Deck 4: Regression Analysis: Exploring Associations Between Variables

Question 1

The scatterplot below shows the number of tackles received and the number of concussions received for a team of football players for the most recent season. Choose the statement that best describes the trend.

A)There is no association between the number of tackles a team receives and the number of concussions.
B)Teams that receive a greater number of tackles tend to have a higher number of concussions.
C)Teams that receive a greater number of tackles tend to receive a lower number of concussions.

Answer 1

Teams that receive a greater number of tackles tend to have a higher number of concussions.

Question 2

Suppose it has been established that "annual income" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Annual Income = $23,400+$7200(Years of College). In this model, "Annual Income" is the
? variable, and "Years of College" is the ? variable. The two variables have a ? linear relationship.

A)Independent; Dependent; Positive
B)Independent; Dependent; Negative
C)Dependent; Independent; Negative
D)Dependent; Independent; Positive

Answer 2

Dependent; Independent; Positive

Question 3

The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below.

A)- 0.99
B)- 0.20
C)0.20
D)0.99

Answer 3

0.99

Question 4

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
What is the predicted number of tickets sold per hour if the temperature is 86°F? Round to the nearest whole ticket.

A)About 252 tickets
B)About 276 tickets
C)About 336 tickets
D)About 301 tickets

Question 5

Doctors believe that smoking cigarettes inflames the bronchial tubes and so makes it harder to breathe. To test this they measured the lung capacity (in liters)and the number of cigarettes smoked in a typical day for a sample of adults. Is the scatterplot below consistent with the researcher's hypothesis?

A)Yes, it is consistent.
B)There is no evidence in support or contradiction of the hypothesis.
C)No, it contradicts this hypothesis.

Question 6

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
Choose the statement that best states the meaning of the slope in this context.

A)The slope tells us that a one degree increase in temperature is associated with an average increase in ticket sales of 11.25 tickets.
B)The slope tells us that if ticket sales are decreasing there must have been a drop in temperature.
C)The slope tells us that high temperatures are causing more people to buy tickets to the water park.
D)None of these

Question 7

What key things should you look for when examining the potential linear association between two variables?

A)A noticeable overall linear shape on the scatterplot.
B)The vertical spread of the points on the scatterplot which indicate the strength of an association.
C)A noticeable positive or negative trend on the scatterplot.
D)All of these.

Question 8

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is and the response variable is .

A)Number of pets; number of fleas spotted in a period of time
B)Slope; intercept
C)Number of fleas spotted in a period of time; number of pets
D)None of these

Question 9

It is determined that a positive linear association exists between age (for children between the ages of 3 and 9 years)and attention span (measured in minutes). The scatterplot below shows the association. The prediction equation is also given. A college instructor uses the model to predict the attention span of the students in her class who have an average age of 29. Choose the best statement to summarize why this is not an appropriate use for the model. attention span = 4.68 + 3.40(age)

A)This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The college instructor is extrapolating.
B)This is an inappropriate use of the model because age does not cause attention span to increase. Correlation does not mean causation.
C)This is an inappropriate use of the model because a 29- year- old person would be an outlier in this context.

Question 10

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
In this context, does the intercept have a reasonable interpretation?

A)Not enough information available
B)No, at a temperature of 0°F, ticket sales would be - 631.25 and it is not reasonable (or possible)to have negative ticket sales.
C)Yes, it is reasonable for people to go to a water park when it is 0°F, so park managers might want to know how many tickets they would sell on average on a 0°F day.

Question 11

r = 0.8670

A)
B)

C)

Question 12

It is determined that a positive linear association exists between amount of a new smoking cessation drug taken (in milliliters)and weight gain in women (in pounds). The scatterplot below shows the association. The prediction equation is also given. A pharmacy technician uses the model to predict the potential weight gain for a man who takes the recommended dosage. Choose the best statement to summarize why this is not an appropriate use for the model.

A)This is an inappropriate use of the model because taking the smoking cessation drug does not cause weight gain. Correlation does not mean causation.
B)This is an inappropriate use of the model because a man would be an outlier in this context.
C)This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The Pharmecy Technician is extrapolating.

Question 13

The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars. The relationship between "car length" and "car weight" can be described as

A)A moderate positive linear relationship
B)A strong positive linear relationship
C)A weak negative relationship
D)A strong negative linear relationship

Question 14

Which of the following statements regarding the correlation coefficient is not true?

