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I need to do a regression hypothesis test on the data below.

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I need to find if...
I need to do a regression hypothesis test on the data below. I need to find if there is a positive relation between literacy rate and unemployment rates.

Country Literacy % Unemployment
Iceland 100 2.7
Luxembourg 100 2.7
Norway 100 3
Denmark 100 5.3
Australia 100 6.4
Finland 100 9.8
Czech Republic 99.9 8.7
Latvia 99.8 8.8
Estonia 99.8 9.2
Slovenia 99.7 9.8
Lithuania 99.6 5.3
Slovakia 99.6 11.5
Switzerland 99 1.9
Netherlands 99 2.6
Japan 99 4.7
United Kingdom 99 5.5
Sweden 99 6
New Zealand 99 6.3
Hungary 99 9.4
France 99 9.7
Germany 99 9.9
Poland 99 12
Submitted: 8 years ago.Category: Math Homework
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Answered in 39 minutes by:
6/14/2010
Math Tutor or Teacher: ExcelSpecialist,
 replied 8 years ago
ExcelSpecialist
Category: Math Homework
Satisfied Customers: 368
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Hello and welcome to JustAnswer,

 

Your null hypothesis and alternate hypothesis are:

H0: ρ = 0

Ha: ρ < 0 (You mention a positive relation, but I assume you want to test for an increasing unemployment rate when the literacy rate decreases, which is a negative correlation? Let me know if this is not what you need.)

 

First we have to calculate r = Sxy/(√(Sxx*Syy)

Sxx = 6*(100-99.47)² + 10*(99-99.47)² + (99.9-99.47)² + 2*(99.8-99.47)² + (99.7-99.47)² + 2*(99.6-99.47)² = 4.384

Syy = 206.524

Sxy = -2.406

 

r = -0.08

 

The test statistic is: t = r√(n-2)/√(1-r²) = -0.359

 

The critical value at significance level 0.05 is t(0.05,20) = 2.086

 

Since the absolute value of the test statistic is smaller than the critical value, you cannot reject the null hypothesis, meaning you cannot conclude that there is a negative correlation between literacy rate and unemployment rate at the 0.05 significance level.

 

 

Let me know if you have any further questions, otherwise don't forget to click the Accept-button.

 

Best regards,

 

Tom

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