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5.07 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

 

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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
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Outcomes

4.1.3.4

interpret relationships in terms of the variables [complex]

4.1.3.6

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

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