1 What does regression add above and beyond what we learn from correlation? Regression allows us to make predictions based on the relation established in the correlation. Regression also allows us to consider the contributions of several variables.
2 Is there any difference between Yˆ and a predicted score for Y? There is no difference between these two terms. They are two options for expressing the same thing.
3 What does the slope tell us? Our slope tells us the amount that the dependent variable changes as the independent variable increases by 1.
4 How are the sign of the correlation coefficient and the sign of the slope related? The sign of the correlation coefficient is the sign of the slope. Meaning if the correlation coefficient is negative, the slope of the regression line is also negative. As the coefficient goes towards 1 or -1, the points gradually comes to together to form a line. At -1 or 1, it forms a perfect line, thus a perfect correlation
5 Given the regression line Y2 = -6 + 0.41 (X), make predictions for each of the following:
a. X = 25
b. X = 50
c. X = 75
6 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.426, Yˆ = 219.974 + 186.595(X).
X Y
0.13 200.00
0.27 98.00
0.49 543.00
0.57 385.00
0.84 420.00
1 .12 312.00
MX = 0.57 MY = 326.333
SDX = 0.333 SDY = 145.752
7. Compute the standardized regression coefficient for the data presented in Exercise 14.26. Remember, r = 0.426, Yˆ = 219.974 + 186.595(X).
X Y
0.1 3 200.00
0.27 98.00
0.49 543.00
0.57 385.00
0.84 420.00
1 .1 2 31 2.00
MX = 0.57 MY = 326.333
SDX = 0.333 SDY = 145.752
8. A regression analysis of data from some of our statistics classes yielded the following regression equation for the independent variable, hours studied, and the dependent variable, grade point average (GPA): Yˆ = 2.96 + 0.02(X).
a. If you plan to study 8 hours per week, what would you predict for your grade?
b. If you plan to study 1 0 hours per week, what would you predict for your grade?
c. Create a graph and draw the regression line based on these two pairs of scores, plus the X value 1 1 and its predicted score on Y.
d. Do some algebra, and determine the number of hours you'd have to study to have a predicted GPA of the maximum possible, 4.0. Why is it misleading to make predictions for anyone who plans to study this many hours (or more)?