Chapter 2 Review

Last updated almost 2 years ago

25 questions

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Library

Chapter 2 Review

Last updated almost 2 years ago

25 questions

Note from the author:

This review is optional, it is excellent practice. The review will give instant feedback or will have answers posted in the 'show your work' section for you to check.

Instructions

This review is optional, it is excellent practice. The review will give instant feedback or will have answers posted in the 'show your work' section for you to check.

Required

2

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in San Antonio. Students were asked if good grades, athletic ability, or being popular was most important to them.
The two-way table summarizes the survey data:

Identify the explanatory and response variables in this context.

Explanatory Variable

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At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict movement?
There might even be an association between babies’ crawling age and the average temperature during the month when they first try to crawl (around 6 months after birth).
Data were collected from parents who reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.
Information was obtained on 414 infants, 208 boys and 206 girls.
Average crawling age is given in weeks, and the average temperature (in degrees Fahrenheit) is for the month that is 6 months after the birth month.

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Create a scatterplot in statsmedic.com/applets, 2 quantitative variables.
Use the data table below, copy and paste the data into statsmedic.
Average Temperature (degrees F): 66, 73, 72, 63, 52, 39, 33, 30, 33, 37, 48, 57
Average crawling age (weeks): 29.84, 30.52, 29.70, 31.84, 28.58, 31.44, 33.64, 32.82, 33.83, 33.35, 33.38, 32.32

Describe the relationship shown in the scatterplot in a complete sentence. Use DOFS.
Enter your answer, then check it with mine in the 'show your work' area.

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How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.
Enter your answer, then check your answer with mine once you have entered it.

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The principal of a high school read a study that reported a positive correlation between the number of calculators owned by high school students and their math achievement.
Based on this study, he decides to buy each student at his school 2 calculators, hoping to improve their math achievement. He believes the strong correlation shows owning calculators will cause a higher achievement in math.

Explain the flaw in the principal’s reasoning.
After you enter your answer, check mine in the 'show your work' area to see how you did.

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A statistics student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms.
Then, she measures the next man each woman dates.
Here are the data (height in inches).
Women's height(in) : 66, 64, 66, 65, 70, 65
Men's height(in): 72, 68, 70, 68, 71, 65
Copy and paste the data into statsmedic, make a scatterplot for these data, using women’s height as the explanatory variable.
Calculate the correlation for these data, enter it below. Keep all decimal places.

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The scatterplot shows the relationship between latitude and mean July temperature (in degrees Fahrenheit) for 12 cities in the United States.

The equation of the regression line relating these variables is
The scatterplot is:

Use the regression equation to predict the mean July temperature in Fairbanks, Alaska, at latitude 65º.
Make sure to include units (use the symbol for degrees & F) and all the decimal places in your answer.

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Using #12: How confident are you in this prediction? Explain, include what this is called.
Use complete sentences.
When you are finished, check the answer in the 'show your work' area to see if you are correct.

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Using #12: Los Angeles, California, is at latitude 34º and has a mean July temperature of 74º.
1st calculate the predicted mean July temperature for 34º.
Then calculate the residual.
Keep all the places past the decimal point.

Did the model over or under predict? Separate your answers with a comma

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Using #12: Interpret the slope of the regression line.
Make sure to include 'we predict' since this is a regression equation and we are using
it to predict y.
Enter your answer, then check your answer with mine in the 'show your work' section.

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Using #12: Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.
Write your answer, then check it with mine in the 'show your work' area.

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We used a least-squares regression line (this means we are checking the linear model) to model the relationship between x = latitude and
y = mean July temperature (in degrees Fahrenheit) for a sample of 12 cities in the United States.
Here is the residual plot for this model.

Explain what the residual plot suggests about the appropriateness of the linear model.

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Using the information about lattitude vs mean July temperature:
The standard deviation of the residuals for this model is s = 6.4.
Interpret this value.
Enter your answer then check the answer I posted in the 'show your work' area.

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Using the information on Lattitude vs Mean July Temperature:

Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

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Using the data from #20 you will compare the s and r^2 values for both regression models.

