WorksheetsAP Statistics Unit 2 Review
Total questions: 50
Worksheet time: 2hrs 40mins
The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is
the correlation
the slope of the least-squares regression line
the square of the correlation coefficient
the intercept of the least-squares regression line
the residual
Of those whose favorite sport to watch on television is football, what fraction are males?
40/81
52/81
40/52
52/81
12/40
If the point with the red x is removed from the scatterplot, what will happen to the slope of the LSRL and the correlation coefficient?
slope increases, r increases
slope decreases, r increases
slope increases, r decreases
slope decreases, r decreases
slope is unchanged, r increases
Measurements on young children in Mumbai, India, found this least-squares line for predicting height (cm) y from arm span (cm) x: y-hat = 6.4 + 0.93x
According to the regression line, the predicted height of a child with an arm span of 100 cm is about106.4 cm
99.4 cm
93 cm
15.7 cm
7.33 cm
Does the residual plot support the appropriateness of a linear model?
Yes because the residual plot has no apparent pattern
Yes because half the residuals are positive and half are negative
No because points appear to be randomly distributed
No because some points are close to the line when others are not
Yes, because as age increases, the residuals increase
What can you know from the relative frequency graph?
The same amount of people were in each continent in 2011 (orange)
More people were in Asia in 2012
More people were in North America overall
More people were in North America in 2010
A greater percentage of people were in North America than the other continents in 2010
For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3*weight Which of the following is NOT correct?
The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.
The predicted tail length of a mouse that weighs 39 grams is 137 millimeters.
By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive.
If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3
One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is -7.
What is the value of the correlation coefficient?
0.891
-0.891
0.875
0.943
-0.943
Describe the mean and median of this distribution.
Due to the skew, the mean is greater than the median
Due to the skew, the median is greater than the mean
The median is equal to the mean
The mean cannot be estimated from the histogram, but the median can
The median cannot be estimated from the histogram, but the mean can
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116. Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 2009 and scored 530. Who did better on the exam, and how can you tell?
Colleen - she scored 30 points higher than Jane
Colleen - her standardized score in higher than Jane's
Jane - her standardized score is higher than Colleen's
Jane - the standard deviation was bigger in 2009
The two sisters did equally well - their z-scores are the same
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
85.5
90
9
95.5
none of these
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?
–2.0
2.0
3.0
93
none of these
A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y-hat= 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true?
For each one-point increase in performance rating, the raise will increase on average by $1400.
The actual relationship between salary raises and performance rating is linear.
The residuals for half the observations in the dataset will be positive.
The correlation between salary raise and performance rating is negative.
If the mean performance rating is 1.2, then the mean raise is $3800.
A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model?
A residual plot is not an appropriate means for evaluating a linear model.
The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.
The curved pattern in the residual plot suggests that the linear model is not appropriate.
There are not enough data points to draw any conclusions from the residual plot.
The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.
One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that
minimizes the sum of the distances between the actual UV values and the predicted UV values.
minimizes the sum of the squared residuals between the actual yield and the predicted yield.
minimizes the sum of the distances between the actual yield and the predicted UV.
minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values.
minimizes the perpendicular distance between the regression line and each data point.
The equation y=−26.16 + 1.58x can be used to predict a student's heart rate after a brisk walk around the school, if their resting heart rate (before the walk) is known. Suppose a student's resting heart rate is 65 bpm, and after the walk their heart rate is 80 bpm. What is the residual for this student?
76.54
3.46
-3.46
-76.54
The correlation (r) between high school students' height (in inches) and weight (in pounds) for a large sample of students is found to be 0.3. If the weight measurements are converted to kg, what will be the resulting correlation?
(1 kg = 2.2 lbs)
0.3
0.66
-0.3
0.136
Data is obtained for a large group of college students relating the time they spent writing an essay and the grade on the essay. The equation is
grade = 30.18 + 6.49(time) with r = 0.724
What percentage of the variation in grades can be explained by looking at time spent on the essay?
52.4%
72.4%
27.6%
47.6%
Interpret the circled point on this relative cumulative frequency graph.
60% of Starbucks drinks have 30g of sugar.
60% of Starbucks drinks have 30g of sugar or more.
60% of Starbucks drinks have 30g of sugar or less
None of these interpretations is correct.
Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. What is the equation for the LSRL?
Caffeine = 2.544 + 0.164(hours)
Hours = 2.544 + 0.164(Caffeine)
Caffeine = 0.164 + 2.544(hours)
Hours = 0.164 + 2.544(Caffeine)
y= 40x+100, where x is number of weeks and y is weight in grams.
What does the y-intercept mean in context of the problem?
What type of correlation best describes the scatter plot shown?
positive, weak
positive, strong
negative, weak
no correlation
Estimate the correlation coefficient for this scatterplot.
r = 1.2
r = 0.89
r = 0
r = -0.89
The scatter plot shows the number coffee shops in different cities and the number of violent crimes. Which of the following is NOT true?
A) As the number of coffee shops increase, violent crimes appears to increase.
B) The line of best fit (regression line) shows a positive correlation
C) The data has a positive correlation coefficient
D) An increase in coffee shops causes an increase in violent crimes
If the correlation coefficient is r = 0.3, what type of data is shown?
Strong positive
Weak positive
Strong negative
Weak negative
When calculating the linear model (which is the equation for the Line of Best Fit for a set of quantitative data) our goal is to...
Minimize the residuals
Maximize the residuals
Ignore the residuals
What are residuals?
I predicted someone would score a 78% on their test, but they actually scored an 81%. What's the residual?
81 - 78 = 3
78 - 81 = -3
What's residual?
(a) is the use of a regression line for prediction outside the interval of x values used to obtain the line.
The ___________________ measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.
coefficient of determination
x2
r2
coefficient of relaxation
Which of the following definitions are true...
Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.
An outlier in regression is a point that does not follow the pattern of the data and has a large residual.
An influential point in regression is any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.
All of the above
Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value. What was the actual activity level rating for the fish at a temperature of 20°C?
87
84
81
66
3
Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value. Which of the following gives a correct interpretation of s in this setting?
For every 1°C increase in temperature, fish activity is predicted to increase by 4.785 units.
The typical distance of the temperature readings from their mean is about 4.785°C.
The typical distance of the activity level ratings from the least-squares line is about 4.785 units.
The typical distance of the activity level readings from their mean is about 4.785 units.
At a temperature of 0°C, this model predicts an activity level of 4.785 units.
The following regression is for the relationship between the length (cm) and weight (g) of a small marine fish. Which of the following is the closest predicted weight of a fish that was 12 cm long according to this model?
2.63 g
3.50 g
13.89 g
33.23 g
426.58 g
This is a computer regression analysis of the relationship between log(Number of Employees at Microsoft) and year. Which of the following is the correct regression equation from this analysis if y=number of employees at Microsoft and x=year?
ŷ = -449.71 + .228x
logŷ = -449.71 + .228x
ŷ = -449.71 + .228(logx)
logŷ = .228 - 449.71x
ŷ = .228 - 449.71(logx)
A
B
C
D
E
A
B
C
D
E
