Question

The manager of a bookstore wants to predict Sales from Number of Sales People Working using the accompanying data set. What is the value of Upper R squared and what does it​ mean? LOADING... Click the icon to view the data. Find and interpret the value of Upper R squared. ​(Round to one decimal place as​ needed.)
A. The value of Upper R squared is nothing​%, which is the percentage of variance in Sales that can be accounted for by the regression of Sales on Number of Sales People Working.
B. The value of Upper R squared is nothing​%, which is the percentage of variance in Sales that can be accounted for by the regression of Number of Sales People Working on Sales.
C. The value of Upper R squared is nothing​%, which is the percentage of variance in Number of Sales People Working that can be accounted for by the regression of Number of Sales People Working on Sales.
D. The value of Upper R squared is nothing​%, which is the percentage of variance in Number of Sales Workers that can be accounted for by the regression of Sales on Number of Sales People Working.

Answer 1

Answer:

n=5 $\sum x = 103, \sum y = 177, \sum xy= 2088, \sum x^2 =1379, \sum y^2 =3359$  

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{10(2088)-(103)(177)}{\sqrt{[10(1379) -(103)^2][10(3359) -(177)^2]}}=0.9877$

So then the correlation coefficient would be r =0.9877

And the determination coefficient for this case would be:

$r^2 = 0.9877^2 = 0.9757 = 97.57 \%$

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 $\sum x = 103, \sum y = 177, \sum xy= 2088, \sum x^2 =1379, \sum y^2 =3359$  

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{10(2088)-(103)(177)}{\sqrt{[10(1379) -(103)^2][10(3359) -(177)^2]}}=0.9877$

So then the correlation coefficient would be r =0.9877

And the determination coefficient for this case would be:

$r^2 = 0.9877^2 = 0.9757 = 97.57 \%$

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.