Unit 5 Day 7 Linear Model Practice: creating, application, check residual plot

4

Data was collected from a group of children.

Enter the data into lists 1 & 2 (stat, edit).
Create a scatter plot (Statplot, scatterplot, make sure Xlist & Ylist are correct, zoomstat),
does it appear that the three conditions are met?
Select the correct answers.

2

In question #1, what variable is being used to predict what variable?

Hint: we use the explanatory variable to predict the response variable...

4

Data was collected from a group of children.

Check the appropriateness of using a linear model by saving the linear equation and graphing the residuals.
1. Stat, calc, #8LinReg, 'store RegEq', VARS, Y-VARS, y=, enter, calculate.
2. Now graph the residuals on a scatterplot:
change the Ylist to RESID (2nd, Stat, choose RESID), zoomstat (zoom9)
What do you see?
Select the two correct answers.

4

Data was collected from a group of children.

Do the linear regression again to find the slope and intercept.
Round the slope (b) and intercept to 2 places past the decimal.
Create the linear model in the space below.
Use ' -hat' to indicate the variable that is being predicted.
Put no spaces between numbers, words and symbols.

Ask me to check your equation if it shows incorrect.

4

Use the linear model (regression equation) from #4 to predict the height of a child who is 4.5 years old.
Hint: you need to change years to months so the units match!

Round your answer as 2 places past the decimal.
Use units in your answer.

4

Use the linear model (regression equation) from #4 to predict the height of someone who is 20 years old.
Hint: you need to change years to months so the units match!

4

Convert your answer from #6 to feet.

Does this make sense?
There are three correct answers.

4

Clear your y= so the regression equation from previous problems is gone.
Use the data in the following table to decide if doing a linear regression to create a linear model is appropriate:

Create a scatter plot of the data above by entering the data into 2 lists, then check the three conditions.
Is it appropriate to calculate the correlation coefficient and create a linear model?
Select one answer.

4

Use the data in the following table to decide if doing a linear regression to create a linear model is appropriate:

Even though the curve in the scatterplot indicates a linear regression is not a good idea, let's create one anyway so we can observe the residuals.
Do a linear regression (stat, calc, #8LinReg)
Make sure to use 'storeRegEqn', VARS, Y-VARS, y=, enter, calculate
Check the Residual Plot - change the ylist to RESID (use 2nd, Stat, select 'RESID'), zoomstat
1. What do you see?
2. What does this mean?
Select BOTH answers.

4

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Create the scatterplot, does it appear appropriate to create a linear model?
Why?
Choose ALL the correct answers.

4

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Now use the data to create the scatterplot of the residuals.

1. Do a linear regression (stat, calc, #8LinReg),
2. store the residuals ('storeRegEqn', VARS, Y-VARS, y=, enter, calculate)
3. For the scatterplot make the YList: RESID (use 2nd, Stat, select RESID)
4. Use zoomstat to show the residual plot.

Does the residual plot show that it is appropriate to use the linear model?
Why, what do you see?
Choose ALL the correct answers.

4

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Which variable will be the explanatory and which will be the response variable?
How will you use the variables to make a comparison?
Select all the correct answers:

4

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Do the linear regression again if you didn't write down the slope and intercept.
Use the 'a' and 'b' values to create the linear model,
round the values to two places past the decimal.

Enter the linear model below with no spaces, be sure to use ' -hat' to indicate which variable is being predicted.

For Speed Limit: use 'speed'
For Avg. # accidents: use 'accidents'

4

Use your linear model for predicting the # of accidents from #13.
Predict the number of accidents that will occur in one week if the speed limit is 35 mph.

Include units in your answer. Keep the places past the decimal.

4

If we had an actual data point for 35 mph of: (35, 18)
Remember ordered pairs are (units x, units y)

What is the residual?
Use units in your answer.

4

What does the residual indicate about the linear model?
(explain the residual)

4

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Using the regression equation from #13, predict the number of accidents for 55 mph.
Enter your answer below, include units.

4

Explain the residual.
Did the linear model overpredict or underpredict?

4

Use the roller coaster data to compare the initial drop height to the maximum speed (the highlighted columns).

1. Observe the scatterplot:
Enter the data into L1 & L2.
Make sure y= is cleared.

2. Now do a linear regression and store the residuals (see #11 for instructions).

3. Create a scatterplot with the residuals, choose Ylist: RESID

Is it appropriate to use the linear model to make predictions?
Choose all correct answers.

4

Use the roller coaster data to compare the initial drop height to the maximum speed (the highlighted columns).

Using the linear regression information from #19, create the linear model for predicting the max speed of the roller coaster based on the initial drop height.
Round to two places past the decimal.
Use ' -hat' to indicate which variable is being predicted.
Use 'speed' and 'height' for your variables.

(Ask me to check your equation if it stays red.)

4

Use your equation from #20 to predict the max speed of the roller coaster Supreme Scream at Knottsberry Farm (I've ridden it! There are no shoulder bars).
The Supreme Scream goes straight up for an initial drop of 252 feet.
How fast does our model predict it goes at it's maximum speed?
I remember it being VERY fast and needing hydraulic brakes to slow down.
Use units in your answer, keep the decimal places.

