Question

Homework problem 50 involves both regression and correlation so we refer to the key elements in both section 10-1 and 10-2. I used a spreadsheet that I developed for another problem with the data provided to find the regression line for predicting the depth of an earthquake from its magnitude. I have attached my spreadsheet. The plot shows a lot of scatter in the data and the calculated linear correlation coefficient r is low: -0.047. We are asked to estimate the earthquake depth for a magnitude of 1.1. We can use the equation but the flowchart on page 484 says that we should do that only if the line is a good one. If not, we use the mean of the depth data previously calculated for the regression analysis as the estimate. From section 10-1, to determine if the regression line is a good one, we check the absolute value of the calculated r against the critical value of the Pearson’s correlation coefficient from the table provided for our sample size and significance level. From the provided table, “NOTE: To test H0​: ρ=0 against H1​: ρ≠​0, reject H0 if the absolute value of r is greater than the critical value in the table.” In my case, the absolute value of the calculated r is 0.047 and the critical value for sample size of 50 and α of 0.05 is 0.279. Do I reject the null hypothesis? What do I conclude about the predicted value of the depth at the magnitude of 1.1? Why?

Answer 1

Answer:

For the given scenario of t test for the population correlation coefficient, the absolute value of the sample correlation coefficient is given as 0.047 and the critical value in the table is given as 0.279.

So, absolute value of sample correlation coefficient is less than critical value.

So, we do not reject the null hypothesis.

So, given correlation coefficient is not statistically significant.

So, we cannot use this correlation coefficient for the prediction of the dependent variable depth based on the independent variable magnitude.

So, we cannot use the regression equation based on this correlation coefficient for the prediction of depth when magnitude is 1.1.