Follow this link to the Regression Models App, which is an online application that allows you to explore regression models without doing the calculations yourself. It’s pretty cool, too!

There is a LOT of information given to you in the app. Watch this video, made by your instructor, to get a tour of the app.

• From the Data Source box on the far left, choose from the Data Frame drop-down box NHANES. (The National Health and Nutrition Examination Survey (NHANES) is a program of studies designed to assess the health and nutritional status of adults and children in the United States. The survey is unique in that it combines interviews and physical examinations.)
• Choose a response variable of mental_health_bad_days and explanatory variable of agefrom the drop-down boxes. View the tab for the Codebook to read a description of the variables. You can leave the Covariate box alone for the moment.
  1. Click New Sample a few times. What patterns do you observe?
     1. Click on the tab Statistics to see the calculation of r (“little r”) and R². You can click New Sample again a few times and watch the statistics change.
  2. Change the sample size. What patterns do you observe as you make the sample smaller compared to making the sample larger?
     1. Click on the tab Statistics to see the calculation of r (“little r”) and R². You can click New Sample again a few times and watch the statistics change.
  3. ****Answer this in the discussion**** Set the Sample Size n to 100. Click New Sample a dozen or so times. Describe the relationship you see between mental_health_bad_days and age. Be sure to speak about the strength of the relationship between the variables, the direction of the relationship, and anything unusual you observe. Include the words “random” and “variation” (or “variability”) in your response.
  4. ****Answer this in the discussion****Now, choose the Covariate of education. Set the Sample Size n to 100. Click New Sample a dozen or so times. Does the level of education that a person has change the relationship between between mental_health_bad_days and age? Explain. (Hint: (On scratch paper) Answer the question from the bullet point above for each different education level. Then, compare and contrast those answers to answer the question for this bullet point.)
• Read through the Explain tab, which gives you another explanation about regression, correlation, and R².
• ****Answer this in the discussion****
  1. Find any response/explanatory pair from the NHANES data set (a sample of size 50 or more) that produce an R² that is close to 1.
     1. Take a screenshot of the scatterplot, then embed or attach the image into your reply.
     2. How close were you able to get to an R² value of 1? What is the value for R²?
     3. Why does it make sense that the variables have an R² value close to 1?
     4. What do you see about the points in the graph that supports an R² value close to 1?
  2. Find any response/explanatory pair from the NHANES data set (a sample of size 50 or more) that produce an R² that is close to 0.
     1. Take a screenshot of the scatterplot, then embed or attach the image into your reply.
     2. How close were you able to get to an R² value of 0? What is the value for R²?
     3. Why does it make sense that the variables have an R² value close to 0?
     4. What do you see about the points in the graph that supports an R² value close to 0?
  3. Reflect on your experience playing with the applet. What ah-ha moments did you have doing this activity?