Module 3 Prelims & Final Quiz

A main purpose of using a scatter plot is to determine...

A. if two variables have a linear association, a non-linear association, or no association

B. the amount of variability a variable has

C. which of two variables has the larger mean

D. if a set of data is skewed left or skewed right

A. if two variables have a linear association, a non-linear association, or no association

A researcher surveyed 100 elderly people. For each person the researcher conducted a questionaire that measures their level of happiness (on a scale from 1 to 20). The researcher also asked each person how many medications they take per week. The correlation coefficient between these two variable was calcualted to be -0.67. According to this information ....

A. we cannot conclude that either variable is causing a change in the other variable because this is an observational study.

B. we can conclude that an elderly person's level of happiness has a negative impact on the number of medications they have to take weekly.

C. we can conclude that the number of medications an elderly person has to take negatively impacts their level of happiness.

D. we can conclude that if we want elderly people to have more happiness in their lives, they should take more weekly medications.

A. we cannot conclude that either variable is causing a change in the other variable because this is an observational study.

The correlation coefficient measures ...

A. the graphical steepness of the association between the two variables

B. how far the plotted points lie from the x and y axes.

C. the slope of the line that would go through the plotted points on the scatterplot

D. the percent of variabilty of the y value that can be explained with a regression equation

E. the strength of the linear association between the two variables

E. the strength of the linear association between the two variables

Which of the following are possible values for a correlation coefficient?

Mark all possible values. (hint: there is more than one)

A. -0.305

B. 0.95

C. 0

D. 2

E. 10

F. -1.5

A. -0.305

B. 0.95

C. 0

Match the given correlation coefficients with their descriptions of linear strength.

___strong negative association

___strong positive association

___weak negative association

___moderate positive association

1.-0.88

2.0.92

3.-0.05

4.0.58

5.-0.48

6.1.25

1,2,3,4

To determine if two variables have a linear association, a non linear association, or no association, we need to....

A. calculate the slope of the regression line

B. create and examine a scatter plot of the data

C. examine the variability of the response variable

D. calculate the correlation coefficient

B. create and examine a scatter plot of the data

Match the definitions to their corresponding associations

___If the value of one variable increases as the value of the other variable increases the variables are said to have a ...

___If the value of one variable increases as the value of the other variable decreases the variables are said to have a ...

1.positive association

2.negative association

3.no association

1,2

When two variables appear to have a linear association, the regression equation we use to represent the association is of the form....

A. y = ax + b

B. x = ay - b

C. y = ax

D. ax = by

A. y = ax + b

A linear regression equation between two quantitative variables was calculated to be y = 14 - 5X and has a correlation coefficient of -0.8. What is the value of the slope in this regression equation?

A. -0.8

B. -5

C. 0.64

D. 14

B. -5

A student's final overall percentage in a course can be predicted using their Midterm Exam score (X) and the regression equation Y = 0.78X + 15.

Use this equation to predict a student's final overall percentage in the course when they got a score of 84 on their Midterm Exam.

A. 84

B. 80.5

C. 88.5

D. 15.6

B. 80.5

The linear association between two variables can be estimated with the linear regression equation Y = 12.4X - 33.1. Using only this information we can assume the two variables have an association that can be described as....

A. strong

B. moderate

C. weak

D. positive

E. negative

D. positive

We can tell if two variables are positively or negatively associated by using the sign of the correlation coefficient (which is not provided here) or the sign of the slope. 

The linear association between the amount of time, in hours, it takes for a monarch butterfly to emerge from its chrysalis and the weight of the caterpillar, in mg,  has a moderate association with a correlation coefficient of 0.61.  The linear regression equation for these variables was found to be y = 1.23x + 33.9.

Using this information, predict the metamorphosis time for a caterpillar that weighs 190 mg.

Round your answer to the nearest integer.  (i.e.  the answer 45.8392 would round to 46)

268

Suppose the age of a feral hog, in years, and the width of the feral hog's hoof, in centimeters, have a linear association where the age of a feral hog (Y) can be estimated using the width of the hoof (X) and the regression equation Y = 1.7X - 3.9. What is the slope and the approriate units for the slope for this regression equation?

