DP IB Maths: AA SL

Topic Questions

4.2 Correlation & Regression

1a
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2 marks

A teacher collected the maths and physics test scores of a number of students and drew a scatter diagram to represent this data.

Thrh_pj__q1a-4-2-correlation-regression-medium-ib-ai-sl-maths-screenshot

Describe the correlation shown by the scatter diagram, and interpret the correlation in context.

1b
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2 marks

An alternative therapist collected data on his clients’ reported levels of anxiety as well as the number of trees they had hugged in the course of therapy. He drew a scatter diagram to represent this data.

dKESSwEn_q1a-2-4-2-correlation-regression-medium-ib-ai-sl-maths-screenshot

Describe the correlation shown by the scatter diagram, and interpret the correlation in context.

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2a
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4 marks

Jennifer sells cups of tea at her shop and has noticed that she sells more tea on cooler days.  On five different days, she records the maximum daily temperature, T, measured in degrees Celsius, and the number of cups of teas sold, C. The results are shown in the following table.

Maximum Daily Temperature, T.

3

5

8

9

12

Cups of tea sold, C

37

34

33

26

21


The relationship between straight T
and straight C can be modelled by the regression line of straight C on straight T with equation C equals a T plus b.

(i)
Find the value of a and the value of b.

(ii)
Write down the value of the Pearson’s product-moment correlation coefficient, r.
2b
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2 marks

Use your regression equation from part (a)(i) to estimate the number of teas that Jennifer will sell on a day when the maximum temperature is 11°C.

2c
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2 marks

Being sure to consider the result from part (a)(ii) in your answer, state how confident you would be in your estimate from part (b).

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3a
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4 marks

The following table shows the mean height, y cm, of primary school children who are age x years old.

Age, x years

6.25

7.35

8.5

9.25

10.75

Mean Height, y cm

115

121

129

136

140

 

The relationship between x and y can be modelled by the regression line of y on x with equation y equals a x plus b.

(i)

Find the value of a and the value of b.


(ii)
Write down the value of the Pearson’s product-moment correlation coefficient, r .
3b
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2 marks

Using the regression equation with your values of  a and b from part (a)(i), estimate the height of a child aged 9 years old.

3c
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1 mark

Explain why it is not appropriate to use the regression equation to estimate the age of a child who is 133 cm tall.

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4a
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4 marks

Rebecca, a regular jogger, ran the “Thao Dien Loop” on 7 consecutive days. The following table shows the distance, x km, that she ran and the corresponding number of calories, y, that she was able to burn during the run. 

Distance (x)

2

5

6

7

10

12

14

Calories (y)

180

315

365

435

619

830

871

 

The number of calories burnt during a run is dependent upon on the length of the run.  The relationship between x and y can be modelled by the regression line of y on x  with equation y equals a x plus b.  

(i)

Find the value of a and the value of b.


(ii)
Write down the value of the Pearson’s product-moment correlation coefficient, r.
4b
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1 mark

Interpret, in the context of the question, the value of a found in part (a)(i).

4c
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2 marks

On the 8th day, Rebecca is only able to run for 8 kilometres.

Use the result from part (a)(i) to estimate the number of calories Rebecca will lose.

4d
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1 mark

Comment on the validity of using the result from part (a)(i) to answer part (c).

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5a
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4 marks

The percentage of people who are willing to get a particular vaccine is dependent on their age. The following table shows the age, A years old, and the corresponding percentage of people, V. that are willing to receive a vaccine for 6 different ages. 

Age, (A)

25

30

35

40

45

50

Percentage of willing people, (V)

57

59

61

62

68

75

 
The relationship between A and V  can be modelled by the regression line of Von A with equation V equals a A plus b.

(i)

Find the value of a and the value of b.

(ii)
Write down the value of the Pearson’s product-moment correlation coefficient, r.
5b
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1 mark

Interpret, in the context of the question, the value of a found in part (a)(i).

5c
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2 marks

Use the result from part (a)(i) to estimate the percentage of people aged 95 years old who are in willing to receive a vaccine.

5d
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1 mark

Comment on the validity of using the result from part (a)(i) to answer part (c).

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6a
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3 marks

The price, $P , of an airline ticket is dependent on the distance,D km, between two cities.  The table below shows the airfares in US dollars from Prague in the Czech Republic, to eight different destinations in Europe.

Distance begin bold style stretchy left parenthesis D stretchy right parenthesis end style  885 340 835 330 1270 295 650 1930
Price begin bold style stretchy left parenthesis P stretchy right parenthesis end style  99 50 90 45 119 42.5 59 139

Let L subscript 1be the regression line of P spaceon D.  The equation of the line L subscript 1 can be written in the form  P equals a D plus b.

Let L subscript 2 space end subscriptbe the regression line of D spaceon P.  The equation of the line L subscript 2 can be written in the form D equals c P plus d.

(i)
Find the value of a and the value of b

 

(ii)
Find the value of c spaceand the value of d
6b
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2 marks

Write down the value of Pearson’s product-moment correlation coefficient,r.

6c
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2 marks

Use the result from part (a)(i) to estimate the price of an airline ticket for a flight from Prague to a destination that is 2635 km away.

6d
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2 marks

The lines L subscript 1 space end subscriptand L subscript 2 space end subscriptboth pass through the same point with coordinates left parenthesis p comma q right parenthesis.

Find the value of p and the value of q

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