Question

# For the following data​ (a) display the data in a scatter​ plot, (b) calculate the correlation...

For the following data​ (a) display the data in a scatter​ plot, (b) calculate the correlation coefficient​ r, and​ (c) make a conclusion about the type of correlation.

The ages​ (in years) of

six

children and the number of words in their vocabulary

Choose the correct scatter plot

​(b) The correlation coefficient r is

____

​(Round to three decimal places as​ needed.)

​(c) Which of the following best describes the type of correlation that exists between age and vocabulary​ size?

A. Weak negative linear correlation

B. Strong negative linear correlation

C. Weak positive linear correlation

D. Strong positive linear correlation

E. No linear correlation

 Age, x Vocabulary size, y 1 500 2 800 3 1100 4 1750 5 2250 6 2700

Ans:

a) b)

 Age, x Vocabulary size, y xy x^2 y^2 1 1 500 500 1 250000 2 2 800 1600 4 640000 3 3 1100 3300 9 1210000 4 4 1750 7000 16 3062500 5 5 2250 11250 25 5062500 6 6 2700 16200 36 7290000 Total 21 9100 39850 91 17515000

correlation coefficient r =(6*39850-21*9100)/SQRT((6*91-21^2)*(6*17515000-9100^2))

r=0.992

c)

Strong positive linear correlation

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