Infestation of Crops by Insects Has Long Been of Great

question 89

Essay

Infestation of crops by insects has long been of great concern to farmers and agricultural scientists. A study reports data on x = age of a cotton plant (days) and y = % damaged squares. Consider the accompanying n = 12 observations: $$\begin{array} { l c c c c c c } \hline x & 9 & 12 & 12 & 15 & 18 & 18 \\\hline y & 11 & 12 & 23 & 30 & 29 & 52 \\\hline & & & & & & \\\hline x & 21 & 21 & 27 & 30 & 30 & 33 \\\hline y & 41 & 65 & 60 & 72 & 84 & 93 \\\hline\end{array}$$
a. Why is the relationship between x and y not deterministic?
b. Does a scatter plot suggest that the simple linear regression model will describe the relationship between the two variables?
c. The summary statistics are $\sum x _ { i} = 246 , \sum x _ {i } ^ { 2 } = 5742 , \sum y _ { i } = 572 , \sum y _ { i } ^ { 2 } = 35,634 , \text { and } \sum x _ {i } y _ { i } = 14,022$
Determine the
equation of the least squares line.
d. Predict the percentage of damaged squares when the age is 20 days by giving an interval of
plausible values.