Question

Because the Florida manatee population is threatened, the Florida Maatee Sanctuary Act of 1978 was enacted to protect the species. Scientists interested in the relationship between the number of manatee deaths and time collected the data shown in the table. Manatee Deaths 174 163 146 192 201 416 242 232 269 272 325 305 380 276 396 416 Manatee Deaths Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 25 62 114 84 63 116 114 81 128 119 122 114 133 168 206(b) Find the linear regression model for these data. (Let y = 1 be the year 1974, Round your coefficients to two decimal places.) M(v)-

(d) Use the linear regression model to predict the year in which the number of manatee deaths will be 490. (Round your answer to the nearest integer.)

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Answer #1

Here we have data:

Year Mantee Deaths
1 7
2 25
3 62
4 114
5 84
6 77
7 63
8 116
9 114
10 81
11 128
12 119
13 122
14 114
15 133
16 168
17 206
18 174
19 163
20 146
21 192
22 201
23 416
24 242
25 232
26 269
27 272
28 325
29 305
30 380
31 276
32 396
33 416

Excel scatter plot output :

40 35 30 25 y 0.0784x+ 2.4161 R2 0.8402 20 15 10 0 100 DiNi 300 400 500

a) y = 0.08X + 2.42

b) x = 490

   y = 0.0784 * 490 + 2.4161 = 41

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