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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Infestation of Crops by Insects Has Long Been of Great