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.

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Definitions:

Medical Settings

Environments or contexts related to the practice of medicine, such as hospitals, clinics, and private practices.

Syphilis

A bacterial infection usually spread by sexual contact that starts as a painless sore and can eventually lead to severe health problems if left untreated.

Stages

Progressive phases or levels in processes, development, or disease progression, used to describe advancement or evolution.

HIV

Human Immunodeficiency Virus, a virus that attacks the immune system and can lead to Acquired Immunodeficiency Syndrome (AIDS) if not treated.