Unit 6 Day 3 Exp vs Power Models

Here is a record of annual world crude oil production from 1900 to 1960 in five year increments
between 1900 and 1960. We will determine which model describes the growth in production over this time frame.


Enter the data into L1 and L2 (Stat, Edit)
HOWEVER: for L1, enter the year as the number of years since 1900. 
Your L1 list will look like this: 0, 5, 10, 15, 20...

6

Create a scatterplot to show the association between years since 1900 and the crude oil production.
y=, Statplot #1 ON, make sure the lists are correct.
Display with zoom, 9
1. Which regression appears to be the most appropriate? Linear or exponential?
2. Why?

4

Double check that this is the correct regression model.

Do a LINEAR REGRESSION (Stat, Calc, #8)
Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)
Observe the residual plot with zoom9.

What do you see?
What does this mean?

4

Triple check that this is the correct regression model.

Now do an EXPONENTIAL REGRESSION (Stat, Calc, #0)
Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)
Observe the residual plot with zoom9.

What do you see?
What does this mean?

4

Use the information from the exponential regression and create the Exponential Regression Equation, enter it below.
Use 'barrels' and 'year' for the variables,
identify the predicted variable with -hat and
round values to three places past the decimal.
No spaces.
Use the math keyboard to put an exponent into your equation.

4

Using the exponential regression equation in number 3, explain the meaning of the rate.
Ex. what is the rate? is the oil production increasing or decreasing each year?
Express it as a % per year.
Use: 'The oil production is ________________ by % each year.'

6

Suppose you have fit a model to some data and now take a look at the residuals (the residual plot).
For which of the possible residual plots would you reject your model?
Why?
Select all answers that apply.

2

Use the situation below to answer the question:

Is this model linear, exponential or power?

4

Does the equation for toxin level show a decrease or an increase and what percent?
How do you know?

Select both answers.

4

Use the situation below to answer the question:

How many milligrams of the toxin were in the water initially?
Use units with your answer.

4

Use the situation below to answer the question:

At what rate does this reaction reduce the level of toxin?
Use: _ per
Make sure to include percent

4

Use the situation below to answer the question:

To what level should the toxin be reduced in half an hour?
Round your answer to two places past the decimal.
Include units.

4

One of the important factors in determining a car's Fuel Efficiency is its Weight.
Look at the relationship for 11 cars.
A linear regression was calculated and the regression equation stored.
Use both the scatterplot and the residual plot to answer the question below.

Do you think the linear model is appropriate for this data?
Use the residual plot to explain your decision, be sure to look at the residual plot from left to right.
I will grade this answer.

4

Using the same data, let's try a power model to look at the association between fuel efficiency and weight of the 11 cars.
The residual plot for the power regression is shown below.

Explain why the power regression model appears to be better than the linear model.
I will grade this question.

4

The following table shows the stopping distances in feet for a car tested 3 times at each of 5 speeds. We hope to create a model that predicts the stopping distance from the speed of the car.

Enter the data into L1 and L2.
NOTE: you will have three entries in L1 for 20, three for 30, three for 40, etc.
There will be a total of 15 entries so each distance is matched with a speed. Ask for help if you have questions.

Observe the scatterplot, then do a linear regression. (Stat, Calc #8)
Record the Coefficient of Determination below.
Round to three places past the decimal.

4

Use the data you have entered for the speed and stopping distance for the car.
Now do an exponential regression (Stat, calc, #0).
What is the coefficient of determination now?
Enter it below, round to three places past the decimal.

4

Use the data you have entered for the speed and stopping distance for the car.
Now do a power regression (Stat, calc, alpha, math).
Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)

What is the coefficient of determination now?
Enter it below, round to three places past the decimal.

4

Based on the Coefficient of Determination:

1. Which regression model do you think is the most appropriate?

2. Now observe the residual plot for the power regression, what do you see?
Select both answers.

4

Use the data for the stopping distance from the speed of the car below.

Using the regression you think is appropriate, enter the equation below using the math keyboard to show exponents.
Use 'speed' and 'distance' for the variables.
No spaces.
Be sure to show which variable is being predicted.
Round to four places past the decimal.
Don't worry about the funny way the letters look for 'distance'.

4

Using your regression equation, estimate the stopping distance for a car traveling 55 mph.
Round to 2 places past the decimal.
Use units.

4

If the residual for 55 mph was -12.6 feet, what was the actual stopping distance for a car going 55 mph?