Linear Regression: (keep all decimal places)
What is the s value? _______  
What is the r^2 value? _______ 

Quadratic Model: (keep all decimal places)
What is the s value? _______ 
What is the r^2 value? _______ 

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Interpret the meaning of the s value for the linear regression model:

Then check the 'show your work' area to compare your answer with mine.

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Interpret the meaning of the r^2 value for the quadratic regression model:

Then check the 'show your work' area to compare your answer with mine.

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Using the quadratic regression model, calculate and interpret the residual for the year 1981, 5 years after the company started.
1st calculate the predicted amount of employees for 1981
2nd use the actual data from the table in #20 to calculate the residual
3rd decide what this means

Select three answers.

Required

1

Explain how you could use residual plots to determine which model is better.

This review is optional, it is excellent practice. The review will give instant feedback or will have answers posted in the 'show your work' section for you to check.

This review is optional, it is excellent practice. The review will give instant feedback or will have answers posted in the 'show your work' section for you to check.

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in San Antonio. Students were asked if good grades, athletic ability, or being popular was most important to them.
The two-way table summarizes the survey data:

Identify the explanatory and response variables in this context.

Grades
Total
6th grade
4th grade
5th grade
What is Most Important?
Athletic
Grade Level
Popular

Explanatory Variable
Response Variable

Using the information from #1, go to statsmedic.com/applets, use 2 categorical variables.
Make a segmented bar chart to show the relationship between grade level and which goal was most important to students.
Based on the graph you made, is there an association between these variables? Explain your reasoning. If there is an association, briefly describe it.

At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict movement?
There might even be an association between babies’ crawling age and the average temperature during the month when they first try to crawl (around 6 months after birth).
Data were collected from parents who reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.
Information was obtained on 414 infants, 208 boys and 206 girls.
Average crawling age is given in weeks, and the average temperature (in degrees Fahrenheit) is for the month that is 6 months after the birth month.

Identify the explanatory and response variables for the study described above if we are trying to determine if the relationship between temperature and the age when crawling begins.
Explain your reasoning.

Create a scatterplot in statsmedic.com/applets, 2 quantitative variables.
Use the data table below, copy and paste the data into statsmedic.
Average Temperature (degrees F): 66, 73, 72, 63, 52, 39, 33, 30, 33, 37, 48, 57
Average crawling age (weeks): 29.84, 30.52, 29.70, 31.84, 28.58, 31.44, 33.64, 32.82, 33.83, 33.35, 33.38, 32.32

Describe the relationship shown in the scatterplot in a complete sentence. Use DOFS.
Enter your answer, then check it with mine in the 'show your work' area.

In #4, we investigated the relationship between the average temperature 6 months after birth (in degrees Fahrenheit) and the average age when babies were able to crawl (in weeks).
Use statsmedic.com/applets, 2 quantitative variables to calculate the equation of the least-squares regression line for these data.
Using your scatterplot from earlier, describe what is unusual about the point representing May.
Choose 4 correct answers.

How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.
Enter your answer, then check your answer with mine once you have entered it.

The principal of a high school read a study that reported a positive correlation between the number of calculators owned by high school students and their math achievement.
Based on this study, he decides to buy each student at his school 2 calculators, hoping to improve their math achievement. He believes the strong correlation shows owning calculators will cause a higher achievement in math.

Explain the flaw in the principal’s reasoning.
After you enter your answer, check mine in the 'show your work' area to see how you did.

A statistics student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms.
Then, she measures the next man each woman dates.
Here are the data (height in inches).
Women's height(in) : 66, 64, 66, 65, 70, 65
Men's height(in): 72, 68, 70, 68, 71, 65
Copy and paste the data into statsmedic, make a scatterplot for these data, using women’s height as the explanatory variable.
Calculate the correlation for these data, enter it below. Keep all decimal places.

What does this correlation tell us?
Select two answers.

What effect does the pair (70, 71) have on the correlation? Explain.

