topic badge

6.05 Making predictions

Interactive practice questions

Scientists conducted a study to see people's reaction times after they've had different amounts of sleep.

The data is presented below with a line of best fit.

Number of hours of sleep ($x$x) $1.1$1.1 $1.5$1.5 $2.1$2.1 $2.5$2.5 $3.5$3.5 $4$4
Reaction time in seconds ($y$y) $4.66$4.66 $4.1$4.1 $4.66$4.66 $3.7$3.7 $3.6$3.6 $3.4$3.4

 

Loading Graph...
A number plane has x-axis ranging from 0 to 5 and the y-axis ranging from 0 to 5. Data points are plotted at $\left(\frac{11}{10},\frac{233}{50}\right)$(1110,23350), $\left(\frac{3}{2},\frac{41}{10}\right)$(32,4110), $\left(\frac{21}{10},\frac{233}{50}\right)$(2110,23350), $\left(\frac{5}{2},\frac{37}{10}\right)$(52,3710), $\left(\frac{7}{2},\frac{18}{5}\right)$(72,185), and $\left(4,\frac{17}{5}\right)$(4,175).  A line of best fit is drawn on the data points to highlight the overall trend.
a

What would be the reaction time for someone who has slept $5$5 hours?

b

Predict the number of hours someone sleeps if they have a reaction time of $4$4 seconds.

Easy
1min

Chirping crickets can be an excellent indication on how hot or cool it is outside. Different species of crickets have different chirping rates but for a particular species the following data was recorded.

Easy
1min

A bivariate data set has a line of best fit with equation $y=8.84x$y=8.84x.

Use this equation to calculate the value of $y$y when $x=7.68$x=7.68.

Easy
1min

A bivariate data set has a line of best fit with equation $y=-8.71x+6.79$y=8.71x+6.79.

Predict the value of $y$y when $x=3.49$x=3.49.

Easy
1min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

ACMEM143

interpret relationships in terms of the variables

ACMEM145

use the line of best fit to make predictions, both by interpolation and extrapolation

ACMEM146

recognise the dangers of extrapolation

What is Mathspace

About Mathspace