Lab4 2022
- 1. Lab 4 Fitting and Using Models
- 2. The point of this lab • Say we want to get really good at guessing the number of jelly beans in a jar • So we decide to practice with a bunch of different jars of jelly beans
- 3. The point of this lab • First, we record our guess of number of jellybeans in each jar • Next, we record the actual number of jellybeans • Based on how off our guesses are, we can know how to “correct” them in the future to get a more accurate prediction Jar Our Guess 252 90 135 63 720 100 Actual # 125 48 70 31 355 Based on how off our guesses were for the first 5 jars, what would you predict the actual # is here?
- 4. The point of this lab Jar Our Guess 252 90 135 63 720 100 Actual # 125 48 70 31 355 We can make a formula to “correct” our guess: 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑔𝑢𝑒𝑠𝑠 = 1 2 × (𝑜𝑢𝑟 𝑔𝑢𝑒𝑠𝑠)
- 5. The point of this lab Another example… • Say we want to get really good at guessing the number of wins the gamecocks will have in their season • We decide to practice guessing for a few seasons to “hone our model”
- 6. The point of this lab Season 2017 2018 2019 2020 2021 2022 Our Guess 5 6 8 2 4 7 Actual # 8 9 11 5 7 Once again, we can make a formula to “correct” our guess: 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑔𝑢𝑒𝑠𝑠 = 𝑜𝑢𝑟 𝑔𝑢𝑒𝑠𝑠 + 3
- 7. What you should learn • What is the meaning of predictor variable and response variable? • How can we use a fitted model (like 𝒚 = 0.5𝒙 + 3 ) to give us a prediction? • Given a fitted model (like 𝒚 = 0.5𝒙 + 3 ), and some data (values for x,y), how do we calculate the residuals? • In the context of predictions, what is the empirical rule for standard deviation? • What does it mean to be a biased guesser?
- 9. Now type your table 4.1 in statcrunch like so…
- 10. Graph → Scatterplot → X variable: Guessed, Y variable: True → Compute Paste this graph to your word document & answer question 2 based on this graph
- 11. Graph → Scatterplot → X variable: Guessed, Y variable: True → → Overlay function of x: x → Compute Paste this graph to your word document & answer question 3 based on this graph
- 12. Stats → Regression → Simple Linear → X variable: Guessed, Y variable: True → Compute Paste the output (tables and such AS WELL as the graph) into your word document
- 13. Paste the output (tables and such AS WELL as the graph) into your word document Stats → Regression → Polynomial → X variable: Guessed, Y variable: True → Compute
- 14. Look at the plot that you made on slide 12 of this powerpoint (NOT SLIDE 10 or 11) and use that to answer the question Look at the plot that you made on slide 13 of this powerpoint and use that to answer the question You found s in the cell to the left of this… just multiply it by 2 You found s in the cell to the left of this… just multiply it by 2
- 15. Write which model (Linear or Quadratic) you found to be best for your data. You will justify this choice later. Circle the reason(s) that made you choose Linear vs. Quadratic This formula can be found on the outputs that you made on slide 12 or 13 (depending if you chose linear or polynomial model) it looks like True = Blah blah Write your guess for the 11th object here. … now plug that x value into the formula that you just wrote, and see what value it spits out for True. I will tell you this value (so you can compare it with your model’s prediction) Calculate this by subtracting your model’s prediction of the weight (value in row 4) from the true weight (value in row 5). Find the value of 2s in table 4.2 (make sure you use the 2s from your chosen model). See if your error value from the row above falls into the interval (−2𝑠, 2𝑠)
- 16. What each person needs to turn in: • Tables 4.1, 4.2, 4.3 • Completed discussion questions • Plots & tables etc. that we made on slides 10 - 13