3. What does the sample correlation coefficient r measure? Whi...

Question

3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r =0.918 or r =- 0.932? Explain your reasoning.

Accepted Answer

Below there today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. If the correlation coefficient between our studied and exam score. Is R equals 0.762 and the correlation coefficient between our slept and exam score is R equals negative 0.801. Which relationship is stronger? Justify your answer. So it appears for this particular problem, we're asked to read off our multiple choice answers and we're asked to determine which relationship represented in our multiple choice answers is stronger, and then we're asked to justify our answer. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. So, A is both are equally strong. B is R equals 0.762 because it is closer to 1. C is R equals negative 0.801 because it is absolute value is greater. And D is R equals 0.762 because it is positive. So once again, We're ultimately, we're trying to determine which relationship is stronger based on our two different correlation coefficient values that are given to us by the problem itself. So now that we know what we're trying to solve for and we've read off Multiple choice answers. Our first step that we need to take is we need to recall a note that for this particular prompt, the sample correlation coefficient, so once again, this sample correlation coefficient are quantifies the strength and direction of a linear relationship between two quantitative variables. Our second step now is we need to recall and note that the strength is measured by the absolute value of R. So with that in mind, our third step is we need to compute the absolute value of 0.762, which is equal to 0.762, and the absolute value of negative 0.801, which, as we should recall, anytime we take the absolute value of a negative value, it becomes positive. So the absolute value of 0.801. will be equal to 0.801, except now that it's positive. Awesome. So with that in mind, our fourth and final step is we need to note that since 0.801 is greater than 0.762, that will mean that R equals -0.801 represents a stronger linear relationship. We also need to recall for our 5th and final step that the sign only indicates direction. So that means our final answer without a doubt will have to be multiple choice answer letter C, which once again is R is equal to 0.801 because it is absolute value is greater, and that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r =0.918 or r =- 0.932? Explain your reasoning.

Key Concepts

Sample Correlation Coefficient (r)

Strength of Correlation

Positive vs. Negative Correlation

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