Cambridge International Mathematics

a Produce a scatter diagram fordagainstn. Does a linear model seem appropriate for this data?

b Findnandd.

c Plot the point (n,d) on the scatter diagram.

d Draw the line of best fit by eye.

e Use the graph to predict the number of diagnosed cases on day 14. Is this predicted value

reliable? Give reasons for your answer.

3 The following table gives peptic ulcer rates per 1000 people for differing family incomes in the

year 1998.

Income(IE 1000 s) 10 15 20 25 30 40 50 60 80

8 : 3 7 : 7 6 : 9 7 : 3 5 : 9 4 : 7 3 : 6 2 : 6 1 : 2

a Draw a scatter diagram for the data.

b Find the equation of the regression line for the data.

c Estimate the peptic ulcer rate in families with an income ofE45 000.

d Explain why the model is inadequate for families with income in excess ofE100 000.

e Later it is realised that one of the figures was written incorrectly.

i Which is it likely to be? Explain your answer.

ii Repeatbandcwithout the incorrect data value.

4 The average value of a circulated 1930 Australian penny sold at auction over

the period from 1962 to 2006 is shown in dollars in the table below.

Year 1962 1972 1977 1985 1991 1996 2002 2006

Value 120 335 615 1528 2712 4720 8763 16 250

Supposexis the number of yearssince 1962 andVis the value of the penny

in dollars.

a Draw a scatter diagram ofVagainstx.

b Comment on the association between the variables.

c Find a linear model forVin terms ofxusing technology.

d Explain why this model is not appropriate and we should not use it.

e How could you estimate the value of the penny in 2012?

468 Two variable analysis (Chapter 22)

Peptic ulcer rate (R)

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Y:\HAESE\IGCSE01\IG01_22\468IGCSE01_22.CDR Tuesday, 18 November 2008 11:16:40 AM PETER