Respuesta :
Answer:
n=20 [tex] \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021[/tex]
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
[tex]r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237[/tex]
And then the determination coeffcient would be:
[tex] r^2 = 0.8237^2= 0.6785 \approx 0.679[/tex]
Step-by-step explanation:
College GPAs ACT Score, x
16 18 24 25 34 27 29 25 30 21 17 21 28 31 35 18 17 26 28 23
College GPA, y
1.85 2.20 2.80 3.50 4.00 3.18 3.90 2.90 4.00 2.60 2.50 3.65 3.10 3.72 3.24 2.30 1.70 3.10 3.50 2.76
From the info given we can calculate the following sums:
n=20 [tex] \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021[/tex]
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
[tex]r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237[/tex]
And then the determination coeffcient would be:
[tex] r^2 = 0.8237^2= 0.6785 \approx 0.679[/tex]
