Question 1

A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y (kilograms) and the weekly time spent working out under the guidance of a trainer x (minutes.) The resulting least-squares regression line for the study is y = 2.04 + 0.12x.
The correlation coefficient for these data is r = 0.95. Which of the following statements is true?

Accepted Answer

A)  Predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. 
B)  Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. 
C)  Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out. 
D)  Predictions using this equation will be fairly good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out.

Question 2

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  Using this line, you predict that the number of days since last visit to the clinic for a 50-year-old patient will be about

Accepted Answer

A)  63 days. 
B)  78 days. 
C)  165 days. 
D)  200 days. 
E)  252 days.

Question 3

Lean body mass (your weight leaving out fat) helps predict metabolic rate (how many calories of energy you burn in an hour). The relationship is roughly a straight line. The least-squares regression line for predicting metabolic rate (y in calories) from lean body mass (x in kilograms) is y = 113.2 + 26.9x.
Using this regression line, you predict that a person with lean body mass 50 kilograms will have metabolic rate equal to about how many calories?

Accepted Answer

A)  140 
B)  1232 
C)  1345 
D)  1458 
E)  5687

Question 4

A study of many countries finds a strong positive correlation between the life expectancy in a country and the number of Facebook users in the country. This means that:

Accepted Answer

A)  Facebook use is a major contributing cause of longer life. 
B)  life expectancy could be significantly increased by having more people start Facebook accounts. 
C)  in countries where life expectancy is high, the number of Facebook accounts tends to be low. 
D)  in countries where the number of Facebook accounts is low, life expectancy tends to be high. 
E)  None of the answer choices are correct.

Question 5

A education researcher measured the IQ test scores of 78 seventh-grade students in a rural school, and also their school grade point average (GPA) measured on a 12-point scale. Here is a graph of GPA versus IQ for these students:  The line drawn on the graph is the least-squares regression line of GPA on IQ. Use this line to predict the GPA of a student with IQ 110. Your prediction is GPA about

Accepted Answer

A)  1.7. 
B) 6) 
C)  7.5. 
D)  9.

Question 6

A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y (kilograms) and the weekly time spent working out under the guidance of a trainer x (minutes.) The resulting least-squares regression line for the study is y = 2.04 + 0.12x.
We can see from the equation of the line that, as the weekly time spent working out x goes up,

Accepted Answer

A)  muscle mass gained y tends to go up because the slope 2.04 is positive. 
B)  muscle mass gained y tends to go up because the slope 0.12 is positive. 
C)  muscle mass gained y tends to go down because the slope 0.12 is less than 2.04. 
D)  muscle mass gained y tends to go down, because the slope 0.12 is less than 52.

Question 7

Perfect correlation means all of the following except

Accepted Answer

A)  r = -1 or r = +1. 
B)  all points on the scatterplot lie on a straight line. 
C)  all variation in one variable is explained by variation in the other variable. 
D)  there is a causal relationship between the variables. 
E)  each variable is a perfect predictor of the other.

Question 8

Consider a large number of countries around the world. There is a positive correlation between the number of cell phones per person x and the average life expectancy y. Does this mean that we could increase the life expectancy in Rwanda by shipping cell phones to that country?

Accepted Answer

A)  Yes. The correlation says that as the number of cell phones per person goes up, so does life expectancy. 
B)  No. If the correlation were negative, we could accept that conclusion, but this correlation is positive. 
C)  Yes. Positive correlation means that, if we increase x, then y will automatically increase. 
D)  No. The positive correlation just shows that richer countries have both more cell phones per person and higher life expectancies. 
E)  It makes no sense to calculate correlation between these variables.

Question 9

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  The slope of this line tells us the

Accepted Answer

A)  correlation between age of patient and days since last visit. 
B)  change in days since last visit for each year older a patient is, on average. 
C)  change in the age of the patient for each extra day since the last visit. 
D)  average days since last visit for all of the patients.

Question 10

What can we say about the relationship between a correlation r and the slope b of the least-squares line for the same set of data?

Accepted Answer

A)  r is always larger than b. 
B)  r and b always have the same sign (+ or -). 
C)  b is always larger than r. 
D)  b and r are measured in the same units. 
E)  Both "b is always larger than r" and "b and r are measured in the same units" are correct.

Question 11

A study of 6,600 men found that those who consumed a moderate amount of alcohol (one drink or less per night) have lower mortality (on the average) than those who drink none. Is this good evidence that drinking a moderate amount causes lower mortality?

Accepted Answer

A)  Yes, because the study is an experiment. 
B)  No, because people who drink a moderate amount may differ from nondrinkers in other ways, such as income and exercise, that affect mortality. 
C)  Yes, because the sample is so large that the margin of error will be quite small. 
D)  No, because we can't generalize from 6,600 people to the millions of adults in the country.

Question 12

Deaths from highway accidents went down after the adoption of a national 55 mile-per-hour speed limit. Can we be confident that the lower speed limit caused the drop in deaths?

Accepted Answer

A)  Yes, because the study was a randomized, comparative experiment. 
B)  No, because the effect of lower speed limits is confounded with the effect of better highways and safer cars. 
C)  Yes, because a drop in deaths over several years can't happen just by chance. 
D)  No, because of the placebo effect. 
E)  Yes, because correlation implies causation.

Question 13

The best way to settle questions of causation is

Accepted Answer

A)  a careful observational study. 
B)  a properly designed experiment. 
C)  to draw a scatterplot. 
D)  to draw a line graph. 
E)  to calculate a correlation.

Question 14

Lean body mass (your weight leaving out fat) helps predict metabolic rate (how many calories of energy you burn in an hour). The relationship is roughly a straight line. The least-squares regression line for predicting metabolic rate (y in calories) from lean body mass (x in kilograms) is y = 113.2 + 26.9x.
The slope of the regression line is

Accepted Answer

A)  113.2-that is, when x = 0, y = 113.2. 
B)  113.2-that is, the mean metabolic rate is 113.2 calories per hour. 
C)  26.9-that is, the mean metabolic rate is 26.9 calories per hour. 
D)  26.9-that is, when lean body mass goes up by 1 kg, metabolic rate goes up by 26.9 calories. 
E)  26.9-that is, when a person weighs 26.9 more kg, metabolic rate goes up by 1 calorie.

Question 15

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  The slope of this line is

Accepted Answer

A)  600.081. 
B)  8.694. 
C)  -8.694. 
D)  600.081 - 8.694 = 591.387.

Question 16

A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. The study found that children who watch more television tend to have lower reading scores than children who watch fewer hours of television. The study report says that "Hours of television watched explained 9% of the observed variation in the reading scores of the 125 subjects." The correlation between hours of TV and reading score must be

Accepted Answer

A)  r = 0.09. 
B)  r = -0.09. 
C)  r = 0.3. 
D)  r = -0.3. 
E)  Can't tell from the information given.

Question 17

A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y (kilograms) and the weekly time spent working out under the guidance of a trainer x (minutes.) The resulting least-squares regression line for the study is y = 2.04 + 0.12x.
Suppose you worked out for two hours (120 minutes) per week, how much muscle mass gain would you predict?

Accepted Answer

A)  14.40 kg 
B)  750.84 kg 
C)  16.44 kg 
D)  18.48 kg 
E)  None of the answers are correct

Exam 15: Describing Relationships: Regression, Prediction, and Causation