Data Set Step 1: Find the equation of the least-squares line for predicting mana
ID: 3314472 • Letter: D
Question
Data Set
Step 1:
Find the equation of the least-squares line for predicting manatees killed from thousands of boats registered.
Because the linear pattern is so strong, we expect predictions from this line to be quite accurate—but only if conditions in Florida remain similar to those of the past 31 years.
Choose the correct answer below:
Step 2:
Manatees are an endangered species. Imagine that Florida were to limit powerboat registration in a given year to 800 thousand. Fill in the blank: The number of manatees killed in such a year would be ____. Round your answer to a whole number.
Step 3:
Explain why we can trust this prediction.
The prediction is not reliable because the regression line explains 95.3% of the variations in y.
The prediction is reliable because of the strong linear association visible in the scatterplot.
The regression line always gives a good prediction.
r2 is very close to 1, thus ensuring a high prediction accuracy.
Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons. Your selections:
Step 4:
Predict manatee deaths if there were 200,000 boats registered in Florida.
Use the prediction equation in part 1 of this question and give your answer to 2 decimal places.
Fill in the blank:
Step 5:
Explain why the predicted count of deaths is impossible.
(We use x = 0 to find the intercept of the regression line, but unless the explanatory variable x actually takes values near 0, prediction for x = 0 is an example of extrapolation.)
Choose the correct answers below:
Because x = 0 is far outside the range of values of the explanatory variable.
Because usually, the intercept is a non-accurate prediction.
Because a negative number of deaths makes no sense.
Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons. Your selections:
= 70.28 + 0.3120x = 50.15 + 0.1412x = 44.72 + 0.1322x = 25.27 + 0.2378xExplanation / Answer
1.
We load the data into R
and then implement a linear regression in R by -
> lm(deaths ~ powerboats, data = data)
Call:
lm(formula = deaths ~ powerboats, data = data)
Coefficients:
(Intercept) powerboats
-44.7218 0.1322
Thus, the predicted value = - 44.72 + 0.1322 * x
Thus, the answer is = option 3
2.
Manatees are an endangered species. Imagine that Florida were to limit powerboat registration in a given year to 800 thousand.
The number of manatees killed in such a year would be:
- 44.72 + 0.1322 * 800
= 61.04
Hence, the answer is = 61
3.
The prediction is reliable because of the strong linear association visible in the scatterplot.
The regression line does not always give a good prediction.
r2 = 0.9073 which is very high
r2 is very close to 1, thus ensuring a high prediction accuracy.
Hence, the answer is = options 2, 4
4.
if there were 200,000 boats registered in Florida.
x = 200
The predicted manatee deaths = - 44.72 + 0.1322 * 200 = -18.28
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