In: Math
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? |
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 |