A)The correlation coefficient measures the strength of the linear relationship between two numerical variables.
B)A value of 0.00 indicates that two variables are perfectly linearly correlated.
C)The correlation coefficient has values that range from - 1.0 to 1.0 inclusive.
D)All of these are true statements.

Question 15

The data in the table represent the amount of raw material (in tons)put into an injection molding machine each day (x), and the amount of scrap plastic (in tons)that is collected from the machine every four weeks (y). Also shown below are the outputs from two different statistical technologies (TI- 83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap from raw material using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest hundredth.

A)scrap = - 2.38 + 2.19(raw material); slope = 2.19 and the intercept is - 2.38.
B)scrap = 2.19 - 2.38(raw material); slope = - 2.38 and the intercept is 2.19.
C)scrap = 2.19 - 2.38(raw material); slope = 2.19 and the intercept is - 2.38.
D)scrap = - 2.38 + 2.19(raw material); slope = - 2.38 and the intercept is 2.19.

Question 16

r = - 0.3120

A)
B)

C)

Question 17

The following model was created to show the association between the number of massages received per month and self- predicted stress level: Stress level = 10 - 0.02(number of massages per month). The coefficient of determination for the model is 0.066 or 6.6%. Choose the true statement regarding this model.

A)The model shows that getting even one massage a month will decrease your stress level.
B)The model shows that there is a negative association between stress level and number of monthly massages, but the relatively small coefficient of determination suggests that very little of the variation is explained by the model, so the model is probably not very good at predicting stress level.
C)The model shows that on average a person getting no massages will always have a stress level of 10.
D)All of these are true statements.

Question 18

r = 0.8787

A)
B)

C)

Question 19

The following calculator screenshots show the scatterplot and the correlation coefficient between the number of days absent and the final grade for a sample of college students in a general education statistics course at a large community college. The relationship between "days absent" and "final grade" can be described as

A)A strong negative linear relationship
B)A strong positive linear relationship
C)A weak negative relationship
D)A moderate positive linear relationship

Question 20

r = - 0.6542

A)
B)

C)

Question 21

Which of the following statements regarding the correlation coefficient is not true?

A)The correlation coefficient has values that range from - 1.0 to 1.0 inclusive.
B)A correlation coefficient value of 0.00 indicates that two variables have no linear correlation at all.
C)The correlation coefficient measures the strength of the linear relationship between two numerical variables.
D)All of these are true statements.

Question 22

In the NHL, the correlation between "Goals scored per game" and "minutes on the ice" for a team of players is found to be 0.8178. Choose the statement that is true about the coefficient of determination.

A)When given as a percent, the coefficient of determination is always between 0 and 100%.
B)The coefficient of determination states that about 66.88% of the variation in goals scored per game is explained by minutes on the ice.
C)The coefficient of determination, r2, is equal to approximately 0.6688.
D)All of these are true statements.

Question 23

A horticulturist conducted an experiment on 110 thirty- six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of tomatoes harvested from the plants. The average amount of plant food given was 27.8 milliliters with a standard deviation of 2.1 milliliters. The average number of tomatoes harvested was 7.5 with a standard deviation of 1.5. The correlation coefficient was 0.7691. Use the information to calculate the slope of the linear model that predicts the number of tomatoes harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

A)1.08
B)0.55
C)- 7.50
D)The slope cannot be determined without the actual data.

Question 24

A horticulturist conducted an experiment on 140 thirty- six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of habanera peppers harvested from the plants. The average amount of plant food given was 17.8 milliliters with a standard deviation of 0.7 milliliters. The average number of habanera peppers harvested was 6.5 with a standard deviation of 1.5. The correlation coefficient was 0.8123. Use the information to calculate the slope of the linear model that predicts the number of habanera peppers harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

A)1.74
B)The slope cannot be determined without the actual data.
C)0.38
D)- 1.50

Question 25

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
What is the predicted number of tickets sold per hour if the temperature is 79°F? Round to the nearest whole ticket.

A)About 257 tickets
B)About 310 tickets
C)About 250 tickets
D)About 258 tickets

Question 26

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

A)Positive
B)Near Zero
C)Negative

Question 27

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot below.

A)The scatterplot does not show a trend that would indicate an association between hat size and IQ scores.
B)As hat size increases, IQ scores tend to increase.
C)Hat size causes IQ to increase.
D)As hat size increases, IQ scores tend to decrease.

Question 28

r = - 0.6542

A)
B)

C)

Question 29

The scatterplot below shows the number of tackles received and the number of concussions received for a team of football players for the most recent season. Choose the statement that best describes the trend.

