Question

which of the following equations is the best model for a line of fit for the data?
$hat{y}=-1.34x + 21.5$
$hat{y}=1.34x + 21.5$
$hat{y}=-0.75x + 17$
$hat{y}=0.75x + 17$

Explanation:

Step1: Observe the trend of data points

As the value of "Money Saved" (x - axis) increases, the value of "Money" (y - axis) decreases. So the slope of the line of fit should be negative.

Step2: Analyze slope - intercept form

The equation of a line is $\hat{y}=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We need to estimate the slope and y - intercept visually. The data points seem to have a moderately steep negative slope. Among the options with negative slopes ($\hat{y}=-1.34x + 21.5$ and $\hat{y}=-0.75x + 17$), by observing the general position of the points, the slope seems to be around - 0.75 and the y - intercept seems to be around 17.

Answer:

$\hat{y}=-0.75x + 17$