Respuesta :
Answer:
n=5 [tex] \sum x = 103, \sum y = 177, \sum xy= 2088, \sum x^2 =1379, \sum y^2 =3359[/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{10(2088)-(103)(177)}{\sqrt{[10(1379) -(103)^2][10(3359) -(177)^2]}}=0.9877[/tex]
So then the correlation coefficient would be r =0.9877
And the determination coefficient for this case would be:
[tex] r^2 = 0.9877^2 = 0.9757 = 97.57 \%[/tex]
And the correct option for this case would be:
A. The value of Upper R squared is 97.57%, which is the percentage of variance in Sales that can be accounted for by the regression of Sales on Number of Sales People working.
Step-by-step explanation:
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
For this case we have the following data:
N. sal. peop. work. Sales (in $1000)
2 10
3 12
6 14
8 15
10 17
10 19
11 19
16 23
17 23
20 25
We assume that the Number of Sales represent (X) and Sales (in $1000) represent (Y), we have this:
n=5 [tex] \sum x = 103, \sum y = 177, \sum xy= 2088, \sum x^2 =1379, \sum y^2 =3359[/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{10(2088)-(103)(177)}{\sqrt{[10(1379) -(103)^2][10(3359) -(177)^2]}}=0.9877[/tex]
So then the correlation coefficient would be r =0.9877
And the determination coefficient for this case would be:
[tex] r^2 = 0.9877^2 = 0.9757 = 97.57 \%[/tex]
And the correct option for this case would be:
A. The value of Upper R squared is 97.57%, which is the percentage of variance in Sales that can be accounted for by the regression of Sales on Number of Sales People working.