4

Keep the data from the roller coasters in your calculator.
NOW we want to predict the initial drop height of a roller coaster based on its max speed.

Remember what we did in our class activity? We reversed the lists and created a NEW equation.
Do that!
1. Do a linear regression (Stat, Calc, #8LinReg), switch the Xlist to L2 (2nd, 2) and the Ylist to L1 (2nd, 1).

2. Store the residuals while doing the regression ('storeRegEqn', VARS, Y-VARS, y=, enter, calculate).

3. Check the residual scatterplot, is it appropriate to use the linear model to predict the initial drop height?

Select all the correct answers.

4

Use the Linear Regression information from #22 (the 'a' and the 'b') to create a linear model for using the max speed to predict the initial drop height of a roller coaster.
Enter your equation, be sure to use ' -hat' to indicate which variable is being predicted.

Use the variables 'speed' and 'height'.
Round the decimals to two places.
Use no spaces.

4

Use the new linear model from #23 to predict the height of the initial drop for a roller coaster that has a max speed of 70 mph (the speed limit on 1604 and parts of Hwy 35!).

Round your answer to 2 places past the decimal.
Include units of 'ft'.

Data was collected from a group of children.Enter the data into lists 1 & 2 (stat, edit).Create a scatter plot (Statplot, scatterplot, make sure Xlist & Ylist are correct, zoomstat), does it appear that the three conditions are met?Select the correct answers.

In question #1, what variable is being used to predict what variable?Hint: we use the explanatory variable to predict the response variable...

Use the linear model (regression equation) from #4 to predict the height of a child who is 4.5 years old.Hint: you need to change years to months so the units match!Round your answer as 2 places past the decimal.Use units in your answer.

Use the linear model (regression equation) from #4 to predict the height of someone who is 20 years old.Hint: you need to change years to months so the units match!

Convert your answer from #6 to feet.Does this make sense?There are three correct answers.

Use the data table below comparing speed limit (mph) vs # accidents(weekly):Create the scatterplot, does it appear appropriate to create a linear model?Why?Choose ALL the correct answers.

Use the data table below comparing speed limit (mph) vs # accidents(weekly):Which variable will be the explanatory and which will be the response variable?How will you use the variables to make a comparison?Select all the correct answers:

Use your linear model for predicting the # of accidents from #13.Predict the number of accidents that will occur in one week if the speed limit is 35 mph.Include units in your answer. Keep the places past the decimal.

If we had an actual data point for 35 mph of: (35, 18)Remember ordered pairs are (units x, units y)What is the residual?Use units in your answer.

What does the residual indicate about the linear model?(explain the residual)

Use the data table below comparing speed limit (mph) vs # accidents(weekly):Using the regression equation from #13, predict the number of accidents for 55 mph.Enter your answer below, include units.

Explain the residual. Did the linear model overpredict or underpredict?

Use the new linear model from #23 to predict the height of the initial drop for a roller coaster that has a max speed of 70 mph (the speed limit on 1604 and parts of Hwy 35!).Round your answer to 2 places past the decimal.Include units of 'ft'.

Data was collected from a group of children.

Enter the data into lists 1 & 2 (stat, edit).
Create a scatter plot (Statplot, scatterplot, make sure Xlist & Ylist are correct, zoomstat),
does it appear that the three conditions are met?
Select the correct answers.

In question #1, what variable is being used to predict what variable?

Hint: we use the explanatory variable to predict the response variable...

Use the linear model (regression equation) from #4 to predict the height of a child who is 4.5 years old.
Hint: you need to change years to months so the units match!

Round your answer as 2 places past the decimal.
Use units in your answer.

Use the linear model (regression equation) from #4 to predict the height of someone who is 20 years old.
Hint: you need to change years to months so the units match!

Convert your answer from #6 to feet.

Does this make sense?
There are three correct answers.

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Create the scatterplot, does it appear appropriate to create a linear model?
Why?
Choose ALL the correct answers.

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Which variable will be the explanatory and which will be the response variable?
How will you use the variables to make a comparison?
Select all the correct answers:

Use your linear model for predicting the # of accidents from #13.
Predict the number of accidents that will occur in one week if the speed limit is 35 mph.

Include units in your answer. Keep the places past the decimal.

If we had an actual data point for 35 mph of: (35, 18)
Remember ordered pairs are (units x, units y)

What is the residual?
Use units in your answer.

What does the residual indicate about the linear model?
(explain the residual)

Use the data table below comparing speed limit (mph) vs # accidents(weekly):

Using the regression equation from #13, predict the number of accidents for 55 mph.
Enter your answer below, include units.

Explain the residual.
Did the linear model overpredict or underpredict?

Use the new linear model from #23 to predict the height of the initial drop for a roller coaster that has a max speed of 70 mph (the speed limit on 1604 and parts of Hwy 35!).

Round your answer to 2 places past the decimal.
Include units of 'ft'.