DESCRIBE THE STRENGTH AND DIRECTION OF THE LINEAR CORRELATION

When the points of a scatter plot are clustered along a line, we say there is a linear correlation between the quantities represented by the data.

(i) Strong positive linear correlation

(ii) Weak positive linear correlation

(iii) No linear correlation

(iv) Strong negative linear correlation

(v) Weak negative linear correlation

Problem 1 :

A group of male children were weighed. Their ages and weights are recorded in table.

Age (Months)

18

20

24

26

27

29

34

39

42

Weight (Pounds)

23

25

24

32

33

29

35

39

44

(i) Draw the scatter plot of these data .

(ii) Describe the strength and direction of the correlation between the age and weight.

Solution :

(i) Scatter plot of the data :

2030402530354045AgeWeight 2030405020304050X AxisY Axis

(ii) There is strong positive correlation between age and weight.

Problem 2 :

The table below shows the average number of additional years a U.S. citizen is expected to live for various ages.

Age(years)

10

20

30

40

50

60

70

Remaining life expectancy

68.5

58.8

49.3

39.9

30.9

22.5

15.1

(a) Draw a scatter plot of these data.

(b) Writing to Learn Describe the strength and direction of the correlation between age and life expectancy.

Solution :

(i) Scatter plot

1020304050304050Age (in years)Remaining life expectancy

(ii) There is no linear relationship between age and remaining life expectancy.

Describe the strength and direction of the linear correlation.

Problem 3 :

Solution :

There is strong positive linear correlation.

Problem 4 :

Solution :

Strong negative correlation.

Problem 5 :

Solution :

There is weak positive linear correlation.

Problem 6 :

Solution :

There is no linear correlation between the quantities.

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