Deck 4: Describing the Relation Between Two Variables

Question 1

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomlyselected adults.

Answer 1

Question 2

In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and theyield of wheat (bushels per acre).

Answer 2

Question 3

In which scatter diagram is r = 1?

A) b
B) a
C) f
D) d

Answer 3

A

Question 4

There is a strong negative correlation between years of education and births per woman.

Question 5

The data below are the final exam scores of 10 randomly selected history students and the number of hoursthey studied for the exam.

Question 6

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) themanagerʹs sales representatives travel per month and the amount of sales (in thousands of dollars) per month.

Question 7

In which scatter diagram is r = 0.01?

Question 8

The data below are the temperatures on randomly chosen days during a summer class and the number ofabsences on those days.

Question 9

In which scatter diagram is r = -1?

A) a
B) b
C) f
D) d

Question 10

The variable is the variable whose value can be explained by the variable.

A) response; predictor
B) response; lurking
C) lurking; response
D) predictor Responselem.

Question 11

The data below are the number of absences and the final grades of 9 randomly selected students from aliterature class.

Question 12

In order for employees of a company to work in a foreign office, they must take a test in the language of thecountry where they plan to work. The data below show the relationship between the number of years thatemployees have studied a particular language and the grades they received on the proficiency exam.

Question 13

A) The variables appear to be positively, linearly related.

B) The variables do not appear to be linearly related.

C) The variables appear to be

D) The variables do not appear to be negatively, linearly related. linearly related.

Question 14

There is no correlation between years of education and births per woman.

Question 15

Five brands of cigarettes were tested for the amounts of tar and nicotine they contained. All measurements arein milligrams per cigarette.

Question 16

The scores of nine members of a local community college womenʹs golf team in two rounds of tournament playare listed below.

Question 17

Which scatter diagram indicates a perfect positive correlation?

A) b
B) a
C) c
D) f

Question 18

A) The variables do not appear to be

B) The variables appear to be linearly related. negatively, linearly related.

C) The variables do not appear to be linearly related.

D) The variables appear to be positively, linearly related.

Question 19

There is a strong positive correlation between years of education and births per woman.

Question 20

A) The variables appear to be

B) The variables do not appear to be positively, linearly related. linearly related.

C) The variables appear to be

D) The variables do not appear to be negatively, linearly related. linearly related.

Question 21

Calculate the linear correlation coefficient for the data below.

A) -0.104
B) -0.132
C) -0.549
D) -0.581

Question 22

A history instructor has given the same pretest and the same final examination each semester. He is interestedin determining if there is a relationship between the scores of the two tests. He computes the linear correlationcoefficient and notes that it is 1.15. What does this correlation coefficient value tell the instructor?

A) The history instructor has made a computational error.
B) There is a strong positive correlation between the tests.
C) There is a strong negative correlation between the tests.
D) The correlation is something other than linear.

Question 23

Calculate the linear correlation coefficient for the data below.

A) -0.995
B) -0.671
C) -0.778
D) -0.885

Question 24

Calculate the linear correlation coefficient for the data below.

A) 0.990
B) 0.881
C) 0.819
D) 0.792

Question 25

The data below are the final exam scores of 10 randomly selected calculus students and the number of hoursthey slept the night before the exam. Calculate the linear correlation coefficient.

A) 0.847
B) 0.991
C) 0.761
D) 0.654

Question 26

True or False: A doctor wishes to determine the relationship between a maleʹs age and that maleʹs totalcholesterol level. He tests 200 males and records each maleʹs age and that maleʹs total cholesterol level. Themales cholesterol level is the predictor variable?

Question 27

The data below represent the numbers of absences and the final grades of 15 randomly selected students froman astronomy class. Construct a scatter diagram for the data. Do you detect a trend?

Question 28

Construct a scatter diagram for the given data. Determine whether there is a positive linear correlation,negative linear correlation, or no linear correlation.

Question 29

A researcher determines that the linear correlation coefficient is 0.85 for a paired data set. This indicates thatthere is

A) a strong positive linear correlation.
B) a strong negative linear correlation.
C) no linear correlation but that there may be some other relationship.
D) insufficient evidence to make any decision about the correlation of the data.

Question 30

Construct a scatter diagram for the given data. Determine whether there is a positive linear correlation,negative linear correlation, or no linear correlation.

Question 31

A medical researcher wishes to determine if there is a relationship between the number of prescriptions writtenby medical professionals, per 100, children and the childʹs age. She surveys all the pediatricianʹs in ageographical region to collect her data. What is the response variable?

A) Age of the child
B) Number of prescriptions written
C) Pediatricians surveyed
D) 100 prescriptions

Question 32

The data below are the number of hours worked (per week) and the final grades of 9 randomly selectedstudents from a drama class. Calculate the linear correlation coefficient.

