In Professor Smith's statistics course, the correlation between students' total scores before the final exam and their final exam scores is r = 0.67. The pre-exam totals for all students in the course have a mean of 275 and a standard deviation of 26. The final exam scores have a mean of 71 and a standard deviation of 6. Professor Smith has lost Jane's final exam, so decides to predict her final exam score based on her pre-exam course total, which is 293. Use least-squares regression to predict Jane's final exam score.
Predicted Final Exam Score =
Please explain to me how to do this. My teacher does not teach this kind of stuff in class and he expects us to know this.
Pre-exam: mean = 275, sd = 26
Final exam: mean = 71, sd = 6
Correlation: r = 0.67
Regression equation is in this format:
predicted y = a + bx
...where a = intercept and b = slope.
To find the equation, you need to substitute the information given in the problem into a workable formula:
predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
Note: xbar = mean of x; ybar = mean of y.
I'll let you take it from here. (Once you calculate the predicted y formula, substitute 293 for x in the formula to predict Jane's final exam score.)
posted by MathGuru
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