# 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)182024262729343942 Weight (Pounds)232524323329353944

(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 :

(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)10203040506070 Remaining life expectancy68.558.849.339.930.922.515.1

(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

(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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