Question Type 4: Using bivariate data to plot scatter diagrams Exercises

A pharmaceutical trial records drug dosage $(x)$ in mg and blood pressure reduction $(y)$ in mmHg: $(10,5)$, $(20,12)$, $(30,18)$, $(40,25)$, $(50,28)$. Plot the scatter diagram, draw a line of best fit, and estimate the dose required for a $35 \text{ mmHg}$ reduction.

The data below show hours studied $(x)$ and exam scores $(y)$ for six students: $(2,60)$, $(3,65)$, $(5,75)$, $(6,80)$, $(8,90)$, $(9,95)$. Plot a scatter diagram, draw a line of best fit by eye, and estimate the exam score for a student who studies for 7 hours.

The points $(1,2)$, $(2,4)$, $(3,6)$ and $(4,8)$ are plotted on a scatter diagram below.

Describe the type and strength of the correlation and, by eye, draw the line of best fit.

A biologist records the age ($x$) in years and height ($y$) in metres of saplings: $(1,1.2)$, $(2,2.3)$, $(3,3.1)$, $(4,3.8)$, $(5,4.5)$.

Plot these points on a scatter diagram, draw a line of best fit, and estimate the height at $2.5$ years.

A café records daily mean temperature ($x$) in $^\circ\text{C}$ and cups of hot chocolate sold ($y$): $(5, 120)$, $(10, 90)$, $(15, 60)$, $(20, 40)$, $(25, 20)$, $(30, 10)$.

Plot a scatter diagram, draw a line of best fit, and estimate the sales at $18^\circ\text{C}$.

A dataset of children’s weight $(x)$ in kg and height $(y)$ in cm is: $(30, 130)$, $(35, 140)$, $(40, 150)$, $(45, 160)$, $(95, 155)$. Plot a scatter diagram, draw a line of best fit ignoring the outlier $(95, 155)$, and estimate the height at $50 \text{ kg}$.

Reaction time $(y)$ in seconds is measured against hours of sleep $(x)$ for six volunteers: $(4, \, 0.6)$, $(5, \, 0.5)$, $(6, \, 0.4)$, $(7, \, 0.35)$, $(8, \, 0.3)$, $(9, \, 0.28)$.

Plot a scatter diagram, draw a best-fit line by eye, and estimate the reaction time at $6.5$ hours of sleep.

Engine size $(x)$ in litres and fuel consumption $(y)$ in L/100 km are recorded for six cars: $(1.0, 6.0)$, $(1.2, 6.5)$, $(1.4, 7.0)$, $(1.6, 7.5)$, $(1.8, 8.0)$, $(2.0, 8.5)$. Plot a scatter diagram, draw a line of best fit, and estimate the consumption at $x=1.5 \text{ L}$.

Rainfall $(x)$ in mm and crop yield $(y)$ in tonnes per hectare are recorded: $(100, 2.0)$, $(200, 3.5)$, $(300, 4.8)$, $(400, 6.0)$, $(500, 6.5)$. Plot the data, draw a line of best fit by eye, and estimate the yield when rainfall is $250 \text{ mm}$.

The floor area $x$, in $\text{m}^2$, and sale price $y$, in thousands of dollars, for five houses are given in the following table.

Plot these points on a suitable pair of axes, draw a line of best fit, and estimate the sale price for a $100 \text{ m}^2$ house.