Day 9 Ch. 6 & 7 Test

Which of the statements below contains a mistake?

Which of the following are conditions that need to be met in order to calculate a correlation coefficient or a linear regression?

The line of best fit is also called the least-squares regression line or LSRL. Think back to the demonstration I did with the online Statistics Applets with the line of best fit, what were we trying to do with the line of best fit?

Which statement below is true?

A linear model (the equation for the line of best fit) makes a prediction for a data value and the residual is measured.

For the linear model equation to be considered appropriate to use to make predictions:

1. What do we check, what plot?

2. What are we looking for if the linear model equation is appropriate to use for predictions?

Select both correct answers below to identify the BEST, MOST ACCURATE way to check the linear model equation:

An independent record label sells mp3's of its songs online.

They have been experimenting with different prices for downloading each song.

Based on their data, the linear equation that models the average sales (in # of songs) for each price (in cents):

Sales-hat = 510,198 - 410(price)

Which sentence accurately describes the slope of this linear model (equation)?

If you need to, rewrite the equation using units instead of the name of the variables, this might help.

An independent record label sells mp3s of its songs online.

They have been experimenting with different prices for downloading each song.

Based on their data, the linear equation that models the average sales (in # of songs) for each price (in cents):

Sales-hat = 510,198 - 410(price)

Which sentence accurately describes the intercept of this linear model (equation)?

Use the data in the table below:

Enter your data into L1 and L2, (Stat, Edit)

Create a scatter plot and check the form. (2nd, y=, turn the statplot 'on', select scatter plot and make sure L1 & L2 are correct)

Is a linear regression appropriate for creating a model? (Hint: remember to check the three conditions)

Why?

Use the data in the table below:

No matter what you answered for the previous question, I would like you to create the linear model.

Use Stat, Calc, #8LinReg

Select the correct equation from the list below:

Which is the correct linear model for the data table?

Use your equation from #5 to predict the number of cars sold after 9 days.

Enter your prediction below, round to the nearest whole car since cars aren't sold at dealerships in factions.

If the dealership actually had a rough day due to cold rainy weather and the residual was -4, what was the actual number of cars sold?

Use your answer to #10 and the equation for calculating residuals.

Did the linear model overpredict or underpredict the number of cars that would be sold?

The scatterplot comparing Age vs Vertical Jump appeared to be approximately linear so a linear regression was calculated and the residuals stored.

Observe the residual plot below:

Which statement best assesses if it is appropriate to use the linear model equation to make predictions?

The linear regression equation:

height-hat = 3 + 1.16(weeks)

This linear model can be used to predict the height of a plant (in centimeters) after an amount of time (in weeks).

The height of a plant was actually 9.2 centimeters after 5 weeks.

Calculate and interpret the residual for this plant after 5 weeks.

Order the following scatterplots from the most negative (strong negative) correlation to the most positive (strong positive).

Data shows a strong positive correlation between ice cream sales and the number of cases of

sunburn in a small town.

r=0.976

Describe what this means, use language a 10 year old would understand.

Does the information in #15 mean that eating ice cream causes sunburn?

Explain using statistical terms not logic.

Be sure to mention a type of variable that we have discussed.

What might be a lurking variable in the situation above with sunburn cases & ice cream sales?

Explain.

In general, if the residual is negative what does this mean?

Use the residual plots shown below:

Which plot shows that it would be appropriate to use the linear model to make predictions? A, B or C

Why? (Make sure to explain your answer for full credit.)

Carbon Monoxide (CO) is a poisonous, colorless, odorless gas produced as a result of incomplete burning of carbon-containing fuels. Cigarette smoke can contain high levels of CO. Below are tar and CO data for 10 brands of popular cigarettes. Question: how is the amount of carbon monoxide produced by these cigarettes related to their tar content?

Calculate the correlation coefficient (r). (Stat, Calc, #8LinReg)

Enter the correlation coefficient below.

Round your answer to three places past the decimal.

Carbon Monoxide (CO) is a poisonous, colorless, odorless gas produced as a result of incomplete burning of carbon-containing fuels. Cigarette smoke can contain high levels of CO. Below are tar and CO data for 10 brands of popular cigarettes. Question: how is the amount of carbon monoxide produced by these cigarettes related to their tar content?

Using the correlation coefficient from above, what does this tell you about the relationship between Tar and Carbon Monoxide (CO)?

Carbon Monoxide (CO) is a poisonous, colorless, odorless gas produced as a result of incomplete burning of carbon-containing fuels. Cigarette smoke can contain high levels of CO. Below are tar and CO data for 10 brands of popular cigarettes. Question: how is the amount of carbon monoxide produced by these cigarettes related to their tar content?

Now that the data is in L1 and L2, redo the linear regression.

This time have your calculator SAVE THE RESIDUALS: Stat, Calc, #8LinReg, 'Store RegEq' 'VARS', 'Y-VARS', enter, enter, enter, enter.

Check the residual plot to see if it is appropriate to use the linear model to make predictions.

Statplot (2nd, y=), choose the scatterplot, change the YList to RESID (2nd, Stat).

Check the graph: Zoomstat (zoom #9)

What do you see?

What does this mean?

Answer both questions.

No matter what you answered in #21, create the linear model.

Round a and b to two places past the decimal.

Match the parts of the linear model to their role or meaning in the equation.

You may need to do another linear regression if you don't remember the values for 'a' and 'b'.

Note: not all values are used.

Interpret the meaning of the intercept.

Your answer needs to include information about both mg Tar and mg CO for full credit.

If a new cigarette was produced by Marlboro that had 32.4 mg Tar, use the linear model to predict the CO that would be produced.

Round your answer to two places past the decimal.

Use units.

Think about #24:

1. What is this type of prediction called?

Hint: we discussed it in class last time.

2. Is this ok to do with our linear model?