How would the correlation change if the heights of the women were measured in centimeters instead of inches? (2.54 cm = 1 inch)

The scatterplot shows the relationship between latitude and mean July temperature (in degrees Fahrenheit) for 12 cities in the United States.

The equation of the regression line relating these variables is
The scatterplot is:

Use the regression equation to predict the mean July temperature in Fairbanks, Alaska, at latitude 65º.
Make sure to include units (use the symbol for degrees & F) and all the decimal places in your answer.

Using #12: How confident are you in this prediction? Explain, include what this is called.
Use complete sentences.
When you are finished, check the answer in the 'show your work' area to see if you are correct.

Using #12: Los Angeles, California, is at latitude 34º and has a mean July temperature of 74º.
1st calculate the predicted mean July temperature for 34º.
Then calculate the residual.
Keep all the places past the decimal point.

Did the model over or under predict? Separate your answers with a comma

Using #12: Interpret the slope of the regression line.
Make sure to include 'we predict' since this is a regression equation and we are using
it to predict y.
Enter your answer, then check your answer with mine in the 'show your work' section.

Using #12: Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.
Write your answer, then check it with mine in the 'show your work' area.

We used a least-squares regression line (this means we are checking the linear model) to model the relationship between x = latitude and
y = mean July temperature (in degrees Fahrenheit) for a sample of 12 cities in the United States.
Here is the residual plot for this model.

Explain what the residual plot suggests about the appropriateness of the linear model.

Using the information about lattitude vs mean July temperature:
The standard deviation of the residuals for this model is s = 6.4.
Interpret this value.
Enter your answer then check the answer I posted in the 'show your work' area.

Using the information on Lattitude vs Mean July Temperature:

Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

For a number of years after it started up, Microsoft Corporation grew quite rapidly.
The table shows the number of Microsoft employees and the number of years since Microsoft started up in 1976.
Years since 1976: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Employess: 7, 9, 13, 28, 40, 128, 220, 476, 608, 910, 1442

Use statsmedic.com/applets, 2 quantitative variables, copy and paste the list of data values.
Create a scatterplot for these data using years as the explanatory variable and employees as the response variable.
Calculate a linear regression model for the data. Check the residual plot.
Then, calculate a quadratic model for these data. Check the residual plot.
Based on the residual plots, which model is best?
Select three correct answers.

Using the data from #20 you will compare the s and r^2 values for both regression models.

Linear Regression: (keep all decimal places)
What is the s value? _______  
What is the r^2 value? _______ 

Quadratic Model: (keep all decimal places)
What is the s value? _______ 
What is the r^2 value? _______ 

Interpret the meaning of the s value for the linear regression model:

Then check the 'show your work' area to compare your answer with mine.

Interpret the meaning of the r^2 value for the quadratic regression model:

Then check the 'show your work' area to compare your answer with mine.

Using the quadratic regression model, calculate and interpret the residual for the year 1981, 5 years after the company started.
1st calculate the predicted amount of employees for 1981
2nd use the actual data from the table in #20 to calculate the residual
3rd decide what this means

Select three answers.

Explain how you could use residual plots to determine which model is better.

Grades

Total

6th grade

4th grade

5th grade

What is Most Important?

Athletic

Grade Level

Popular

Response Variable

Using the information from #1, go to statsmedic.com/applets, use 2 categorical variables.
Make a segmented bar chart to show the relationship between grade level and which goal was most important to students.
Based on the graph you made, is there an association between these variables? Explain your reasoning. If there is an association, briefly describe it.

6th graders are more likely to want to be popular than have good grades.

No, there is not an association between grade level and topic that is important.

We can tell because the segmented bar not charts are different.

All the conditional distribution percentages are very similar, within 5% of each other.

We can tell because the segmented bar charts are different.

Yes, there is an association between grade level and topic that is important.

Identify the explanatory and response variables for the study described above if we are trying to determine if the relationship between temperature and the age when crawling begins. 
Explain your reasoning.

Average temperature would be the explanatory variable.

Average age crawling would be the explanatory variable.

Average age crawling would be the response variable.

