Calculating Correlation

[alfrea11]

I am having particular trouble in finding the correlation -- if I had a set of data to plug into my calculator, I would not be struggling as much, haha. But I have no idea how to calculate the correlation without it, and I am looking for some input. I know that there is a crazy equation, but I don't know how to use it.

Students in last year’s statistics course at a local high school took a midterm exam and then the AP Exam near the end of the course. Imagine a scatterplot in which the score on the midterm exam is graphed on the x-axis and the score on the AP Exam is graphed on the y-axis. The correlation between the two scores is 0.8. The mean for the scores on the midterm is 82, and the standard deviation is 8. The mean for the scores on the AP Exam is 3.6, and the standard deviation is 0.6.



Find the equation of the least squares regression line for predicting a score on the AP Exam from a score on the midterm exam. Use the equation b[sub:2rbzfbuc]1[/sub:2rbzfbuc] = r(s[sub:2rbzfbuc]y[/sub:2rbzfbuc] / s[sub:2rbzfbuc]x[/sub:2rbzfbuc]) to help. Write your equation in terms of x and y.

Predict the score on the AP Exam from a score of 90 on the midterm.

 

[kristopher0123]

It would seem the Correlation is given to you as .8 for the given problem...

"The correlation between the two scores is 0.8."

As to finding the Least Squares Regression Line (y = a + bx) with this information, you will need to use the equation (format issue fixed) b = r(Sy / Sx) where r is the given correlation, 0.8, and Sy is the standard devation of the response variable, which in this case is the score on the AP Exam, given as .6, and Sx is the stand. dev. of the explanitory variable, which in this problem is the score on the midterm, given as 8. So to find b in the LSRL equation, plug in the numbers.

To find a, the equation is a = ? - b? where ? is the mean of the explanitory variable, given as 82 (score on midterm, usually an x with a bar over it, which i couldn't find...) and ? is the mean of the response variable, given as 3.6 (score on AP Exam, usually a y with a bar over it, which again couldn't find...) and b is the number which is found as shown above.

Finally, to predict the AP Exam score of someone who scored 90 on the midterm, simply plug 90 into the X in the LSRL equation and solve.