Which of the following are conditions that need to be met in order to calculate a correlation coefficient or a linear regression?
Question 3
3.
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?
Question 4
4.
Question 5
5.
Question 6
6.
Question 7
7.
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?
Question 8
8.
Question 9
9.
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.
Question 10
10.
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?
Question 11
11.
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?
Question 12
12.
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?
Question 13
13.
Question 14
14.
Order the following scatterplots from the most negative (strong negative) correlation to the most positive (strong positive).
Question 15
15.
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.
Question 16
16.
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.
Question 17
17.
What might be a lurking variable in the situation above with sunburn cases & ice cream sales?
Explain.
Question 18
18.
In general, if the residual is negative what does this mean?
Question 19
19.
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.)
Question 20
20.
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.
Question 21
21.
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)?
Question 22
22.
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.
Question 23
23.
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.
Draggable item
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Corresponding Item
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Question 24
24.
Interpret the meaning of the intercept.
Your answer needs to include information about both mg Tar and mg CO for full credit.
Question 25
25.
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.
Question 26
26.
The scatterplot must show a linear association.
The histogram needs to show a roughly symmetric distribution.
The scatterplot cannot show any outliers.
The data must come from a random sample.
The line is located on a scatterplot so that it maximizes the squared distances from the points to the line.
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:
Check the residual plot of the explanatory variable and the residuals.
Random scatter.
A definite pattern.
Check the scatter plot of the explanatory and response variables.
A strong linear relationship.
A definite curve.
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.
Sales are predicted to go as low as $510,198.
Sales decrease by approximately 410 for each 1 cent increase in price.
If the songs were free 410 people would download them.
An increase in prices of 1 cent predicts approximately 410 sales.
Approximately 510,200 customers will pay any price for a download.
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)?
An increase in prices of 1 cent predicts approximately 410 sales.
If the songs were free 410 people would download them.
Approximately 510,200 customers will pay any price for a download.
If the songs were free, then 510,198 downloads would occur.
Sales are predicted to go as low as $510,198.
Yes, the scatterplot does not show a linear relationship, there appear to be large outliers.
Yes, the scatterplot shows a nearly linear relationship, no large outliers and the data is quantitative.
No, the scatterplot does not show a linear relationship, there appear to be large outliers.
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?
D
Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.
Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern, it is not appropriate to use the line of best fit to predict vertical jump based on age.
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.
The residual of 0.4 indicates that the linear model under predicted the plant's height.
The residual of -6.96 indicates that the linear model over predicted the plant's height.
The residual of 0.4 indicates that the linear model over predicted the plant's height.
The residual of -0.4 indicates that the linear model under predicted the plant's height.
The residual of -0.4 indicates that the linear model over predicted the plant's height.
The residual of 6.96 indicates that the linear model under predicted the plant's height.
C, D, B, A
C, D, A, B
D, C, B, A
mg Tar
The intercept, units are mg Tar.
3.83
The slope, units are _______ mg CO per 1 mg Tar.
0.71
Explanatory variable
mg CO
Response variable
0.978
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?
No, it is risky to make predictions beyond our data values.
Interpolation
Quantitative Data Condition
Lurking Variable
Yes, we can use our linear model to make predictions.