Question

The line of best fit helps to understand the trend of the data set.
It predict the data values at any unknown points.

• A. also helps to
• B. does not
• C. may or may not

Answer 1

The correct option is A also helps to

$\bullet$ The line of best fit helps to more accurately understand the trend of the data set.

$\bullet$ The line of best fit also helps to predict the data values at any unknown points.

Let's understand the above two usages of the line of best fit with an example:

The mass (independent variable) of different fluids and the respective volumes (dependent variable) occupied by those fluids are measured, and graphed in the below scatter plot.


In the above scatter plot, the cyan line represents the line of best fit, which accurately depicts the trend of the data set, i.e., if the mass of fluid increases, the corresponding volume also increases.

We can also predict the volume occupied by a fluid, which has a certain mass.

Let's predict the volume for $10$ gram mass of a liquid.

Before going for the prediction, we need to find out the equation of the line of best fit, which passess through the points $(x_1,y_1)=(4,4)$ and $(x_2,y_2)=(8,8)$.

The slope of the line of best fit is
$m=\frac{y_2-y_1}{x_2-x_1}$
$\Rightarrow$ m = $\frac{8-4}{8-4}=1$

Hence, the equation of the line of best fit is

$y-y_1=m(x-x_1)$
$\Rightarrow y-4=1(x-4)$
$\Rightarrow y=x$

For the mass of a fluid as $x=10\text{g},$ the corresponding volume is
$y=x=10$ milliliter,

$\therefore$ The predicted volume of $10$ g of fluid is $10$ milliliter.