Correlation Coefficient and Linear regression equation.
Throughout the fall harvest season in the United States, pumpkins are sold in large quantities at farm stands. Often, instead of weighing the pumpkins prior to sale, farm stand operator will just place the pumpkin in the appropriate circular cutout on the counter. When asked why this was done, one farmer replied, "I can tell the weight of the pumpkin from its circumference." To find out whether this was really true, a sample of 15 pumpkins were measured for circumference and weighed with the following results.
Circumference (CM)

Weight (Grams)

50

1200

55

2000

54

1500

52

1700

37

500

52

1000

53

1500

47

1400

51

1500

63

2500

33

500

66

2500

83

4600

60

2300

59

2100

1. Assume a linear relationship, use the least squares method to find the regression coefficients b_{0} and b_{1}.
2. Interpret the meaning of slope b_{1} in this problem.
3. Predict the average weight for a pumpkin that is 60 centimeters in circumference.
4. At the 0.05 level of significance, is there evidence of a linear relationship between the circumference and the weight of a pumpkin? describe.
5. Find out the coefficient of determination, r^{2} and interpret its meaning.