A. 1.7 years / centimeter

B. 1.7 centimeters / year

C. 1.7 centimeters

D. 3.9 centimeters/year

E. 1.7 years

F. 3.9 years

G. 3.9 years/centimeter

H. 3.9 centimeters

A. 1.7 years / centimeter

slope is defined as rise over run which would be y-variable units over x-variable units

A waiter at a restaurant created a regression equation that allows them to predict the length of time a person will have to wait to receive their food (in minutes) after ordering, by using the amount of money the food costs (in dollars). The regression equation is Y = 0.34X + 3.1 or Time = 0.34(Cost) + 3.1

An interpretation of the slope is...

A. for every 1 minute longer the food takes, it will cost $3.10 more

B. for every additional dollar the food costs, it will take an additional 3.1 minutes to get their food

C. For evey additional $1 the food costs, it will take an additional 0.34 minutes to get their food

D. for every additional minute the food takes, it costs an additional $0.34

C. For evey additional $1 the food costs, it will take an additional 0.34 minutes to get their food

A linear association exists between the amount of time that passes since an item was placed into a freezer and the temperature of the item.

A regression equation will be calculated that can predict time using the temperature.

For this regression equation, which variable is the independent (X) variable?

A. time

B. temperature

C. freezer

D. not enough information provided

B. temperature

During the first two years of their life, the age, in months, of a koala bear has a linear association with the koala bear's weight, in pounds.  The ages and weights of five koala bears were recorded.  Calculate the slope of the linear regression equation that can be used to predict a koala bear's age using their weight.   Use technology to find the answer.

Age (months)   24     15      10       6      32

Weight (lbs)     18     11       5        3      19

 Round your answer to two decimal places.  Enter only your answer.   (e.g.  1.25)

1.40

If your answer is less than one, you may be finding the regression equation that predicts the koala's weight using their age, which is not what the question is requesting. Switch your variables.

During the first two years of their life, the age, in months, of a koala bear has a linear association with the koala bear's weight, in pounds.  The ages and weights of five koala bears were recorded.  Calculate the y-intercept  of the linear regression equation that can be used to predict a koala bear's age using their weight.   Use technology to find the answer.

Age (months)   24     15      10       6      32

Weight (lbs)     18     11       5        3      19

 Round your answer to two decimal places.  Enter only your answer.   (e.g.  1.25)

1.68

During the first two years of their life, the age, in months, of a koala bear has a linear association with the koala bear's weight, in pounds.  The ages and weights of five koala bears were recorded.  Calculate the correlation coefficient to measure the linear strength of these variables. Use technology to find the answer.

Age (months)   24     15      10       6      32

Weight (lbs)     18     11       5        3      19

 Round your answer to two decimal places.  Enter only your answer.   (e.g.  0.25)

0.97

The cost of shingling a house is linearly related to the square feet of the roof.  Below is a table of the square feet of six randomly selected homes and the cost to shingle them.  Use this data to create a simple linear regression equation and then use it to predict the cost of shingling a home that has 820 square feet of roof.

Square feet	449	651	388	501	909	855
Cost ($)	9807	12420	8540	9975	15531	13704

Round your final answer to the nearest dollar.  Do not include the $ sign and do not include the comma.  For example, if your answer was $38.948 you should enter  38948

14,016

Data was collected from a sample of used Honda Odysseys to determine how the number of miles they have been driven affects their retail price.

miles 52,400 120,200 84,300 36,100 61,000 25,900 67,800price 21,400 8,10018,300 24,000 19,50025,80017,700

Find the linear regression equation that can be used to predict the price of a used Odyssey when the mileage is known.

A. y = -0.1778 + 30630(X)

B. Y = -5.357(X) + 167125

C. y = -0.1778(X) + 30630

D. Y = -5.357 + 167125(X)

C. y = -0.1778(X) + 30630

Data was collected from a sample of used Honda Odysseys to determine how the number of miles they have been driven affects their retail price.

miles 52,400 120,200 84,300 36,100 61,000 25,900 67,800price21,4008,10018,30024,00019,500 25,800 17,700

Find the correlation coefficient for this data.