A) -0.991
B) -0.888
C) -0.918
D) -0.899

Question 33

There is a causal relationship between years of education and births per woman.

Question 34

The data below are the average one-way commute times (in minutes) of selected students during a summerliterature class and the number of absences for those students for the term. Calculate the linear correlationcoefficient.

A) 0.980
B) 0.890
C) 0.881
D) 0.819

Question 35

An instructor wishes to determine if there is a relationship between the number of absences from his class anda studentʹs final grade in the course. What is the predictor variable?

A) Absences
B) Final Grade
C) The instructorʹs point scale for attendance
D) Studentʹs performance on the final examination

Question 36

Construct a scatter diagram for the given data. Determine whether there is a positive linear correlation,negative linear correlation, or no linear correlation.

Question 37

A scatter diagram locates a point in a two dimensional plane. The diagram locates thevariable on the horizontal axis and the variable on the vertical axis.

A) predictor; response
B) response; predictor
C) response; study
D) study; predictor

Question 38

The data below are the ages and annual pharmacy b ills (in dollars) of 9 randomly selected employees.Calculate the linear correlation coefficient.

A) 0.960
B) 0.998
C) 0.890
D) 0.908

Question 39

The numbers of home runs that Mark McGwire hit in the first 13 years of his major league baseball career arelisted below. (Source: Major League Handbook) Construct a scatter diagram for the data. Is there a relationshipbetween the home runs and the batting averages?

Question 40

A traffic officer is compiling information about the relationship between the hour or the day and the speed overthe limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tellthe officer?

A) There is a weak positive linear correlation.
B) There is a moderate positive linear correlation.
C) There is a moderate negative linear correlation.
D) There is insufficient evidence to make any conclusions about the relationship between the variables.

Question 41

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

Question 42

A manager wishes to determine the relationship between the number of years the managerʹs salesrepresentatives have been with the company and their average monthly sales (in thousands of dollars).Calculate the linear correlation coefficient.

A) 0.632
B) 0.561
C) 0.717
D) 0.791

Question 43

A) r=0.708 ; linear relation exists
B) r=0.235 ; no linear relation exists
C) r=-0.708 ; linear relation exists
D) r=0.708 ; no linear relation exists

Question 44

For a random sample of 100 American cities, the linear correlation coefficient between the number of robberieslast year and the number of schools in the city was found to be r = 0.725. What does this imply? Does thissuggest that building more schools in a city could lead to more robberies? Why or why not? What is a likelylurking variable?

Question 45

A) r=-0.335 ; no linear relation exists
B) r=0.462 ; linear relation exists
C) r=-0.335 ; linear relation exists
D) r=-0.284 ; no linear relation exists

Question 46

For a random sample of 30 countries, the linear correlation coefficient between the infant mortality rate and theaverage number of cars per capita was found to be r = -0.717. What does this imply? Does this suggest that ifpeople buy more cars, this could lower the infant mortality rate? Why or why not? What is a likely lurkingvariable?

Question 47

The table below shows the scores on an end-of-year project of 10 randomly selected architecture students andthe number of days each student spent working on the project.

Question 48

In order for a companyʹs employees to work in a foreign office, they must take a test in the language of thecountry where they plan to work. The data below shows the relationship between the number of years thatemployees have studied a particular language and the grades they received on the proficiency exam. Calculatethe linear correlation coefficient.

A) 0.934
B) 0.911
C) 0.891
D) 0.902

Question 49

A) r=0.983 ; linear relation exists
B) r=0.983 ; no linear relation exists
C) r=0.883 ; linear relation exists
D) r=0.883 ; no linear relation exists

Question 50

A) r=-0.995 ; linear relation exists
B) r=-0.995 ; no linear relation exists
C) r=-0.885 ; no linear relation exists
D) r=-0.885 ; linear relation exists

Question 51

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

Question 52

A) r=0.990 ; linear relation exists
B) r=0.881 ; no linear relation exists
C) r=0.819 ; linear relation exists
D) r=0.792 ; no linear relation exists

Question 53

The table shows the number of days off last year and the earnings for the year (in thousands of dollars) for ninerandomly selected insurance salesmen.

Question 54

Calculate the coefficient of correlation, r, letting Row 1 represent the x-values and Row 2 represent they-values. Now calculate the coefficient of correlation, r, letting Row 2 represent the x-values and Row 1represent the y-values. What effect does switching the explanatory and response variables have on the linearcorrelation coefficient? 4 Determine whether a linear relation exists between two variables.

Question 55

The table below shows the ages and weights (in pounds) of 9 randomly selected tennis coaches.

