Source : https://www.hackerrank.com/challenges/s10-mcq-7
The regression line of on is , and the regression line of on is . What is the value of the Pearson correlation coefficient?
Note: If you haven't seen it already, you may find our Pearson Correlation Coefficient Tutorial helpful in answering this question.
Source : https://www.hackerrank.com/challenges/s10-mcq-7
Solution
| Karthikalapati.blogspot.com | |
| Answer: -3/4 | |
| *** Step 1: Rewrite the 2 lines in proper form *** | |
| Rewrite the 2 lines as: | |
| y = -2 + (-3/4) * x | |
| x = -7/4 + (-3/4) * y | |
| so b1 = -3/4 and b2 = -3/4 | |
| *** Step 2: Apply Pearson's Coefficient formula *** | |
| Let p = pearson coefficient | |
| Let x_std = standard deviation of x | |
| Let y_std = standard deviation of y | |
| p = b1 (x_std / y_std) | |
| p = b2 (y_std / x_std) | |
| Multiplying these 2 equations together we get | |
| p^2 = b1 * b2 | |
| p^2 = (-3/4) * (-3/4) | |
| p^2 = 9/16 | |
| p = 3/4 or -3/4 (depending on correlation of x and y) | |
| *** Step 3: Find out if p is postive or negative *** | |
| Notice that both of the original line equations have negative slopes, | |
| so x and y are negatively correlated by definition. So, p = -3/4 |
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