Question

The Regression Equation Suppose in this semester, our Exam 1 average was about 85 with an SD of about 12. Suppose the correlation between our Exam 1 and Exam 2 scores will be similar to what it has been in the past, about 0.6, and finally, suppose our Exam 2 scores will be similar to previous semesters' Exam 2 scores with an average of 82 and a SD of 8.2. Use this information to answer the following questions: What is the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores? Round to 3 decimal places.

Answer 1

Answer:

0.410

Step-by-step explanation:

We are predicting exam 2 scores from exam 1 scores so the dependent variable y is exam 2 scores and independent variable is exam 1 scores x.

The regression equation is

y=a+bx

Where y is exam 2 scores and x is exam 1 scores.

We are given that

correlation coefficient=r=0.6.

Mean and standard deviation of x are xbarx=85 and Sx=12.

Mean and standard deviation of y are xbary=82 and Sy=8.2.

The slope b for this scenario can be found as

$slope=b=r\frac{Sy}{Sx}$

$slope=b=0.6(\frac{8.2}{12} )$

$slope=b=0.6(0.6833)$

$slope=b=0.41$

Thus, the slope of the regression equation for predicting  Exam 2 scores from Exam 1 scores is 0.410.