Unit 6 Day 5. Quiz

4

Which is true?
I. Random scatter in the residuals indicates a model with high predictive power.
II. The ressidual plot is used to check the appropriateness of a model for making predictions.
III. Residual = Predicted - Actual

4

Write an equation for the following situation:
A water tank had 75 gallons in it, it sprung a leak and started leaking 2.3 gallons each hour.

Use the time that has passed to predict the gallons left in the tank.

Use 'gallons' and 'hours' for variables.
No spaces.
Be sure to indicate which variable is being predicted.

4

If America's Biggest Loser contestant weighed 421 lb at the start and lost about 5.2% of their weight each week...

is this equation going to be linear, exponential or power?

2

To more easily determine the age of a tree (without cutting it down and counting the rings) a forester measured 27 trees of the same species that had been cut down and counted the rings to determine if the ages were correlated to the diameter of the trunk.
The computer output information is shown below, age is in years and diameter is in cm:

Variable Coefficient R-Squared: 81.9% S: 5.5764
Constant -0.8561
Diameter 3.6314

What is the correlation coefficient of the relationship between the tree diameter in cm and age in years?
Round to three places past the decimal.
Hint: you will need to use a number above and do a calculation.
Another hint: what letter represents the correlation coefficient?

4

To more easily determine the age of a tree (without cutting it down and counting the rings) a forester measured 27 trees of the same species that had been cut down and counted the rings to determine if the ages were correlated to the diameter of the trunk.
The computer output information is shown below, age is in years and diameter is in cm:

Variable Coefficient R-Squared: 81.9% S: 5.5764
Constant -0.8561
Diameter 3.6314

Set up the linear regression equation to predict the age of the tree based on the diameter.
Use 'years' and 'diameter' for the variable names.
Make sure to indicate which variable is being predicted.
Keep all decimal places.
No spaces

4

Use your equation for predicting the age of the tree to calculate the age of a tree that was 29.4 cm in diameter.

Round to two decimal places.

4

If our calculation of the tree's age gave a residual of -5.68, what was the tree's actual age?

Keep all decimal places.

4

A rapidly growing bacteria has been discovered. Its growth rate is shown in the chart.

Enter your data into L1 and L2.
Do an Exponential Regression (stat, calc, 0) to predict the number of bacteria using the number of days that have passed.
Create the equation below.

Round the decimals to three places past the decimal point.
Use the math keyboard to create an exponent if needed.
Use 'bacteria' and 'days' for variable names.
No spaces.

4

Using your equation for predicting the number of bacteria based on the number of days that have passed, explain the rate of increase/decrease.

Use units and %.

Ex. The _____ decrease/increase by % per .

6

Predict the number of bacteria present after 12 days.
1. Enter your prediction rounded to the nearest whole bacteria.
2. What kind of a prediction is this? Why?
3. Is this a wise or risky thing to do?

Answer all three questions for full credit.

6

The following data table includes information on the number of fireworks used per year in the United States.

Enter the data into L1 and L2 of your calculator.
Create a scatterplot to observe the relationship between time and fireworks used.
Describe it below:

4

Which regression seems to be the best model after looking ONLY at the scatterplot.

4

Do a linear regression (stat, calc, 8), store the regression equation (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)

Observe the residual plot, what do you see? (2nd, y=, change the ylist to RESID with 2nd, Stat, then zoom 9)

4

Now check the exponential regression model, do an Exponential Regression (Stat, calc, 0)

Store the regression equation. (StoreRegEqn: VARS, Y-VARS, enter, enter, enter, enter)

Observe the residual plot (see the previous question with instructions). (2nd, y=, change Ylist: RESID)
then zoom 9
What do you see and what does this mean?

4

We are only considering the Linear Regression model or the Exponential Regression model.
Check the Coefficient of Determination (Rsquared) to decide which is the better model to use.

Redo the linear regression, this time noting the Rsquared value.

Select the Rsquared value for the linear regression:
LOOK CAREFULLY!

4

We are only considering the Linear Regression model or the Exponential Regression model.
Check the Coefficient of Determination (Rsquared) to decide which is the better model to use.

Redo the exponential regression, this time noting the Rsquared value.
Select the Rsquared value for the exponential regression:
LOOK CAREFULLY!

4

Based on your calculations and comparison of the Rsquared values, which regression is the better model?
Linear or Exponential?
Explain why for full credit.

4

Create the regression equation for making predictions of the fireworks usage based on the elapsed time since 1990.

Use 'years' and 'fireworks' for the variable names.
Indicate which variable is being predicted.
Round to three places past the decimal point.
No spaces.

4

Observe your regression equation carefully, explain the rate/slope clearly.
Make sure to include units.
Note that the fireworks values are in millions of pounds.
Ex. use 'The ____ decreases/increases per .'

4

Observe the residual plots shown below:
1. 2. 3. 4.
If each plot represents the residual plot from a regression equation, which plot(s) would cause you to accept the regression equation?
Why?

