Question

In: Math

As the climate grows warmer, we expect many animal species to move towards the poles in...

As the climate grows warmer, we expect many animal species to move towards the poles in an attempt to maintain their
preferred temperature range. Do data on fish in the North Sea confirm this expectation? Data for 25 years, 1977 through 2001,
on mean winter temperatures at the bottom of the North Sea (degrees Celsius) and on the center of the distribution of anglerfish
in degrees of North latitude are given below. Does the fish distribution depend on temperature?
Year Degrees North Latitude Temp (oC)
1977 57.20 6.26
1978 57.96 6.26
1979 57.65 6.27
1980 57.59 6.31
1981 58.01 6.34
1982 59.06 6.32
1983 56.85 6.37
1984 56.87 6.39
1985 57.43 6.42
1986 57.72 6.52
1987 57.83 6.68
1988 57.87 6.76
1989 57.48 6.78
1990 58.13 6.89
1991 58.52 6.9
1992 58.48 6.93
1993 57.89 6.98
1994 58.71 7.02
1995 58.07 7.09
1996 58.49 7.13
1997 58.28 7.15
1998 58.49 7.29
1999 58.01 7.34
2000 58.57 7.57
2001 58.90 7.65

a)

Ho:
Ha:
test-statistic:
df:
Exact P value for the test-statistic
Conclusion relative to the hypothesis:
ts= ,df= ,P=

b)

What is the equation for the regression?

c)

What is the estimate of the amount of variance in Y which is due to its regression on the independent variable?

Solutions

Expert Solution

Ans.

Solve Using Excel:

Year Degrees North Latitude Temp (oC)
1977 57.2 6.26
1978 57.96 6.26
1979 57.65 6.27
1980 57.59 6.31
1981 58.01 6.34
1982 59.06 6.32
1983 56.85 6.37
1984 56.87 6.39
1985 57.43 6.42
1986 57.72 6.52
1987 57.83 6.68
1988 57.87 6.76
1989 57.48 6.78
1990 58.13 6.89
1991 58.52 6.9
1992 58.48 6.93
1993 57.89 6.98
1994 58.71 7.02
1995 58.07 7.09
1996 58.49 7.13
1997 58.28 7.15
1998 58.49 7.29
1999 58.01 7.34
2000 58.57 7.57
2001 58.9 7.65
n 25
r 0.603379776
sx 0.42871047
sy 0.581200482
sxy 0.473449102
b 0.817998723
sb 0.225425783
t 3.628683078
df 23
p-value 0.001407517
alpha 0.05
t-crit 2.06865761
Significant Yes

a)

Ho: β_1=0
Ha: β_1≠0
test-statistic: 3.628683078
df: 23
Exact P value for the test-statistic 0.0014
Conclusion relative to the hypothesis: Fish Distribution depends on Temperature
ts=3.6287 ,df=n-2=24 ,P=0.0014

b)

Rgression Model
y=52.4524+0.8180*Temp

c) 0.3640

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.603379776
R Square 0.364067154 Rgression Model
Adjusted R Square 0.3364179 y=52.4524+0.8180*Temp
Standard Error 0.473449102
Observations 25
ANOVA
df SS MS F Significance F
Regression 1 2.951512809 2.951512809 13.16734088 0.001407517
Residual 23 5.155543191 0.224154052
Total 24 8.107056
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 52.45244226 1.532397184 34.22901244 3.10416E-21 49.28243717 55.62244736
Temp (oC) 0.817998723 0.225425783 3.628683078 0.001407517 0.351669962 1.284327484

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