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

The points $(1,2)$, $(2,4)$, $(3,6)$ and $(4,8)$ are plotted on a scatter diagram. Describe the type and strength of the correlation and, by eye, draw the line of best fit.

A café records daily mean temperature $(x)$ in °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 $18 \text{°C}$.

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.

House floor area $(x)$ in m² and sale price $(y)$ in thousands of dollars: $(50,100)$, $(70,150)$, $(90,180)$, $(110,210)$, $(130,260)$. Plot these points, draw a line of best fit, and estimate the sale price for a $100 \text{ m}^2$ house.

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.

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.

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 $x=1.5 \text{ L}$.

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 $50 \text{ kg}$.

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 $250 \text{ mm}$.

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.

Class size $(x)$ and average test score $(y)$ for six classes are: $(10,78)$, $(20,75)$, $(30,72)$, $(40,70)$, $(50,68)$, $(60,65)$. Plot a scatter diagram, draw a line of best fit by eye, estimate the average score for a class of 25 students, and comment on the correlation.

Given data $(0,2)$, $(2,5)$, $(4,9)$, $(6,12)$, $(8,16)$, plot a scatter diagram, draw a line of best fit, determine its approximate equation by selecting two points on the line, and predict $y$ at $x=10$ using your equation.