A)Teams that receive a greater number of tackles tend to have a higher number of concussions.
B)There is no association between the number of tackles a team receives and the number of concussions.
C)Teams that receive a greater number of tackles tend to receive a lower number of concussions.

Question 30

Doctors hypothesize that smoking cigarettes inflames the bronchial tubes and so makes it harder to breathe. To test this they measured the lung capacity (in liters)and the number of cigarettes smoked in a typical day for a sample of adults. Is the scatterplot below consistent with the researcher's hypothesis?

A)No, it contradicts this hypothesis.
B)There is no evidence in support or contradiction of the hypothesis.
C)Yes, it is consistent.

Question 31

A concert ticket agent is going to investigate whether an increase in money spent on radio advertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, the response variable is and the explanatory variable is .

A)Slope; intercept
B)Amount of radio advertisement money spent; concert ticket sales
C)Concert ticket sales; amount of radio advertisement money spent
D)None of these

Question 32

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

A)Negative
B)Positive
C)Near Zero

Question 33

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
Choose the statement that best states the meaning of the slope in this context.

A)The slope tells us that if ticket sales are decreasing there must have been a drop in temperature.
B)The slope tells us that high temperatures are causing more people to buy tickets to the water park.
C)The slope tells us that a one degree increase in temperature is associated with an average increase in ticket sales of 11.25 tickets.
D)None of these

Question 34

The following model was created to show the association between the number of massages received per month and self- predicted stress level: Stress level = 10 - 0.02(number of massages per month). The coefficient of determination for the model is 0.066 or 6.6%. Choose the true statement regarding this model.

A)The model shows that there is a negative association between stress level and number of monthly massages, but the relatively small coefficient of determination suggests that very little of the variation is explained by the model, so the model is probably not very good at predicting stress level.
B)The model shows that on average a person getting no massages will always have a stress level of 10.
C)The model shows that getting even one massage a month will decrease your stress level.
D)None of these.

Question 35

r = - 0.3526

A)
B)

C)

Question 36

The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below.

A)- 0.30
B)0.99
C)0.30
D)- 0.99

Question 37

Suppose it has been established that "home value" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Home value = $75,000+$12,500(Years of College). In this model, "years of college" is the
? variable, and "home value" is the ? variable. The two variables have a ? .

A)Independent; Dependent; Positive
B)Dependent; Independent; Positive
C)Independent; Dependent; Negative
D)Dependent; Independent; Negative

Question 38

The data in the table represent the amount of pressure (psi)exerted by a stamping machine (x), and the amount of scrap brass shavings (in pounds)that are collected from the machine each hour (y). Also shown below are the outputs from two different statistical technologies (TI- 83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap brass shavings using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest thousandth.

A)scrap = - 2.019 + 2.134(pressure); slope = - 2.019 and the intercept is 2.134.
B)scrap = 2.134 - 2.019(pressure); slope = - 2.019 and the intercept is 2.134.
C)scrap = - 2.019 + 2.134(pressure); slope = 2.134 and the intercept is - 2.019.
D)scrap = 2.134 - 2.019(pressure); slope = 2.134 and the intercept is - 2.019.

Question 39

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
In the NBA, the correlation between "steals per game" and "blocked shots per game" is found to be 0.8045. Choose the statement that is true about the coefficient of determination.

A)The coefficient of determination states that about 64.72% of the variation in blocked shots per game is explained by steals per game.
B)The coefficient of determination, r2, is equal to approximately 0.6472.
C)When given as a percent, the coefficient of determination is always between 0 and 100%.
D)All of these are true statements.

Question 40

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = - 631.25 + 11.25(current temperature in °F)
In this context, does the intercept have a reasonable interpretation?

A)No, at a temperature of 0°F, ticket sales would be - 631.25 and it is not reasonable (or possible)to have negative ticket sales.
B)Not enough information available
C)Yes, it is reasonable for people to go to a water park when it is 0°F, so park managers might want to know how many tickets they would sell on average on a 0°F day.

Question 41

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars.

Suppose each of these families is given a grocery credit of $100, therefore reducing expenditures in the table by one unit (since this variable was recorded in hundreds of dollars). Estimate the new correlation with city size. What happens to the correlation when a constant is added (in this case - 100 dollars is added to each number)? Explain your reasoning.

Question 42

The following regression equation was found to model commute distance (in miles)and number of minor accidents per year for a group of adults.
Minor accidents per year = 1.204 + 0.024(commute distance)
What is the intercept? What is the interpretation of the intercept in this context? Does it make sense to interpret the intercept in this context?

