Pre- study scores versus post- study scores for a class of 120 college freshman english students were considerated. The residual plot for the least squares regression line showed no pattern. The least squares regression line was y^=0.2+0.9x withwith a correlation coefficient r=0.76. What percent of the variation of post-study scores can be explained bt the variation in pre- study scores? A. 76.0% B. 52.0% C. 57.8% D. 87.2%
Well, well, well! It seems we have a statistics question on our hands. Don't worry, I've got just the right amount of funny to make this topic less daunting.
First of all, we should give a round of applause to those 120 college freshman English students. They're working hard! 🎉
Now, let's tackle this question. The correlation coefficient (r) is 0.76. That's a good sign, as it indicates a moderately strong positive relationship between pre-study and post-study scores. But we're interested in the percent of the variation in post-study scores that can be explained by pre-study scores.
Here's where the least squares regression line comes in. It's y^ = 0.2 + 0.9x. But hold your laughter, because I need you to know something important! The square of the correlation coefficient (r^2) tells us the proportion of the variation in the dependent variable (post-study scores) that can be explained by the independent variable (pre-study scores). In other words, it tells us the percent of the variation we're looking for.
So, let's calculate it together. What's 0.76 squared? That's right, 0.5776!
Now all we have to do is convert it to a percentage. Multiplying 0.5776 by 100, we get 57.76%. But let's not forget to round it to the nearest tenth. Drumroll, please... 🥁
The answer is C. 57.8%! That's the percent of the variation in post-study scores that can be explained by the variation in pre-study scores.
I hope that put a smile on your face, and as always, remember that statistics can be fun too! 🤡
To determine what percent of the variation of post-study scores can be explained by the variation in pre-study scores, we can square the correlation coefficient r and convert it to a percentage.
The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. In this case, it measures the relationship between pre-study scores (x) and post-study scores (y).
Given that the correlation coefficient, r, is 0.76, we can square it to get 0.76^2 = 0.5776.
To convert this to a percentage, we multiply by 100: 0.5776 * 100 = 57.76%.
Therefore, approximately 57.8% of the variation in post-study scores can be explained by the variation in pre-study scores.
The correct answer is C. 57.8%.