Ball Bounce Lab

As you work through the ball bounce lab, there are a couple of topics that will require you to do a little research.

Residuals

• What is a residual?
• How do you make a residual plot on your TI-83? or look here (if you have headphones).

Writing the equation of the LSRL by hand.

• What point does it always pass through?
• How can we determine slope?

Interpreting The value of R^2.

• What does R-squared mean?

Do your best.  Feel free to contact me if you have questions.

Ch. 8 Linear Regression Guiding Questions

When would you use linear regression?

What are residuals?

How do you know if a regression line is a good fit?

How can you get a regression equation?  With technology? Without technology?

What assumptions and conditions must be met to procede with linear regression?

What is a residual plot?

Is a regression line a perfect predictor?

Does a regression line mean that all of the change in the response variable is due to the change in the explanatory variable?

Using the data from the # of beers and Blood Alcohol level.  Calculate the LSRL.

Can you guess the correlation?

Go to the following website to get practice with matching scatterplots to correlation values.

http://istics.net/stat/Correlations/

Correlation and Lurking Variables

Please comment on the following questions:

1) What is the difference between correlation and association?

2) If a scatterplot shows a very strong linear relationship, what value(s) should the correlation be close to?

3) If a scatterplot shows a very weak linear relationship, what value(s) should the correlation be close to?

4) Is it possible to have a strong association, but a weak correlation?

5) What is a lurking variable? What kind of affect can it have on the relationship between two quantitative variables?

How fast can you write?

You and a partner will collect data on how fast you can write as sentence with your dominant hand, and then again with your non-dominant hand?

And then describe the relationship between between righting speeds for each hand. Use either your phone, the wall clock or an online timer and then record your data in the google form below.


After the data is collected (we should have data from both east and west campuses) analyze the data using a scatterplot.

Be sure to comment on direction, form, strength, and unusual features. Do you think there is an association, what about correlation?

Here is the sentence you will write.  First with your dominant hand, and then again with your non-dominant hand.

“Mos Eisley spaceport. You will never find a more wretched hive of scum and villainy.”




You can view the results of the form here.

Make a copy of the file before you make a scatterplot.

You can learn how to make a scatter plot in google docs here.

Exploring Bi-variate Data Day 2

Some things to think about...9/20

posted by Ms. McCarthy 

Here are a few questions I would like you to answer on your team wikipage today

1) Define explanatory variables and response variables.

2) What four things do you need to mention when describing a scatterplot?

3) In context, please describe the following scatterplot:

This is data collected from students in statistics classes including their heights (inches) and weights (pounds).

 

4)  What conditions must be met for correlation and how do you check those conditions?

5) A Statistics teacher is collecting data in an introductory statistics course about the average number of hours students studied each week and their college GPA.  Which variable would you use as the explanatory variable and which as the response variable?  Why?

6) How can you make a scatterplot using your graphing calculator?  Where can you find the correlation?   

Unit II Exploring Bivariate Data

The first Major Topic in AP Statistics is Exploring Data. In Unit I we explored Categorical and Quantitative Data (univariate). In this unit we will look at how two quantitative variables relate.

From the AP Statistics Topic list, here is what we will be focusing on in this unit.

I. Exploring Data: Describing patterns and departures from patterns (20%-30%)

D. Exploring bivariate data

1. Analyzing patterns in scatterplots (Chapter 7)
2. Correlation and linearity (Chapter 7)
3. Least-squares regression line (Chapter 8)
4. Residual plots, outliers, and influential points (Chapter 9)
5. Transformations to achieve linearity: logarithmic and power transformations (Chapter 10)

All homework will be through Math XL, assignments have been set up for each unit.  Due dates are set.  

To get you started consider the following...

