Question

The scatter plot of the speed of a bike with respect to time is shown below for multiple trials.
Predict the correlation between the speed of bike and time elapsed and guess the slope of the line of best fit.

• A. No correlation
• B. Positive correlation
• C. Slope $=5$ units
• D. Slope $=10$ units

Answer 1

Answer: (B), (C)

Slope $=5$ units

From the scatter plot, it is evident that as the time elapsed, the speed of the bike increased.
Hence, the correlation between speed of bike and elapsed time is positive, i.e., option (b) is correct.

This is the case when the bike is accelerating, i.e., speed increases with time.

To determine the slope of the line of best fit, let's draw an approximate line.

A trend line is a line around which all the given points are equally scattered. The trend line that captures the essence of the data is called the line of best fit.
Let the line passes through the points $(x_1,y_1)=(1,5)\text{and}(x_2,y_2)=(3.5,18)$

Slope of the line$\left(m\right)$
$=\frac{y_2-y_1}{x_2-x_1}$
$=\frac{18-5}{3.5-1}$
$=\frac{13}{2.5}$
$=\frac{13\times 2}{2.5\times 2}$
$=\frac{26}{5}$
$=5.2$ units

From the given options, $5$ is the closest value.
$\therefore$ Option (c) is correct.