### True coefficient of correlation

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1. Testing the null hypothesis that the slope of the true regression line equals zero is equivalent to testing whether the true coefficient of correlation could be zero. Why?

2. For n 5 15 data points, r2 5 0.81. At the 0.05 level of significance, can we conclude that the true coefficient of correlation could be zero?

3. For n 5 37 data points, r2 5 0.29. At the 0.02 level of significance, can we conclude that the true coefficient of correlation could be zero?

4. Based on sample data, the 90% confidence interval for the slope of the population regression line is found to be from -2.5 to 1.4. Based on this information, what is the most accurate statement that can be made about the p-value in testing H0: /31 5 0 versus H1: /31 * 0? Explain.

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