Question

Asylum Applications and GDP

Economic research provides evidence for a positive relationship between Gross Domestic Product (GDP) and Asylum Applications across the EU. This provides support for the view that a strong economy tend to have higher level of asylum applications.

The Table below gives Asylum Applications and an index of GDP per capita (written as GDP for short) for each year from 2003 to 2014. A regression analysis with Asylum Applications as the response variable and GDP as the predictor variable is shown at the end of the question.

Table: Asylum Applications and GDP in each year

	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014
GDP	140	145	147	148	148	134	129	130	131	132	133	137
Asylum Applications	7,483	4,766	4,323	4,314	3,985	3,866	2,860	1,935	1,290	955	945	1,450

Regression Analysis: Asylum Applications versus GDP (GDP per Capita (index))

1. Discuss the interpretation of the panel in the Regression Analysis output below which relates to the regression coefficients stating the Null Hypothesis
2. Obtain and interpret a confidence interval for the slope parameter and explain how it relates to the corresponding t-test of part (a)

3. How would you interpret the expected response of the Asylum Applications to an increase of 1 unit in GDP per capita?

4. The output contains intervals corresponding to values for GDP of 140 and 177 respectively. Explain how the two types of interval should be interpreted for both levels of absences

5. Given the true GDP value in 2015 turned out to be 177 and the actual level of Asylum Applications was 3,276, would you be willing to use this model for future predictions?Explain your answer taking into consideration the Adj-R squared value

Explain your answer taking into consideration the Adj-R squared value

Regression Equation

Asylum Applications = -19.720 + 166 GDP

Predictor	Coef	SE Coef	T-Value	P-Value
Constant	-19,720	9,104	-2.16	0.06
GDP	166	66	2.51	0.03
Adj-R-Squared	33%

Analysis of Variance

Source	DF	SS (000)	MS(000)	F-Value	P-Value
GDP	1	16,695	16,695	6.33	0.031
Error	10	26,355	2,635
Total	11	43,050

Predicted Values for New Observations

GDP	Fit	SE Fit	95% CI	95% PI
140	3,526	469	(2,440, 4,611)	(-235, 7,305)
177	9,668	2,634	(3,839, 15,499)	(2,806, 16,351) XX

XX denotes an extremely unusual point relative to predictor levels used to fit the model

Answer 1

1)

The regression equation is defined as,

The estimated regression equation is,

Now, the null hypothesis for the regression coefficients are defined as, there is no significant effect of regression coefficient in the regression analysis such that the coefficient values are zero

For Intercept coefficient,

Null Hypothesis:

The hypothesis test can be performed by calculating the t-value and the corresponding significance P-value.

From the regression output summary,

Predictor	Coef	T-Value	P-Value
Constant	-19,720	-2.16	0.06

Let the predetermined significance level,

The P-value = 0.06 is greater than 0.05 at 5% significance level, the null hypothesis is not rejected. Now we can state that

For Slope coefficient,

Null Hypothesis:

From the regression output summary,

Predictor	Coef	T-Value	P-Value
Constant	166	2.51	0.03

The P-value = 0.03 is less than 0.05 at 5% significance level, the null hypothesis is rejected. Now we can state that

2)

The confidence interval for regression coefficients are obtained using the formula,

For Intercept coefficient,

The t-critical value is obtained from t distribution table for degree of freedom = n - 2 = 10 and significance level = 0.05 for 95% confidence interval. (t-critical = 2.228)

Interpretation: there is 95% evidence that the estimated intercept value lies in the range (-40005, 564.976)

For Slope coefficient,

The t-critical value is obtained from t distribution table for degree of freedom = n - 2 = 10 and significance level = 0.05 for 95% confidence interval. (t-critical = 2.228)

Interpretation: there is 95% evidence that the estimated slope value lies in the range (18.94, 313.06)

The t-value for the estimated coefficient value gives the significance of that estimated coefficient to test whether the estimated coefficient takes the hypothesized value and the confidence interval gives the range of the estimated coefficient value for a predetermined significance level and we test whether the confidence interval takes the hypothesized value.

3)

The slope coefficient value is 166 which indicate that for one unit increase in GDP, the Asylum Applications will have an increase of 166.

4)

The confidence interval of Asylum Application for the given GDP value gives the range of expected value for Asylum Applications while the prediction interval gives the range of Asylum Applications for the next predicted value.

5)

From the result summary, the calculated confidence interval and prediction interval are,

GDP	95% CI	95% PI
140	(2,440, 4,611)	(-235, 7,305)
177	(3,839, 15,499)	(2,806, 16,351)

For X = 177, Y = 3276 which doesn't lies in the confidence interval and the prediction interval says the value of predictor variable is vary unusual and the adjusted R-square value for the regression model takes low value( 0.33) based on these evidence we can not go to use this model for future predictions.