Hint, use the equation: Residual = Actual - Predicted

Create a scatterplot to show the association between years since 1900 and the crude oil production.y=, Statplot #1 ON, make sure the lists are correct.Display with zoom, 91. Which regression appears to be the most appropriate? Linear or exponential?2. Why?

Double check that this is the correct regression model. Do a LINEAR REGRESSION (Stat, Calc, #8)Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)Observe the residual plot with zoom9.What do you see?What does this mean?

Triple check that this is the correct regression model. Now do an EXPONENTIAL REGRESSION (Stat, Calc, #0)Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)Observe the residual plot with zoom9.What do you see?What does this mean?

Using the exponential regression equation in number 3, explain the meaning of the rate.Ex. what is the rate? is the oil production increasing or decreasing each year?Express it as a % per year.Use: 'The oil production is ______________________ by ______ % each year.'

Suppose you have fit a model to some data and now take a look at the residuals (the residual plot). For which of the possible residual plots would you reject your model?Why?Select all answers that apply.

Use the situation below to answer the question:Is this model linear, exponential or power?

Does the equation for toxin level show a decrease or an increase and what percent?How do you know?Select both answers.

Use the situation below to answer the question:How many milligrams of the toxin were in the water initially?Use units with your answer.

Use the situation below to answer the question:At what rate does this reaction reduce the level of toxin?Use: _________________ per ________________Make sure to include percent

Use the situation below to answer the question:To what level should the toxin be reduced in half an hour?Round your answer to two places past the decimal.Include units.

Using the same data, let's try a power model to look at the association between fuel efficiency and weight of the 11 cars.The residual plot for the power regression is shown below.Explain why the power regression model appears to be better than the linear model.I will grade this question.

Use the data you have entered for the speed and stopping distance for the car.Now do an exponential regression (Stat, calc, #0).What is the coefficient of determination now?Enter it below, round to three places past the decimal.

Based on the Coefficient of Determination: 1. Which regression model do you think is the most appropriate?2. Now observe the residual plot for the power regression, what do you see?Select both answers.

Using your regression equation, estimate the stopping distance for a car traveling 55 mph.Round to 2 places past the decimal.Use units.

If the residual for 55 mph was -12.6 feet, what was the actual stopping distance for a car going 55 mph?Hint, use the equation: Residual = Actual - Predicted

Create a scatterplot to show the association between years since 1900 and the crude oil production.
y=, Statplot #1 ON, make sure the lists are correct.
Display with zoom, 9
1. Which regression appears to be the most appropriate? Linear or exponential?
2. Why?

Double check that this is the correct regression model.

Do a LINEAR REGRESSION (Stat, Calc, #8)
Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)
Observe the residual plot with zoom9.

What do you see?
What does this mean?

Triple check that this is the correct regression model.

Now do an EXPONENTIAL REGRESSION (Stat, Calc, #0)
Store the regression equation & save the residuals (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)
Observe the residual plot with zoom9.

What do you see?
What does this mean?

Using the exponential regression equation in number 3, explain the meaning of the rate.
Ex. what is the rate? is the oil production increasing or decreasing each year?
Express it as a % per year.
Use: 'The oil production is ________________ by % each year.'

Suppose you have fit a model to some data and now take a look at the residuals (the residual plot).
For which of the possible residual plots would you reject your model?
Why?
Select all answers that apply.

Use the situation below to answer the question:

Is this model linear, exponential or power?

Does the equation for toxin level show a decrease or an increase and what percent?
How do you know?

Select both answers.

Use the situation below to answer the question:

How many milligrams of the toxin were in the water initially?
Use units with your answer.

Use the situation below to answer the question:

At what rate does this reaction reduce the level of toxin?
Use: _ per
Make sure to include percent

Use the situation below to answer the question:

To what level should the toxin be reduced in half an hour?
Round your answer to two places past the decimal.
Include units.

Using the same data, let's try a power model to look at the association between fuel efficiency and weight of the 11 cars.
The residual plot for the power regression is shown below.

Explain why the power regression model appears to be better than the linear model.
I will grade this question.

Use the data you have entered for the speed and stopping distance for the car.
Now do an exponential regression (Stat, calc, #0).
What is the coefficient of determination now?
Enter it below, round to three places past the decimal.

Based on the Coefficient of Determination:

1. Which regression model do you think is the most appropriate?

2. Now observe the residual plot for the power regression, what do you see?
Select both answers.

Using your regression equation, estimate the stopping distance for a car traveling 55 mph.
Round to 2 places past the decimal.
Use units.

If the residual for 55 mph was -12.6 feet, what was the actual stopping distance for a car going 55 mph?

Hint, use the equation: Residual = Actual - Predicted