Select all answers.

0

BONUS
If a company being studied originally had $869,000 worth of sales and increased them by 11.3% each year , create an equation to predict their sales based on the years that had passed.

Use the correct notation to show what variable is being predicted.
Use the math keyboard to insert an exponent if needed.
No spaces3

0

BONUS:
If a person started out on America's Biggest Loser weighing 379 lb and lost at a rate of 6.2% each week, create a regression equation to predict their weight based on the number of weeks that had elapsed.

Use the correct notation to show what variable is being predicted.
Use the math keyboard to insert an exponent if needed.
No spaces.

Which is true?I. Random scatter in the residuals indicates a model with high predictive power.II. The ressidual plot is used to check the appropriateness of a model for making predictions.III. Residual = Predicted - Actual

If America's Biggest Loser contestant weighed 421 lb at the start and lost about 5.2% of their weight each week...is this equation going to be linear, exponential or power?

Use your equation for predicting the age of the tree to calculate the age of a tree that was 29.4 cm in diameter.Round to two decimal places.

If our calculation of the tree's age gave a residual of -5.68, what was the tree's actual age?Keep all decimal places.

Using your equation for predicting the number of bacteria based on the number of days that have passed, explain the rate of increase/decrease.Use units and %.Ex. The _____________________ decrease/increase by __________ % per ______________.

Predict the number of bacteria present after 12 days.1. Enter your prediction rounded to the nearest whole bacteria.2. What kind of a prediction is this? Why?3. Is this a wise or risky thing to do?Answer all three questions for full credit.

The following data table includes information on the number of fireworks used per year in the United States.Enter the data into L1 and L2 of your calculator.Create a scatterplot to observe the relationship between time and fireworks used.Describe it below:

Which regression seems to be the best model after looking ONLY at the scatterplot.

Do a linear regression (stat, calc, 8), store the regression equation (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)Observe the residual plot, what do you see? (2nd, y=, change the ylist to RESID with 2nd, Stat, then zoom 9)

Based on your calculations and comparison of the Rsquared values, which regression is the better model?Linear or Exponential?Explain why for full credit.

Create the regression equation for making predictions of the fireworks usage based on the elapsed time since 1990.Use 'years' and 'fireworks' for the variable names.Indicate which variable is being predicted.Round to three places past the decimal point.No spaces.

Observe your regression equation carefully, explain the rate/slope clearly.Make sure to include units. Note that the fireworks values are in millions of pounds.Ex. use 'The __________________ decreases/increases ____________ per ______________.'

Observe the residual plots shown below: 1. 2. 3. 4. If each plot represents the residual plot from a regression equation, which plot(s) would cause you to accept the regression equation?Why?Select all answers.

Which is true?
I. Random scatter in the residuals indicates a model with high predictive power.
II. The ressidual plot is used to check the appropriateness of a model for making predictions.
III. Residual = Predicted - Actual

If America's Biggest Loser contestant weighed 421 lb at the start and lost about 5.2% of their weight each week...

is this equation going to be linear, exponential or power?

Use your equation for predicting the age of the tree to calculate the age of a tree that was 29.4 cm in diameter.

Round to two decimal places.

If our calculation of the tree's age gave a residual of -5.68, what was the tree's actual age?

Keep all decimal places.

Using your equation for predicting the number of bacteria based on the number of days that have passed, explain the rate of increase/decrease.

Use units and %.

Ex. The _____ decrease/increase by % per .

Predict the number of bacteria present after 12 days.
1. Enter your prediction rounded to the nearest whole bacteria.
2. What kind of a prediction is this? Why?
3. Is this a wise or risky thing to do?

Answer all three questions for full credit.

The following data table includes information on the number of fireworks used per year in the United States.

Enter the data into L1 and L2 of your calculator.
Create a scatterplot to observe the relationship between time and fireworks used.
Describe it below:

Do a linear regression (stat, calc, 8), store the regression equation (StoreRegEq: VARS, Y-VARS, enter, enter, enter, enter)

Observe the residual plot, what do you see? (2nd, y=, change the ylist to RESID with 2nd, Stat, then zoom 9)

Based on your calculations and comparison of the Rsquared values, which regression is the better model?
Linear or Exponential?
Explain why for full credit.

Create the regression equation for making predictions of the fireworks usage based on the elapsed time since 1990.

Use 'years' and 'fireworks' for the variable names.
Indicate which variable is being predicted.
Round to three places past the decimal point.
No spaces.

Observe your regression equation carefully, explain the rate/slope clearly.
Make sure to include units.
Note that the fireworks values are in millions of pounds.
Ex. use 'The ____ decreases/increases per .'

Observe the residual plots shown below:
1. 2. 3. 4.
If each plot represents the residual plot from a regression equation, which plot(s) would cause you to accept the regression equation?
Why?

Select all answers.