Average temperature would be the response variable.

We are trying to determine if temperature impacts or predicts the average age of crawling.

We are trying to determine if the average age of crawling predicts the temperature outside.

In #4, we investigated the relationship between the average temperature 6 months after birth (in degrees Fahrenheit) and the average age when babies were able to crawl (in weeks).
Use statsmedic.com/applets, 2 quantitative variables to calculate the equation of the least-squares regression line for these data.
Using your scatterplot from earlier, describe what is unusual about the point representing May.
Choose 4 correct answers.

The point for May pulls the regrssion line toward itself.

The point for May follows the pattern of the data.

The point for May is outside the pattern for the data, it is an outlier.

The point for May weakens the relationship between temperature and average age when the babies first crawled.

The point for May strengthens the relationship between the temperature and the average age when the babies first crawled.

The point for May increases the y-intercept.

The point for May does not impact the y-intercept at all.

What does this correlation tell us? 
Select two answers.

The correlation is negative.

The correlation is positive.

The correlation is strong.

The correlation is moderate.

The correlation is weak.

The correlation is linear.

The correlation is nonlinear.

What effect does the pair (70, 71) have on the correlation? Explain.

It strengthens the relationship, 

It weakens the relationship,

it makes the correlation weaker and closer to 0.

it makes the correlation stronger and a higher r value.

It does not affect the correlation,

it keeps the correlation the same value.

How would the correlation change if the heights of the women were measured in centimeters instead of inches? (2.54 cm = 1 inch)

The correlation would change and get stronger.

All of the values for heights would get larger.

The correlation would change and get weaker.

The values for heights would remain the same.

All of the values for heights would get smaller.

The correlation would remain the same.

There appears to be a pattern and not random scatter.

this means the linear model is appropriate.

There appears to be random scatter.

For a number of years after it started up, Microsoft Corporation grew quite rapidly. 
The table shows the number of Microsoft employees and the number of years since Microsoft started up in 1976.
Years since 1976: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Employess: 7, 9, 13, 28, 40, 128, 220, 476, 608, 910, 1442


Use statsmedic.com/applets, 2 quantitative variables, copy and paste the list of data values.
Create a scatterplot for these data using years as the explanatory variable and employees as the response variable.
Calculate a linear regression model for the data. Check the residual plot.
Then, calculate a quadratic model for these data. Check the residual plot.
Based on the residual plots, which model is best?
Select three correct answers.

The linear regression model is best, the residual plot shows more random scatter.

The linear regression model is best, the scatterplot shows a nearly straight line.

The quadratic regression model is best, the residual plot shows more random scatter.

The equation we use is: Residual = Actual - Predicted

The quadatic regression model over predicted.

The residual was -9 employees

The residual was 9 employees

The quadratic regression model under predicted.

Chapter 2 Review

Chapter 2 Review

How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.Enter your answer, then check your answer with mine once you have entered it.

Using #12: How confident are you in this prediction? Explain, include what this is called.Use complete sentences. When you are finished, check the answer in the 'show your work' area to see if you are correct.

Using #12: Los Angeles, California, is at latitude 34º and has a mean July temperature of 74º. 1st calculate the predicted mean July temperature for 34º.Then calculate the residual. Keep all the places past the decimal point.Did the model over or under predict? Separate your answers with a comma

Using #12: Interpret the slope of the regression line.Make sure to include 'we predict' since this is a regression equation and we are usingit to predict y.Enter your answer, then check your answer with mine in the 'show your work' section.

Using #12: Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.Write your answer, then check it with mine in the 'show your work' area.

Using the information about lattitude vs mean July temperature:The standard deviation of the residuals for this model is s = 6.4. Interpret this value.Enter your answer then check the answer I posted in the 'show your work' area.

Using the information on Lattitude vs Mean July Temperature:Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

Interpret the meaning of the s value for the linear regression model:Then check the 'show your work' area to compare your answer with mine.

Interpret the meaning of the r^2 value for the quadratic regression model:Then check the 'show your work' area to compare your answer with mine.

