Question

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

Answer 1

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