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 6 children and the number of words in their vocabulary Age, x 1. 2 3 4 5 6 Vocabulary size, y 500 450 1350 1750 2300 2300 (a) Choose the correct scatter plot below. A. B. c. D. 2350+.. 7 2350- 2350- Vocabulary Age Vocabulary Vocabulary . 0 0- 0 Ly 7 0 0 0 7 2350 Vocabulary Age Age Age (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. No linear correlation

Answer 1

a)

Ans:

у 2500 2000 1500 1000 y 500 0 0 1 2 3 4 5 6 7

graph D) is correct

b)

Ans:

sr	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
1	1	500	6.25	886736.11	2354.166667
2	2	450	2.25	983402.78	1487.5
3	3	1350	0.25	8402.7778	45.83333333
4	4	1750	0.25	95069.444	154.1666667
5	5	2300	2.25	736736.11	1287.5
6	6	2300	6.25	736736.11	2145.833333
sum	21	8650	17.5	3447083.3	7475
mean	3.5	1441.666667	SXX	SYY	Sxy

correlation

r = Sxy / Sx*Sy

r = 7475 / sqrt(17.5*3447083.3)

r = 0.962

c)

Ans: strong positive linear correlation