Explain how you could use residual plots to determine which model is better.

Identify the explanatory and response variables for the study described above if we are trying to determine if the relationship between temperature and the age when crawling begins. Explain your reasoning.

How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.Enter your answer, then check your answer with mine once you have entered it.

What does this correlation tell us? Select two answers.

What effect does the pair (70, 71) have on the correlation? Explain.

How would the correlation change if the heights of the women were measured in centimeters instead of inches? (2.54 cm = 1 inch)

Using #12: How confident are you in this prediction? Explain, include what this is called.Use complete sentences. When you are finished, check the answer in the 'show your work' area to see if you are correct.

Using #12: Los Angeles, California, is at latitude 34º and has a mean July temperature of 74º. 1st calculate the predicted mean July temperature for 34º.Then calculate the residual. Keep all the places past the decimal point.Did the model over or under predict? Separate your answers with a comma

Using #12: Interpret the slope of the regression line.Make sure to include 'we predict' since this is a regression equation and we are usingit to predict y.Enter your answer, then check your answer with mine in the 'show your work' section.

Using #12: Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.Write your answer, then check it with mine in the 'show your work' area.

Using the information about lattitude vs mean July temperature:The standard deviation of the residuals for this model is s = 6.4. Interpret this value.Enter your answer then check the answer I posted in the 'show your work' area.

Using the information on Lattitude vs Mean July Temperature:Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

Interpret the meaning of the s value for the linear regression model:Then check the 'show your work' area to compare your answer with mine.

Interpret the meaning of the r^2 value for the quadratic regression model:Then check the 'show your work' area to compare your answer with mine.

Explain how you could use residual plots to determine which model is better.

How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.
Enter your answer, then check your answer with mine once you have entered it.

Using #12: How confident are you in this prediction? Explain, include what this is called.
Use complete sentences.
When you are finished, check the answer in the 'show your work' area to see if you are correct.

Using #12: Interpret the slope of the regression line.
Make sure to include 'we predict' since this is a regression equation and we are using
it to predict y.
Enter your answer, then check your answer with mine in the 'show your work' section.

Using #12: Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.
Write your answer, then check it with mine in the 'show your work' area.

Using the information about lattitude vs mean July temperature:
The standard deviation of the residuals for this model is s = 6.4.
Interpret this value.
Enter your answer then check the answer I posted in the 'show your work' area.

Using the information on Lattitude vs Mean July Temperature:

Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

Interpret the meaning of the s value for the linear regression model:

Then check the 'show your work' area to compare your answer with mine.

Interpret the meaning of the r^2 value for the quadratic regression model:

Then check the 'show your work' area to compare your answer with mine.

Identify the explanatory and response variables for the study described above if we are trying to determine if the relationship between temperature and the age when crawling begins.
Explain your reasoning.

How does the point representing May affect the equation of the least-squares regression line? Use your answer from #4 to explain using complete sentences.
Enter your answer, then check your answer with mine once you have entered it.

What does this correlation tell us?
Select two answers.

Using #12: How confident are you in this prediction? Explain, include what this is called.
Use complete sentences.
When you are finished, check the answer in the 'show your work' area to see if you are correct.

Using #12: Interpret the slope of the regression line.
Make sure to include 'we predict' since this is a regression equation and we are using
it to predict y.
Enter your answer, then check your answer with mine in the 'show your work' section.

Using #12: Does the value of the y intercept have meaning in this context?
If so, interpret the y intercept. If not, explain why.
Write your answer, then check it with mine in the 'show your work' area.

Using the information about lattitude vs mean July temperature:
The standard deviation of the residuals for this model is s = 6.4.
Interpret this value.
Enter your answer then check the answer I posted in the 'show your work' area.

Using the information on Lattitude vs Mean July Temperature:

Interpret this value. Enter your answer, then check the answer posted in 'show your work'.

Interpret the meaning of the s value for the linear regression model:

Then check the 'show your work' area to compare your answer with mine.

Interpret the meaning of the r^2 value for the quadratic regression model:

Then check the 'show your work' area to compare your answer with mine.