Mary Sue problem: Scatter Diagram, Sample Correlation Coefficient, Coefficient of determination
Mary Sue wants to know if there is a connection between attendance at craft fairs and number of exhibitors who have booths at the fair. For a random sample of seven local craft fairs, she chose a random day of the fair and recorded the number of exhibitors. In the data below, x represents the number of exhibitors and y represents the attendance in hundreds of people.
|
X
|
35
|
55
|
75
|
95
|
100
|
135
|
150
|
|
Y
|
1.2
|
2.1
|
4.2
|
5.4
|
5.8
|
6.2
|
9.5
|
a. illustrate the scatter diagram for the data.
b. estimate the sample correlation coefficient, r.
c. compute the coefficient of determination, r^2.
d. What does the coefficient of determination tell you about the variation attendance and the variation in the number of exhibitors?