AP Statistics
Chapter 3 More Review
Name ________________________________
True or False
________1. The correlation is to bivariate data what the standard deviation is to univariate data
________2. The correlation measures direction and strength but not shape
________3. If the correlation is near 0, knowing the value of one variable gives you a narrow interval
of likely values for the other variable.
________4. No matter what data set you look at, the correlation coefficient, r, and lease squares slope,
b1, will always have the same sign.
5. In a study of 190 nations, the LSRL for the relationship between birthrate (per thousand per year) and
female literacy rate (in percent) is predicted birthrate = -0.38 literacy + 53.5, with r = 0.8. Uganda
has a birthrate of 47 and a female literacy rate of 60. What is the residual for Uganda?
(a) -17.1
(b) 29.3
(c) 16.3
(d) 64.1
(e) 69.8
6. In a linear regression of heights of a group of trees versus their circumferences, the pattern of
residuals is U-shaped. Which of the following must be true?
I. A nonlinear regression would be a better model.
II. For trees near the middle of the range of tree circumferences studied, the predicted tree
height tends to be too tall.
III. r will be close to 0.
(a) II only
(b) III only
(c) I and II
(d) I and III
(e) I, II, and III.
7. The Barbarian Aptitude Test (BAT) gives each Barbarian two scores, one for pillaging and one for
burning. The scores range from a low of 0 to a high of 50. The least squares equation for a large
group of Barbarians who took the BAT is burning = 0.3 pillaging + 19, with r = 0.6. Which is the
best interpretation of the slope of this line?
(a) A Barbarian who studies harder and improves her pillaging score by 1 point on the next BAT
will tend to increase her burning score by about 0.3 points as well.
(b) Barbarians tend to score about 0.3 point higher on burning than on pillaging.
(c) Barbarians score about 30% as many points on burning as on pillaging.
(d) The burning score is highly correlated with the pillaging score.
(e) A Barbarian who earned one more point on pillaging than another Barbarian tended to earn
only 0.3 point more on burning.
8. A least squares regression analysis using a rating of each Barbarian’s personal cleanliness as the
explanatory variable and the number of raids he or she has carried out as the response variable found
a positive relationship with r2 = 0.81. Which is not a correct interpretation of this information?
(a) The correlation between personal cleanliness and the number of raids is 0.9.
(b) There is a strong relationship between personal cleanliness and number of raids among
Barbarians.
(c) A Barbarian who is more personally clean than another also tends to have made more raids.
(d) There is an 81% chance that the relationship between personal cleanliness and number of
raids is linear.
(e) 81% of the variation in number of raids conducted by a Barbarian can be explained by the
linear relationship between number of raids and personal cleanliness in Barbarians.
9. Rank these summaries for three sets of bivariate data by the strength of the relationship, from
weakest to strongest.
A: ŷ = 90 +100x
x
!12
3
C: ŷ = 1.05 + 0.01x
B: ŷ =
sx = 5
sy = 1000
sx = 0.9
sy = 1 sx = 0.05
sy = 0.002 The following display shows the calorie and fat content of 5 oz of various kinds of pizza. (Data from Consumer Reports, January 2002). Pizza Pizza Hut’s Hand Tossed Domino’s Deep Dish Pizza Hut’s Pan Domino’s Hand Tossed Little Caesar’s Original Round Little Caesar’s Deep Dish Pizza Hut’s Stuffed Crust Fat (g) 9 19.5 14 12 8 14.2 15 Calories 230 385 280 305 230 350 370 10. Plot the points and describe what you see. 11. Is a linear regression model appropriate for these data? Explain.
12. What is the equation of the least-squares regression line?
13. If a pizza has 13 grams of fat, what do we predict the calorie content to be?
14. What is the residual for Pizza Hut’s Pan?
15. What is the coefficient of determination for this relationship?
Explain what it means, in context.
16. Interpret the slope of the LSRL in context.
ANSWERS
1. True
2. True
3. False
4. True
5. c
6. e
7. e
8. D
9. C, B, A
10. These data exhibit a moderately strong, linear trend in a positive direction.
11. Yes, a linear regression model appears to be appropriate for these data. A residual plot of the data
shows reasonably random scatter. There is no clear pattern in the residuals.
12. ŷ = 111.626 +14.925x with x = fat (g) and y = calories.
13. 305.65 calories.
14. -40.575
2
15. r = .824; 82.4% of the variability in calories in pizza can be explained by the least squares
relationship between fat and calories.
16. For each additional gram of fat in a pizza, we expect, on average, to find an additional 14.9 calories.