A. -0.976

B. 0.177

C. 0,953

D. -0.177

A. -0.976

A researcher recently collected data on two quantitative variables from a sample of Reggal spiders from Eastern Africa. In order to tell if the two variables have a linear association, a non linear association, or no association, the researcher should ....

A. examine the variability of the response variable

B. calculate the slope of the regression line

C. calculate the correlation coefficient

D. examine a scatter plot of the data

D. examine a scatter plot of the data

If the correlation coefficient for two variables was caclulated to be 0.64, we assume the two variables...

A. have no association

B. have a moderate positive association

C. have a strong positive association

D. have a weak positive association

B. have a moderate positive association

Which of the following are NOT possible values for a correlation coefficient?

Mark all values that are not possible. (hint: there is more than one)

A. 4

B. -0.02

C. 3.3

D. 0.85

E. -0.5

F. 0.7

A. 4

C. 3.3

A researcher created a regression equation that predicts an elderly persons reaction time (in tenths of seconds) using their age (in years) as the explanatory variable. The regression equation is time = 0.37(age) - 11.4

An interpretation of the slope is...

A. for every 1 year of age, reaction time decreases by 0.37 tenths of a second (was quicker to react)

B. for every 1 year of age, reaction time increases by 0.37 tenths of a second (was slower to react)

C. for every 1 year of age, reaction time decreases by 11.4 tenths of a second (was quicker to react)

D. for every 1 year of age, reaction time increases by 11.4 tenths of a second (was slower to react)

B. for every 1 year of age, reaction time increases by 0.37 tenths of a second (was slower to react)

Match the statistics with their descriptions

___estimates the change in the response variable for a one unit change in the explanatory variable

___measures the linear strength between the response and explanatory variables

___estimates the value of the response variable when the explanatory variable has a value of zero

1.Slope of the regression line

2.Y-intercept of the regression line

3.Correlation coefficient

1,3,2

Suppose we collected data from a random sample of similar sized homes in Canada during the month of January. The two variables we collected were 1) the cost of heating the home for the month of January and 2) the average temperature outside during the month of January. These two variables will be used to create a regression equation that can be used to predict the cost of heating one of these similar sized homes using the average temperature outside.

1) Would the two variables mentioned have a positive or negative association?

2) Which variable is the explanatory variable in the mentioned regression equation?

A. 1) negative and 2) cost to heat

B. 1) positive and 2) cost ot heat

C. 1) positive and 2) average temperature

D. 1) negative and 2) average temperature

D. 1) negative and 2) average temperature

For a specific item, the weight of the item is linearly related to the cost of the item.  Weights and costs were recorded for several of these items.  Using the data, find the slope of the regression equation that can be used to predict the price of one of these items knowing how much is weighs.  Use your calculator to find an answer.

Round answer to two decimal places  (e.g.  5.1764 would round to 5.18)

Cost in $	25.0	30.3	26.0	28.2	32.8	28.2
Weight in pounds	7.8	9.0	6.5	6.8	9.4	8.5

Don't forget to round your answer to two decimal places.

1.80

Data was collected by randomly selecting different sizes of cheese pizza from various restaurants. For each pizza the diameter in inches (distance across the middle) and the price in dollars were recorded.  The data was used to create a regression equation that allows the price of a pizza to be predicted by knowing the diameter.  

The equation was Y = 1.18X - 7.6.

Predict the price of a cheese pizza that has a diameter of 13.2 inches. 

Round your answer to two decimal places. Enter the number only.  Do not include a $ sign.

7.98

A set of paired quantitative variables are provided.  Calculate the requested regression statistics using this data.

X	12	9	15	14	14	10	11	12
Y	44	55	30	41	44	52	52	47

___correlation coefficient

___slope of the regression equation

___y-tinercept of the regression equation

1.87.5

2.-5.93

3.-0.91

4.0.63

5.-3.45

3,5,1

If the value of one variable increases as the value of the other variable decreases the variables are said to have a ...

A. positive association

B. negative association

C. constant association

D. no association

B. negative association