Unit 6 Day 6 Ch. 7 & 8 Regression Test

10

There are 4,000 bacteria in a wound. Antiseptic is applied and 500 bacteria die each minute.
The price of silver was $17 per ounce and then decreased by 5% each year.
The price of gold was $1180 per ounce and then increased by 5% each year.

Linear
Exponential
Power

4

Which statement about residuals plots for linear models is true?
A curved pattern of points indicates nonlinear association between the variables.
A random scatter of points suggests that the chosen model is a reasonable fit.

4

Data collected from internet ads for 1999 Subarus were used to create a model to estimate the asking price of the car based on the number of miles it had been driven.
The model has the equation:

The plot of residuals versus the predicted price is shown below.

Is the given price model equation linear, exponential, or power?

4

Interpret the slope of the line in context.
Use units and the rate.

4

Do you think this model is appropriate for these data?
Explain clearly.

4

The residual using this model for a 1999 Subaru with 12,000 miles was $642.
What is the predicted value for a car with 12,000 miles?
Use units.

4

The residual using this model for a 1999 Subaru with 12,000 miles was $642.
What was the actual asking price?
Use units.

4

Doctors studying how the human body assimilates medication inject a patient with penicillin, and then monitor the concentration of the drug in the patient’s blood for several hours.
The data are shown in the table.

Find a linear model for predicting the concentration of penicillin.
Enter the data into L1 and L2, do a linear regression.
No spaces.
Use 'concentration' and 'hours' for the variable names.
Round decimals to two places if needed.

4

Doctors studying how the human body assimilates medication inject a patient with penicillin, and then monitor the concentration of the drug in the patient’s blood for several hours.
The data are shown in the table.

Now do an exponential regression for predicting the concentration of penicillin.
Stat, edit, 0

Set up your equation.
No spaces.
Use 'concentration' and 'hours' for variable names.
Round to 3 places past the decimal point.

4

Find the R-squared for the linear regression equation.
Redo the linear regression, note the R-squared value.
Round the R-squared to four places past the decimal.

4

Find the R-squared for the exponential regression equation.
Redo the exponential regressin, note the
Round the R-squared to four places past the decimal.

4

Based on your previous two answers, compare the R-squared values for the linear and exponential regressions.
Which is the better regression equation?
Why?

4

Use the model you chose to estimate what the concentration of penicillin will be after 8 hours.

Use units with your answer. (see the table for the units)

Round to two places past the decimal.

4

If the actual concentration of penicillin was 2.48 unit/cc,
1. calculate the residual and
2. explain what that means about our regression model in this context.

4

According to the Federal Government, the United State National debt as grown since 1980 as shown in the following scatterplot:

A computer gives the equation of the regression line as

You decide to take a look at a residuals plot before making any predictions.

Based on the residuals plot above, does linear regression seem appropriate for these data?
Explain for full credit.

4

Enter your data into L1 and L2.
Create a scatterplot of the data comparing the diameter and the length of the shaft of the humerus bone for African Antelopes.
You will use the diameter of the humerus bone to predict the length.
Describe the relationship below.

4

Using the data for the African Antelope, calculate a linear regression model.
Make sure to store the regression equation.

Enter it below, no spaces.
Use 'diameter' and 'length' for variable names.
Round to three places past the decimal.

4

Explain the meaning of the slope in the context of the humerus bone diameter and length.

Be sure to use the specific rate and units.

The increases/decreases per _.

4

Observe the residual plot. (make sure you stored the regression equation, change the statplot ylist to RESID)

What do you see?
What does this mean about the linear model?
Answer both questions.

4

Using the data for the African Antelope, calculate an exponential regression model.
Make sure to store the regression equation.

Enter it below, no spaces.
Use 'diameter' and 'length' for variable names.
Round to three places past the decimal.

4

Explain the meaning of the rate in the context of the diameter and the length of the humerus bone.
Be sure to use the % and the units.
Ex.
The _ decreases/increases % per __

4

Observe the residual plot for the exponential regression.
What do you see?
What does this mean about the exponential model?

4

Our last model to try is the Power model.
Do a power regression: Stat, Calc, Alpha, Math. (or Stat, Calc, scroll to 'A')
Store the regression equation.
Enter the power model equation below:
Round decimals to four places this time.

4

Observe the residuals for the Power Regression Model.
What do you see? What does this mean about the Power model compared to the other two models you tried?

4

Use the best of the three regression models to make a prediction for the length of a humerus bone that is
42.6 mm in diameter.
Round your answer to two places past the decimal.
Include units.

4

Enter your data into L1 and L2, calculate an exponential regression.
Enter the equation below.
Use 'box office gross' and 'weekend' for variable names.
No spaces.

4

Interpret the rate of decrease/increase below.
Be sure to include the % and units.
The __________ decreases/increases _% per _____________

4

Enter the data into L1 and L2.
For L1 years: use years since 1900. Your list should look like: 10, 20, 30, 40, 50, 60, 70,...
Calculate an Exponential regression.

Create an exponential regression equation, enter it below.
No spaces.
Use 'debt' and 'year' for variable names.
Round decimals to three places.

4

Which statement about residuals plots for linear models is true?A curved pattern of points indicates nonlinear association between the variables.A random scatter of points suggests that the chosen model is a reasonable fit.

Interpret the slope of the line in context.Use units and the rate.

Do you think this model is appropriate for these data? Explain clearly.

The residual using this model for a 1999 Subaru with 12,000 miles was $642. What is the predicted value for a car with 12,000 miles?Use units.

The residual using this model for a 1999 Subaru with 12,000 miles was $642.What was the actual asking price?Use units.

Find the R-squared for the linear regression equation.Redo the linear regression, note the R-squared value.Round the R-squared to four places past the decimal.