In February 1986, 16 students at The Ohio State University Participated in an experiment to explore the relationship between Blood Alcohol Level (BAC) and other variables such as amount of alcohol consumed, weight, gender and age. 16 students participated in the experiment. OSU Police administered a  breathalyzer to verify initial BAC was zero. They were randomly assigned by drawing a ticket from a bowl the number of beers to be consumed (1 to 9) of 12 oz beers. Thirty minutes after consuming their final beer, students took another BAC.  

How might you analyze this data?  Is there a relationship between any of the variables?  Don't forget make a picture, make a picture, make a picture.


What about this data?

Test Moved to Friday!

It is official, the test is Friday.

But don't forget to read the post below and complete the lab from class today.

Is the distribution approximately Normal?

You will work on a lab today in class, but part of what you will need to do is justify whether or not the distribution is approximately Normal or not.

Some things to think about.

How does your data fit the 68-95-99.7 rule?

What is a normal probability plot?  How can that help?

Here are your instructions for tonight...


You should have completed your data collection.  If you did not, then you will need to proceed with your data set (it should be fine).

Using your data set, complete #2 on the lab worksheet.

To answer #3 see the above questions to guide your work.

For #4 Use this google doc which was shared with you via email.  Enter your data at the bottom of the list in column A.  I started it off with two entries (I did the trials in my office, so they are not fake entries).  In columns C and D you will see a summary table of the data.  This will be updated real time as you enter your data.  Use this for your histogram for number 4.  (Note: not everyone will have the same totals unless we all wait for the last person to enter his/her info.  As long as there is at least 140 trials you may procede with your histogram.  It may be interesting to see the differences, Also since you and your partner have the same data please record in column B your name and your parnter's name, so that your partner knows he or she doesn't need to enter the data).

Continue with the rest of the worksheet.

Text me using the number to the right if you have questions.

Mr. Babel

Comments on the spot check...

The scores of the ACT are approximately normally distributed with a mean of 18 and a standard deviation of 6. According to Illinois State Universities Admissions website, the top 25% of their students scored a 27 or higher. *What percent of the students that take the ACT scored lower than the 27?

•  68%
•  75%
•  93%
•  95%

The most commonly chosen answer was 75%.  This was probably based on the information about ISU, the top 25% scored 27 and higher, so the bottom 75% must have scored lower.  But the question is about the percentage of students that take the ACT, not the percentage of students accepted into ISU.

For this we need to know how many standard deviations away from the mean 27 is, in other words the z-score.  z =(27-18)/6 = 1.5.  

The percent of students that scored below 27, is the same as on a Standard Normal model, the percent of a z-score being less than 1.5.  

There are multiple ways we can find this information.  One would come from the diagram I saw a couple of groups posted on the wiki.  

If you add up all the percentages from the left all the way up to 1.5 (or just do 100 - the percents to the right) you get 93.3%.  So about 93% of all scores are less than a 27. 

You could also use your calculator, there is a function called normalcdf(). 

And finally you have a table in the back of the book (something you would also have with you when you take the AP Test). 

Again assuming a Normal model with mean 18 and standard deviation 6, what percent of students would score between 24 and 30? *

•  50
•  34
•  13.5
•  2.5
•  .15

This problem can be done using the graph above or the less complicated 68-95-99.7 rule/picture.  

For the ACT, 24 is exactly 1 standard deviation above the mean, and 30 is exactly two standard deviations above the mean.  So we can use the 68-95-99.7 rule.

Since 95 percent of the data is between 6 and 30, that means 47.5% between 18 and 30.  

Since 68 percent of the data is between 12 and 24 that means 34% is between 18 and 24.  

47.5% - 34% = 13.5%.  

I'm not in class today

A message from Mr. Babel to the most amazing second period class (at East Leyden, in room 139, in the school year 2011-12) in the universe.




You may or may not have noticed, but I'm not in class with you today.  I have a meeting that I needed to attend.  Thank you to Ms. Kinnane for subbing.

1.  Your task for the day.  Continue with the Normal model and z-scores.  I've posted comments on your work on the wiki, for many groups that will serve as a guide to how to move forward.

