The endangered manatee - The table below gives 39 years of data on boats registe

Question

The endangered manatee - The table below gives 39 years of data on boats registered in Florida and manatees killed by boats. Data from the Florida Highway Safety and Motor Vehicles (FHSMV) and Florida Fish and Wildlife Research Institute (FWRI). Florida boat Manatees Answer only the questions below registrations killed a. Make a scatterplot of the manatees killed by boat from the data in columns B and C. Year (thousands) by boat Be sure the scatterplot contains the 5 important points of a chart or graph. 1977 447 13 1978 460 21 b. Find the equation of the regressioin line for predicting manatees killed from thousands of boats registered. 1979 481 24 1980 498 16 c. Find the correlation for the data in this scatterplot. Explain why this is or is not a valid correlation. 1981 513 24 1982 512 20 d. Explain the proportion of variation in Y. 1983 526 15 1984 559 34 e. In 2016, there were 950,000 boats registered in Florida. Predict the number of manatees 1985 585 33 killed by boats in 2016. Explain why we can trust this prediction. 1986 614 33 1987 645 39 f. Predict manatee deaths if there were 200,000 boats registered in Florida. 1988 675 43 Explain why the predicted count of deaths is impossible. 1989 711 50 1990 719 47 g. For every 100,000 boats registered in Florida, how much will it change the manatee death rate by boats. 1991 681 53 1992 679 38 1993 678 35 1994 696 49 1995 713 42 1996 732 60 1997 755 54 1998 809 66 1999 830 82 2000 880 78 2001 944 81 2002 962 95 2003 978 73 2004 983 69 2005 1010 79 2006 1024 92 2007 1027 73 2008 1010 90 2009 982 97 2010 942 83 2011 922 88 2012 902 82 2013 897 73 2014 900 69 2015 916 86 The endangered manatee - The table below gives 39 years of data on boats registered in Florida and manatees killed by boats. Data from the Florida Highway Safety and Motor Vehicles (FHSMV) and Florida Fish and Wildlife Research Institute (FWRI). Florida boat Manatees Answer only the questions below registrations killed a. Make a scatterplot of the manatees killed by boat from the data in columns B and C. Year (thousands) by boat Be sure the scatterplot contains the 5 important points of a chart or graph. 1977 447 13 1978 460 21 b. Find the equation of the regressioin line for predicting manatees killed from thousands of boats registered. 1979 481 24 1980 498 16 c. Find the correlation for the data in this scatterplot. Explain why this is or is not a valid correlation. 1981 513 24 1982 512 20 d. Explain the proportion of variation in Y. 1983 526 15 1984 559 34 e. In 2016, there were 950,000 boats registered in Florida. Predict the number of manatees 1985 585 33 killed by boats in 2016. Explain why we can trust this prediction. 1986 614 33 1987 645 39 f. Predict manatee deaths if there were 200,000 boats registered in Florida. 1988 675 43 Explain why the predicted count of deaths is impossible. 1989 711 50 1990 719 47 g. For every 100,000 boats registered in Florida, how much will it change the manatee death rate by boats. 1991 681 53 1992 679 38 1993 678 35 1994 696 49 1995 713 42 1996 732 60 1997 755 54 1998 809 66 1999 830 82 2000 880 78 2001 944 81 2002 962 95 2003 978 73 2004 983 69 2005 1010 79 2006 1024 92 2007 1027 73 2008 1010 90 2009 982 97 2010 942 83 2011 922 88 2012 902 82 2013 897 73 2014 900 69 2015 916 86

Explanation / Answer

All the questions have been addressed in the following R program:

> manatees <- read.csv("clipboard",sep=" ",header=TRUE)
> head(manatees
+ )
Year registrations Manatees
1 1977           447       13
2 1978           460       21
3 1979           481       24
4 1980           498       16
5 1981           513       24
6 1982           512       20
> plot(manatees$registrations,manatees$Manatees)
> mana_lm <- lm(Manatees~registrations,manatees)
> summary(mana_lm)

Call:
lm(formula = Manatees ~ registrations, data = manatees)

Residuals:
   Min     1Q Median     3Q    Max
-18.37 -4.21   0.67   5.17 16.84

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)   -45.27011    5.46341   -8.29 5.9e-10 ***
registrations   0.13305    0.00695   19.13 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.95 on 37 degrees of freedom
Multiple R-squared: 0.908,     Adjusted R-squared: 0.906
F-statistic: 366 on 1 and 37 DF, p-value: <2e-16

> cor(manatees[,2:3])
              registrations Manatees
registrations         1.000    0.953
Manatees              0.953    1.000
> predict(mana_lm,newdata=list(registrations=950))
    1
81.13
> predict(mana_lm,newdata=list(registrations=200))
     1
-18.66

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