Question

1. Conduct a 95% hypothesis test for your slope coefficient (a t-test). Interpret, in words and with numerical evidence, the conclusion of that hypothesis test.
2. Conduct a 95% hypothesis test for your model (a F-test). Interpret, in words and with numerical evidence, the conclusion of this hypothesis test.

   Temp Anomaly (deg. C)	Northern Sea Ice Extent (10^6 sq km)
   0.2	12.49
   0.34	12.32
   0.43	12.33
   0.14	12.14
   0.39	12.44
   0.21	12.34
   0.2	11.91
   0.25	11.99
   0.41	12.21
   0.52	11.40
   0.38	12.09
   0.53	11.97
   0.53	11.69
   0.24	11.75
   0.28	12.11
   0.39	11.92
   0.57	12.01
   0.49	11.42
   0.55	11.84
   0.85	11.67
   0.6	11.76
   0.58	11.69
   0.68	11.51
   0.8	11.60
   0.78	11.36
   0.69	11.40
   0.88	11.24
   0.78	10.91
   0.86	10.77
   0.65	10.47
   0.79	10.98
   0.92	10.93
   0.79	10.71
   0.77	10.48
   0.81	10.41
   0.88	10.90
   0.96	10.79
   1.23	10.57

Answer 1

Independent variable, X: Temp Anomaly (deg. C)

Dependent variable, Y: Northern Sea Ice Extent (10^6 sq km)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.808271102
R Square	0.653302174
Adjusted R Square	0.643671679
Standard Error	0.36926187
Observations	38
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9.249844167	9.249844167	67.83682085	8.44226E-10
Residual	36	4.908755833	0.136354329
Total	37	14.1586
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	12.66751422	0.149427773	84.77349245	4.77333E-43	12.36446065	12.97056779
Temp Anomaly (deg. C), X	-1.917026418	0.232753036	-8.236311119	8.44226E-10	-2.38907145	-1.444981385

1:

Hypotheses are:

The test statistics is

t = -8.236

The p-value is: 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis at 5% level of significance. That is slope is significant to model.

2:

Hypotheses are:

The test statistics is

F = 67.837

The p-value is: 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis at 5% level of significance. That is model is not significant to model.