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Use the following results obtained from a simple linear regression analysis with 12 observations. = 37.2895...

Use the following results obtained from a simple linear regression analysis with 12 observations.

= 37.2895 − (1.2024)X
r2 = .6744sb = .2934

Test to determine if there is a significant negative relationship between the independent and dependent variables at α = .05. Give the test statistic and the resulting conclusion.  

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Answer #1

The following needs to be tested:

where \rhoρ corresponds to the population correlation.

The sample size is n = 12 so then the number of degrees of freedom is df = n-2 = 12 - 2 = 10

The corresponding t-statistic to test for the significance of the correlation is:

The p-value is computed as follows:

Since we have that p = 0.9919 ≥0.05, it is concluded that the null hypothesis H0​ is not rejected.

Therefore, based on the sample correlation provided, it is concluded that there is not enough evidence to claim that the population correlation ρ is less than 0, at the 0.05 significance level.

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