would be positive, negative, or close to zero with reason, by imagine drawing a line through the data that appears to fit the data well.

Answer to Problem 1CP

Solution:

The line passing through the points on scatter plot is slant upward, so the slope of the line would be positive.

Explanation of Solution

Given information:

The data below show the “zestimate”-the selling price of a home as predicted by the folks at Zillow and the actual selling price of the home, for the home in Oak Park Illinois.

$\begin{array}{|cc|}\hline \text{Zestimate(\$}\text{thousands)}& \text{Selling}\text{Price(\$}\text{thousands)}\\ 291.5& 268\\ 320& 305\\ 371.5& 375\\ 303.5& 283\\ 351.5& 350\\ 314& 275\\ 332.5& 356\\ 295& 300\\ 313& 285\\ 368& 385\\ \hline\end{array}$

The graph below, called a scatter diagram, shows the points $\left(291.5,268\right)$, $\left(320,305\right),...,$$\left(368,385\right)$ in a Cartesian plane. From the graph, it appears that the data follow a linear relation.

Explanation:

It is observed that, line passing through the points on scatter plot is slant upward.

It is known that, when the slope of the line is positive, the line slants upward.

When the slope of the line is negative, the line slants downward.

When the slope of the line is zero, the line is horizontal.

When the slope of the line is undefined, the line is vertical.

The line passing through the points on scatter plot is slant upward, so the slope of the line would be positive.