Question

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?

Answer 1

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