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. (b) The correlation coefficient r is nothing. (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 positive linear correlation B. No linear correlation C. Strong positive linear correlation D. Strong negative linear correlation E. Weak negative linear correlation
Age, x Vocabulary size, y
1 100
2 1050
3 1400
4 1300
5 2100
6 2500
X | Y | X * Y | X^{2} | Y^{2} | |
1 | 100 | 100 | 1 | 10000 | |
2 | 1050 | 2100 | 4 | 1102500 | |
3 | 1400 | 4200 | 9 | 1960000 | |
4 | 1300 | 5200 | 16 | 1690000 | |
5 | 2100 | 10500 | 25 | 4410000 | |
6 | 2500 | 15000 | 36 | 6250000 | |
Total | 21 | 8450 | 37100 | 91 | 15422500 |
r = 0.958
There is positive correlation between variable X and Y.
C. Strong positive linear correlation
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