Find the R-squared for the exponential regression equation.Redo the exponential regressin, note theRound the R-squared to four places past the decimal.

Based on your previous two answers, compare the R-squared values for the linear and exponential regressions.Which is the better regression equation?Why?

Use the model you chose to estimate what the concentration of penicillin will be after 8 hours.Use units with your answer. (see the table for the units)Round to two places past the decimal.

If the actual concentration of penicillin was 2.48 unit/cc, 1. calculate the residual and 2. explain what that means about our regression model in this context.

Enter your data into L1 and L2.Create a scatterplot of the data comparing the diameter and the length of the shaft of the humerus bone for African Antelopes.You will use the diameter of the humerus bone to predict the length.Describe the relationship below.

Using the data for the African Antelope, calculate a linear regression model.Make sure to store the regression equation.Enter it below, no spaces.Use 'diameter' and 'length' for variable names.Round to three places past the decimal.

Explain the meaning of the slope in the context of the humerus bone diameter and length.Be sure to use the specific rate and units.The ____________________ increases/decreases ______________________ per ___________________.

Observe the residual plot. (make sure you stored the regression equation, change the statplot ylist to RESID)What do you see?What does this mean about the linear model?Answer both questions.

Using the data for the African Antelope, calculate an exponential regression model.Make sure to store the regression equation.Enter it below, no spaces.Use 'diameter' and 'length' for variable names.Round to three places past the decimal.

Explain the meaning of the rate in the context of the diameter and the length of the humerus bone.Be sure to use the % and the units.Ex.The _____________________ decreases/increases ______________% per ____________________

Observe the residual plot for the exponential regression.What do you see?What does this mean about the exponential model?

Our last model to try is the Power model.Do a power regression: Stat, Calc, Alpha, Math. (or Stat, Calc, scroll to 'A')Store the regression equation.Enter the power model equation below:Round decimals to four places this time.

Observe the residuals for the Power Regression Model.What do you see? What does this mean about the Power model compared to the other two models you tried?

Use the best of the three regression models to make a prediction for the length of a humerus bone that is 42.6 mm in diameter.Round your answer to two places past the decimal.Include units.

Enter your data into L1 and L2, calculate an exponential regression.Enter the equation below.Use 'box office gross' and 'weekend' for variable names.No spaces.

Interpret the rate of decrease/increase below.Be sure to include the % and units.The __________________ decreases/increases _______________% per ___________________

Interpret the rate of decrease/increase below.Be sure to include the % and units.The __________________ decreases/increases _______________% per ___________________

Which statement about residuals plots for linear models is true?
A curved pattern of points indicates nonlinear association between the variables.
A random scatter of points suggests that the chosen model is a reasonable fit.

Interpret the slope of the line in context.
Use units and the rate.

Do you think this model is appropriate for these data?
Explain clearly.

The residual using this model for a 1999 Subaru with 12,000 miles was $642.
What is the predicted value for a car with 12,000 miles?
Use units.

The residual using this model for a 1999 Subaru with 12,000 miles was $642.
What was the actual asking price?
Use units.

Find the R-squared for the linear regression equation.
Redo the linear regression, note the R-squared value.
Round the R-squared to four places past the decimal.

Find the R-squared for the exponential regression equation.
Redo the exponential regressin, note the
Round the R-squared to four places past the decimal.

Based on your previous two answers, compare the R-squared values for the linear and exponential regressions.
Which is the better regression equation?
Why?

Use the model you chose to estimate what the concentration of penicillin will be after 8 hours.

Use units with your answer. (see the table for the units)

Round to two places past the decimal.

If the actual concentration of penicillin was 2.48 unit/cc,
1. calculate the residual and
2. explain what that means about our regression model in this context.

Enter your data into L1 and L2.
Create a scatterplot of the data comparing the diameter and the length of the shaft of the humerus bone for African Antelopes.
You will use the diameter of the humerus bone to predict the length.
Describe the relationship below.

Using the data for the African Antelope, calculate a linear regression model.
Make sure to store the regression equation.

Enter it below, no spaces.
Use 'diameter' and 'length' for variable names.
Round to three places past the decimal.

Explain the meaning of the slope in the context of the humerus bone diameter and length.

Be sure to use the specific rate and units.

The increases/decreases per _.

Observe the residual plot. (make sure you stored the regression equation, change the statplot ylist to RESID)

What do you see?
What does this mean about the linear model?
Answer both questions.

Using the data for the African Antelope, calculate an exponential regression model.
Make sure to store the regression equation.

Enter it below, no spaces.
Use 'diameter' and 'length' for variable names.
Round to three places past the decimal.

Explain the meaning of the rate in the context of the diameter and the length of the humerus bone.
Be sure to use the % and the units.
Ex.
The _ decreases/increases % per __

Observe the residual plot for the exponential regression.
What do you see?
What does this mean about the exponential model?

Our last model to try is the Power model.
Do a power regression: Stat, Calc, Alpha, Math. (or Stat, Calc, scroll to 'A')
Store the regression equation.
Enter the power model equation below:
Round decimals to four places this time.

Observe the residuals for the Power Regression Model.
What do you see? What does this mean about the Power model compared to the other two models you tried?

Use the best of the three regression models to make a prediction for the length of a humerus bone that is
42.6 mm in diameter.
Round your answer to two places past the decimal.
Include units.

Enter your data into L1 and L2, calculate an exponential regression.
Enter the equation below.
Use 'box office gross' and 'weekend' for variable names.
No spaces.

Interpret the rate of decrease/increase below.
Be sure to include the % and units.
The __________ decreases/increases _% per _____________

Interpret the rate of decrease/increase below.
Be sure to include the % and units.
The __________ decreases/increases _% per _____________