Reference no: EM132404095

A study was carried out to determine the relationship between cone length and the number of seeds extracted from Douglas-fir cones. The following data were recorded:

Cone Length, cm (X) Number of Seeds (Y)

8.2 41

7.5 38

6.6 29

6.3 33

6.1 30

6.1 28

5.7 22

5.3 24

5.1 26

a) Discuss why cone length was chosen as the independent variable over number of seeds.

b) Plot the observations to check if a linear relationship is reasonable. Is the relationship positive or negative?

c) Fit the linear regression line: y' = a + bx. Include the line in your scatter plot.

d) Calculate the Pearson product moment correlation coefficient. Discuss your results.

e) Calculate the coefficient of determination and the standard error of estimate. Explain their meaning.

f) Calculate the number of seeds contained within a Douglas-fir cone that measures 6.5 cm in length and determine the 95% prediction interval. Discuss your findings (SSX = 8.02).

g) Can we predict the number of seeds in a Douglas-fir cone that measures 10 cm in length? Why or why not?