Name: ____________________
2 AP Quiz Regression - Practice
This is an AP Exam Quiz. Please answer the two multiple choice questions below and then complete the free response
question. Remember to be thorough in your free response solution. You have 40 minutes to complete the quiz.
1. Thomas’ AP Statistics teacher was teaching a lesson and concluded a question by stating that “64% of the
variation in the dependent variable could be explained by the independent variable.” What can Thomas
conclude from such a statement?
a. There is a reasonable certainty that the independent variable causes the dependent variable.
b. The least squares regression line is positively sloped.
c. The least squares regression line is negatively sloped.
d. The correlation is either 0.8 or -0.8.
e. None of the above.
2. A residual plot was constructed after having performed Linear Regression on a data set. The residual plot is
shown below.
Based on the residual plot, one could conclude that…
a. a linear model was appropriate.
b. a linear model was inappropriate.
c. the data set was biased.
d. the data set had insufficient size.
e. None of the above
3. A scientist was concerned with the transmission of a particular chemical (HX1) across a particular membrane. He
noticed that as the membrane grew thicker (measured in mm), the transmission rate (in molecules per minute)
declined according to a fixed rate. He gathered 30 data points and conducted a Linear Least Squares Regression
T Test. His data is shown below.
Predictor
Coef
SE Coef
T
P
Constant
1542
11.3
1.25
.381
Membrane Thickness
-74
3.1
5.4
.0001
S = 0.314
R-Sq = .951
R-Sq (adj) = .921
a. Find the equation of the regression line and the correlation coefficient.
b. What is the predicted transmission rate at a membrane thickness of 5 mm?
c. If the actual transmission rate at a membrane thickness of 5mm was measured to be 1204
molecules per minute, what is the residual at this membrane thickness?
d. The scientist’s initial measurements had involved membranes varying in thickness from 1
mm to 30 mm. To which thickness membranes should he feel comfortable using his model?