Question 56

A manager wishes to determine whether there is a relationship between the number of years her salesrepresentatives have been with the company and their average monthly sales. The table shows the years ofservice for each of her sales representatives and their average monthly sales (in thousands of dollars).

Question 57

To investigate the relationship between yield of soybeans and the amount of fertilizer used, a researcherdivides a field into eight plots of equal size and applies a different amount of fertilizer to each plot. The tableshows the yield of soybeans and the amount of fertilizer used for each plot. 5 Explain the difference between correlation and causation.

Question 58

A variable that is related to either the response variable or the predictor variable or both, but which is excludedfrom the analysis is a

A) lurking variable.
B) random variable.
C) discrete variable.
D) qualitative variable.

Question 59

A random sample of 200 men aged between 20 and 60 was selected from a certain city. The linear correlationcoefficient between income and blood pressure was found to be r = 0.807. What does this imply? Does thissuggest that if a man gets a salary raise his blood pressure is likely to rise? Why or why not? What are likelylurking variables?4.2 Least-Squares Regression1 Find the least-squares regression line and use the line to make predictions.

Question 60

In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and theyield of wheat (bushels per acre). Calculate the linear correlation coefficient.

A) 0.981
B) 0.998
C) 0.900
D) 0.899

Question 61

The data below are the number of absences and the final grades of 9 randomly selected students from aliterature class. Find the equation of the regression line for the given data. What would be the predicted finalgrade if a student was absent 14 times? Round the regression line values to the nearest hundredth. Round thepredicted grade to the nearest whole number.

Question 62

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

Question 63

A manager wishes to determine the relationship between the number of years her sales representatives havebeen employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation ofthe regression line for the given data. What would be the predicted sales if the sales representative wasemployed by the firm for 30 years Is this reasonable? Why or why not? Round the regression line values to thenearest hundredth.

Question 64

The data below are the final exam scores of 10 randomly selected history students and the number of hoursthey slept the night before the exam. Find the equation of the regression line for the given data. What would bethe predicted score for a history student who slept 15 hours the previous night? Is this a reasonable question?Round your predicted score to the nearest whole number. Round the regression line values to the nearesthundredth.

Question 65

In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and theyield of wheat (bushels per acre). Find the equation of the regression line for the given data. Round theregression line values to the nearest thousandth.

Question 66

A manager wishes to determine the relationship between the number of miles traveled (in hundreds of miles)by her sales representatives and their amount of sales (in thousands of dollars) per month. Find the equation ofthe regression line for the given data. What would be the predicted sales if the sales representative traveled 0miles? Is this reasonable? Why or why not? Round the regression line values to the nearest hundredth.

Question 67

The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomlyselected adults. Find the equation of the regression line for the given data. What would be the predictedpressure if the age was 60? Round the predicted pressure to the nearest whole number. Round the regressionline values to the nearest hundredth.

Question 68

The data below are the final exam scores of 10 randomly selected history students and the number of hoursthey slept the night before the exam. Find the equation of the regression line for the given data. What would bethe predicted score for a history student who slept 7 hours the previous night? Is this a reasonable question?Round the regression line values to the nearest hundredth, and round the predicted score to the nearest wholenumber.

Question 69

The data below are the average one-way commute times (in minutes) for selected students and the number ofabsences for those students during the term. Find the equation of the regression line for the given data. Whatwould be the predicted number of absences if the commute time was 95 minutes? Is this a reasonable question?Round the predicted number of absences to the nearest whole number. Round the regression line values to thenearest hundredth. $\begin{array} { | l | c | c | c | c | c | c | c | c | c | } \text { Commute time } ( \mathrm { min } ) , \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \\\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5\end{array}$

A) $\hat { y } = 0.45 \mathrm { x } - 30.27 ; 12$ absences; $Y e s$ , it is reasonable.
B) $\hat { y } = 0.45 \mathrm { x } - 30.27 ; 12$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.
C) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 73$ absences; Yes, it is reasonable.
D) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 73$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.

Question 70

In order for a companyʹs employees to work in a foreign office, they must take a test in the language of thecountry where they plan to work. The data below shows the relationship between the number of years thatemployees have studied a particular language and the grades they received on the proficiency exam. Find theequation of the regression line for the given data. Round the regression line values to the nearest hundredth.

Question 71

The data below are the average one-way commute times (in minutes) for selected students and the number ofabsences for those students during the term. Find the equation of the regression line for the given data. Whatwould be the predicted number of absences if the commute time was 40 minutes? Is this a reasonable question?Round the predicted number of absences to the nearest whole number. Round the regression line values to thenearest hundredth.

Question 72

Find the equation of the regression line by letting Row 1 represent the x-values and Row 2 represent they-values. Now find the equation of the regression line letting Row 2 represent the x-values and Row 1represent the y-values. What effect does switching the explanatory and response variables have on theregression line?