Question 43

Explain in your own words what extrapolation is and give an example. Why should extrapolation be avoided when doing regression analysis?

Question 44

Use the following information to answer the question. A scatterplot of data from a large sample of adult women shows that height in inches and weight in pounds have a linear association. Shown below are the outputs from two different statistical technologies (TI- 83/84 Calculator and Excel).

Height and weight charts for women show that a woman who is 71 inches tall has a target weight between 135 and 176 pounds. Would the regression model you found for the large sample of (in question 15)place a woman who was 71 inches tall within this range?

Question 45

State the explanatory variable and the response variable.

Question 46

If the correlation between whole milk content per serving and calories per serving for several brands of ice cream is 0.71, report the coefficient of determination (rounded to the nearest tenth of a percent)and explain what it means using a complete sentence. Assume that whole milk content is the predictor and calories per serving is the response, and assume that the association between whole milk content and calories is linear.

Question 47

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars.

Using the data from the table, sketch a scatterplot (by hand or with the aid of technology)of the data. Describe any association that you see. Would it be appropriate to fit a linear model to this data?

Question 48

The scatterplot below shows the ice cream sales and daily high temperatures for a three week period of time during the summer. Does there appear to be an association between these two variables? If so, describe the pattern. Be sure to comment on trend, shape, and the strength of the association.

Question 49

The following regression equation was found to model commute distance (in miles)and number of minor accidents per year for a group of adults.
Minor accidents per year = 1.204 + 0.024(commute distance)Identify the independent variable and the dependent variable.

Question 50

Use the regression equation to predict how many children a married couple will have if they live in city with a population of 40,000 people.

Question 51

A horticulturist conducted an experiment on 120 thirty- six inch flower boxes to see if the amount of plant food given to the flower boxes was associated with the number of blooms on the plants. The average amount of plant food given was 31.6 milliliters with a standard deviation of 2.2 milliliters. The average number of blooms was 10.5 with a standard deviation of 1.5. The correlation coefficient was 0.8891. Use the information to calculate the slope of the linear model that predicts the number of blooms from the amount of plant food given. Show your work and round to the nearest hundredth. Write a sentence explaining the meaning of the slope in this context.

Question 52

Use the following information to answer the question. A scatterplot of data from a large sample of adult women shows that height in inches and weight in pounds have a linear association. Shown below are the outputs from two different statistical technologies (TI- 83/84 Calculator and Excel).

Report the equation for predicting weight in pounds from height in inches using words such as weight, not x and y.

Question 53

State the slope and intercept of the regression line and explain each in context. Be sure to explain whether the intercept has a practical meaning in this context.

Question 54

Suppose that environmentalists monitor algae levels in a river and determine that there is a linear association between local rainfall and algae levels. The determine that the best fitting linear model to predict algae cell counts per milliliter from rainfall in inches is:
Algae cell count = 229.32 + 79.81(Rainfall in inches)with r² = 0.604 How will a rainfall that is 3 inches above average affect the algae cell count?

Question 55

The figures below show the relationship between salary and personal lunch expenses on week days for a group of business men. Comment on the difference in graphs and in the coefficient of determination between the graph that includes a data point of someone who reported earnings of $21,000 per year and weekly personal lunch expenses of $100 per week (second graph)and the graph that did not include this data point (first graph).

Question 56

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars.

Based on the scatterplots below, what is the better predictor for head circumference-- height or shoulder width? Explain how you made your decision.

Question 57

The scatterplot below shows the number of alcoholic drinks consumed and memory test results for some college students. Is there an association? If so, describe the pattern. Be sure to comment on trend, shape, and the strength of the association.

Question 58

Suppose that runner height (in inches)and finish time in a 5k (in seconds)have a linear association as evidenced by a scatterplot showing a roughly linear pattern, explain the purpose of finding the equation for the regression line that will relate runner height and finish time. What are the limitations of the regression line? Explain the meaning of the slope and intercept of such a model?

Question 59

Suppose that in the Midwest, it is shown that there is trend between home insurance claims in dollars and the number of cattle owned by the home owner. The trend shows that higher claims were paid out to homeowners that owned more cattle. Does this trend prove that owning more cattle causes higher insurance claims? Be sure to explain your reasoning, don't just answer yes or no. What is a potential hidden variable in this context?

Question 60

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars.

Based on the scatterplot, estimate the correlation coefficient between city size and expenditures for these eight families. Explain your reasons for choosing your estimate.