• First after you and your teams check out the wiki, I want you to take about 5 minutes talking to someone from another team.  See what they have learned, share what you have learned.  

• Then comeback to your groups and share what you found out from another group.

2.  You have a worksheet of problems, can you answer those yet?  If not continue to look for ways to do so. 

•  You may need to google "normalcdf" TI-83 Normal model.  This could help with finding specific percentiles.  
• Or the ti-83 lab that I posted yesterday could be helpful.

3.  Here is the full topic list that I posted on Tuesday.  

• What are z-scores?  How are they used?
• How does rescaling data affect shape, center and spread?
• What is a Normal Model?
• What about the Standard Normal Model?
• When can we use the Normal Model?  Under what conditions?
• What does the 68-95-99.7 Rule mean?

How are you doing on this list? Does your wiki address all of these questions?

4. Take a quiz that will be emailed to you in about 15 minutes (not a real, quiz more of a spot-check) I just want to see how you are doing, it isn't for a grade.

5. Have a nice day

6. Did you notice the phone number on the left side of the screen? (Ok fine my left your right) I set up this google voice number so that you can text me when you have questions. I'm old, I email. Your young you text. This can help bridge that gap. Your texts will come to my email, and my email response will be texted back to you. If you call that number it would ring my office phone. But keep in mind you will need to identify yourself by name in the text message. You have my permission to text me today during class (make sure Ms. Kinnane reads this so you don't get in trouble). I will try to respond from my meeting (but only if it doesn't cause a distraction, because that would be rude of me).

7. You should be continuing to work on things outside of class, I should be seeing posts on the wiki, or comments on the blog, and as of today texts from you.

8. Check out my blog post from yesterday, some awesome student created videos from some NJ stats students. Amazing work by these students.

Awesome!
Check out these student created videos on statistics, most of them are from a high school in NJ...

http://www.youtube.com/MrAPStatistics

Very Helpful...

Thanks to Joe S. for posting this on his team's page...

http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm

Additional Resources for learning about the Normal Model

Here is an activity using your TI-83/84

Here are a lot of links related to the normal model

And don't forget to check what your classmates are posting on the wiki.

Check out what your classmates put on the wiki

Based on the different conversations I was listening to during class you should take a look at the project wiki and see what other teams put together.  I think that if we put it all together, you would have an even better understanding of the Normal Model.

Just how normal are you?

The mean height of men (20 years and over) in the US is approximately 69.4 inches, with a standard deviation of 3.1 inches.

The mean height of women (20 years and over) in the US is approximately 63.8 inches, with a standard deviation of 2.7 inches.

According to the CDC.

But what does that mean?  How "interesting" is your height?  What would make a height interesting?

Personally, I (Mr. Babel am about at the 50th percentile for height.  How can the above information be used to determine my height.

This chapter is about the normal model and z-scores.  You will investigate these topics and be able to answer questions like the ones above.

What are other measurements that we talk about in terms of percentiles?  How are these percentiles calculated?

Go to the AP Stats wiki.  You have been assigned to a team study and post what you have learned about the normal model.

Why Statistics Matters

As we approach the tenth anniversary of the 9/11 attacks reports of a possible association between serving at ground zero and cancer is in the news.


Not recognizing that there is an association means that workers and their families of the workers at 9/11 do not receive financial support for treatment of their cancer.

Looks like we could do a little more updating on our class wiki page.

I've gone through and updated the home page to be more of a navigation page to other areas.  I've linked the work some of you have done directly to the text I copied directly from the College Board AP Statistics Topic list.

Take a few minutes to add some important details to pages like shape, center, spread.
Add a page called box plots (or edit it if someone beats you too it).
How about gaps and outliers,
IQR, and how to determine if a data set has outliers.
mean, and standard deviation, median and IQR and how to decide.

Just click the link to the wiki and have at it.