Cambridge International Mathematics

Lettbe the number of years since 1960 andCbe the CO 2

concentration.

a Obtain a scatter diagram for the data. Is a linear

model appropriate?

b Find the equation of the linear regression line.

c Estimate the CO 2 concentration for 1987.

d If CO 2 emission continues at the same rate, estimate

the concentration in 2020.

6 Safety authorities advise drivers to travel 3 seconds behind the car in front of them. This provides the

driver with a greater chance of avoiding a collision if the car in front has to brake quickly or is itself

involved in an accident. A test was carried out to find out how long it would take a driver to bring a

car to rest from the time a red light was flashed. Thisstopping timeincludes both the reaction time

of the driver and the braking time for the car. The following results are for one driver in the same car

under the same test conditions:

Speed (vkm/h) 10 20 30 40 50 60 70 80 90

Stopping time (ts) 1 : 23 1 : 54 1 : 88 2 : 20 2 : 52 2 : 83 3 : 15 3 : 45 3 : 83

a Produce a scatter diagram for the data.

b Find the linear model which best fits the data.

c Use the model to estimate the stopping time for a speed of:

i 55 km/h ii 110 km/h

d Comment on the reliability of your results inc.

e Interpret the vertical intercept of the line of best fit.

f Explain why the 3 second rule applies at all speeds, with a good safety margin.

Review set 22A

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1 The scatter diagram shows the number of defective items made

by each employee of a factory, plotted against the employee’s

number of weeks of experience.

a What are the independent and dependent variables?

b Is the association between the variables:

i weak or strong ii positive or negative?

2

Number of paddlers,x 4 6 10 18 30

Maximum speed,ykm/h 8 11 13 16 25

a Draw a scatter diagram for the data.

b Findxandy:

c Plot the point (x,y) on the scatter diagram.

d Draw the line of best fit by eye on the scatter diagram.

e Predict the maximum speed of a dragonboat with: i 24 paddlers ii 40 paddlers.

Defective items

Weeks of experience

The maximum speed of a Chinese dragonboat with different

numbers of paddlers is recorded in the table below:

466 Two variable analysis (Chapter 22)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_22\466IGCSE01_22.CDR Monday, 27 October 2008 2:15:08 PM PETER