StatisticsdrillCorrelation from a slope
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
A least squares line predicting y from x has slope b = 3.8. The sample standard deviation of x is 1 and the sample standard deviation of y is 4. What is the correlation coefficient r? Round to 3 decimal places.
What this problem teaches
The formula: b = r × s_y / s_x, so r = b × s_x / s_y. r always has the same sign as the slope, and it has no units: it is the slope after both variables are put in standard deviation units.
A hint if you get stuck
The slope and the correlation are linked by b = r × s_y / s_x, so r = b × s_x / s_y.
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