An agronomist wanted to investigate the factors that determine crop yield. Accordingly, she undertook an experiment wherein a farm was divided into 30 one-acre plots. The amount of fertilizer applied to each plot was varied. Corn was then planted, and the amount of corn harvested at the end of the season was recorded.
a. Find the sample regression line, and interpret the coefficients.
b. Can the agronomist conclude that there is a linear relationship between the amount of fertilizer and the crop yield?
c. Find the coefficient of determination, and interpret its value.
d. Does the simple linear model appear to be a useful tool in predicting crop yield from the amount of fertilizer applied? If so, produce a 95% prediction interval of the crop yield when 300 pounds of fertilizer are applied. If not, explain why not.