Question

A)Test the significance of the population correlation coefficient r (t-test using        α = 5%)

B)Test the significance of the population regression coefficient b₁ (t-test using        α = 5%)

C)Interpret the Coefficient of Determination as measure of the goodness of the fit (R²). Data sets are below and Thanks!

Unemployment	Inflation
4.0	3.0
4.1	4.1
4.0	5.9
3.8	-0.6
4.0	1.8
4.0	5.8
4.0	2.9
4.1	0.0
3.9	5.2
3.9	1.7
3.9	1.7
3.9	2.3
4.2	5.7
4.2	2.3
4.3	0.6
4.4	1.7
4.3	5.1
4.5	2.3
4.6	-1.7
4.9	0.0
5.0	4.0
5.3	-2.8
5.5	-0.6
5.7	-0.6
5.7	1.7
5.7	1.7
5.7	3.4
5.9	3.9
5.8	0.6
5.8	1.1
5.8	2.2
5.7	2.8
5.7	1.7
5.7	2.2
5.9	1.7
6.0	1.1
5.8	3.3
5.9	5.5
5.9	4.4
6.0	-4.4
6.1	-0.6
6.3	1.1
6.2	2.2
6.1	3.8
6.1	2.7
6.0	-0.5
5.9	-1.1
5.7	2.2
5.7	4.3
5.6	3.2
5.7	4.3
5.5	1.1
5.6	5.9
5.6	3.2
5.5	0.0
5.4	1.1
5.4	1.6
5.4	5.8
5.4	2.1
5.4	0.0
5.2	1.1
5.4	3.7
5.1	5.7
5.1	4.7
5.1	-0.5
5.0	-0.5
5.0	6.2
4.9	5.6
5.1	12.2
4.9	2.5
5.0	-6.5
4.9	-0.5

Answer 1

Independent variable, X: Unemployment

Dependent variable, Y: Inflation

Following is the output of regression analysis;

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.127383261
R Square	0.016226495
Adjusted R Square	0.002172588
Standard Error	2.7536036
Observations	72
ANOVA
	df	SS	MS	F	Significance F
Regression	1	8.75448263	8.75448263	1.154589606	0.286280391
Residual	70	530.7632951	7.582332788
Total	71	539.5177778
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.693261456	2.337815171	2.007541706	0.048553722	0.030636179	9.355886732
Unemployment, X	-0.480458221	0.447138234	-1.074518314	0.286280391	-1.372247297	0.411330855

A)

Hypotheses are:

The correlation coeffciient is:

r = -0.12738

Degree of freedom: df=n-2=70

Test statistics:

The p-value is: 0.2863

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

b)

Hypotheses are:

Test statistics:

The p-value is: 0.2863

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

C)

The R-square is:

R -square = 0.0162

That is 1.62% of variation in dependent variable is explained by independent variable.