Please explain 15 The following scatterplot shows the relat

Please explain :)

15. The following scatterplot shows the relationship between number of registered boats in Florida and the number of manatees killed by boats between 1977 and 2009 and the equation of the regression line.

a) What are the explanatory and response variables in this regression equation?
b) Interpret the slope of the regression equation in the context of the problem.
c) Interpret the intercept in the context of the problem. Does it have practical significance?
d) Assuming that this trend continues, predict the number of manatees that would be killed if the
number of registered boats in Florida increases to 1.2 million.
e) Interpret the coefficient of determination in the context of the problem.

Florida Manatess Killed by Boats 1977-2009 100 y = 0.1292x-43.172 R2 = 0.905 80 % 60 40 20 0 400 500 600 700 800 900 1000 1100 Boats registered in Florida (thousands)

Solution

a)

The explanatory variable is the independent variable which explains the variation in the dependent variable.

Here, the variable \'Number of boats registered in Florida\' explains the variation in the death of Manatess.

So, the explantory variable is - \'The number of boats registered\'.

And, the response variable is - \'Number of manatess killed\'.

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b)

The slope of a linear regression explains the change in the response variable with a unit change in the explanatory variable.

In this case, the slope of 0.1292 means that with an increase of 1 registered boats in Florida, there is an increase of 0.1292 manatess death. In other words we can say that every 100 increase in number of boats registered, kills approximately 13 manatess.

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c)

The value of the intercept here is \'-43.172\'. The intercept value of the linear regression explains the value of the response variable when the explantory variable takes the value 0.

In this case, the value \'-43.172\' represents the number of deaths of mantess when there is no registered boat in Florida. But as the number of deaths can not be negative, it means that if there is no registered boat then there will be no death of manatess.

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d)

1.2 million = 1.2 x 1000 thousands = 1200 thousands

So for X = 1200, the estimated death of manatess is -

Y = 0.1292 (1200) - 43.172 = 155.04 - 43.172 = 111.868

Hence, the predicted number of deaths of mantess for 1200 thousands registered boats = 111.868 = 112.

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e) The coefficient of determination explains the variation in the response variable caused due to the explanatory variable. If the coefficient of determination is greater than 0.9, it means that the variation in the response variable is well explained by the explanatory variable.

In this case, the value of 0.905 means that, about 90.5% of the variation in the number of deaths of manatess is explained by the number of registered boats on florida beach. So, this is a good model to estimate the number of deaths of mantess using the number of registered boats.