11th octoberalg2
- 2. WALT : Correction of Homework Quiz 4 Use of residuals to compute error in prediction. Lesson 15/16 Practice in interpreting residual data Residual Plots WILF : A lesson won’t make sense unless you always review what we have done before TIB :Whenever predicting,having a percent error helps determine the confidence
- 3. Apologies for delay in grading quiz 3, you’ll have it by next session. My next office hours are Tuesday 16th October.
- 4. A linear model is represented with the form of equation : 𝑦 = 𝑚𝑥 + 𝑏 Residual : Difference between predicted and actual y-values Residual = actual y-value – predictedy-value To interpret the residuals,we need to square each one and add them up => The least squares line
- 5. The line of best fit to a linear relationship is the one that has the smallest sum of squared residuals min( 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑠 2 )
- 6. Khanacademy skills posted on classroom
- 7. Spread the chairs Individual , no discussion Any attempt at cheating will result in a 0
- 8. Knowing the residuals,we can calculate the error of prediction Small residuals => Good fit => Low error in prediction Big residuals => Bad fit => Big error in prediction
- 11. Answer on the worksheet handed out per group • Listen carefully to the instructions • Take 10 minutes to do the exercises. • Stay focused • Voice level 1 discussions (no excessive noise) • Raise your hand quietly for questions and wait for me to come
- 14. When a least squares line is used to calculate a predicted value, the prediction error can be measured by residual On the graph, the residuals are the vertical distances of the points from the least squares line. The residuals give us an idea how close a prediction might be when the least squares line is used to make a prediction for a value that is not included in the data set.
- 15. We’ll practice computing residuals,interpreting them and even graphing them. Let’s consider an example together Terminology : The curb weight of a car is the weight of the car without luggage or passengers. Fuel efficiency : how many miles per gallon
- 18. Will the residual for the car whose curb weight is 𝟐5.33 hundred pounds be positive or negative? Roughly what is the value of the residual for this point? Positive residual of 𝟑 mpg; the actual value is approximately 𝟑 units above the line. Will the residual for the car whose curb weight is 𝟐7 hundred pounds be positive or negative? Roughly what is the value of the residual for this point? Negative residual of −𝟔 mpg; the actual value is 𝟔 units below the line.
- 20. With a lot of data,these residual tables could get very lengthy,Is there any easier way ? Yes,through graphing What do we call a graph of residuals ? Residual Plot What is the usefulness of a residual plot ? It shows how predictive the model is. What does a good predictive model mean ? Low error in prediction
- 22. We plot residuals on y-axis for each x value We add the horizontal line at 0 and leave space for both positive and negative residuals
- 24. By reading the residual plot, you should be able to guess what the original data looks like. It is crucial to understand the mechanism with which we compute residuals. Video : https://www.youtube.com/watch?v=EB5a_vE Nd5Q
- 25. Student Warning 1 Warning 2 Demerit
- 26. Do not talk unless you have permission (Raise your hand) No talking back (Come see in end of class) Stay focused and on task Respect your classmates and teacher Be prepared
- 27. You are expected to do your homework on the due date (no excuses) Every time you miss a homework you get a strike,after 3 your parents are informed Not doing your homework will negatively affect your grade in participation and quizzes
- 28. The corrected quiz as well as rubrics will be posted on Engrade. An individual assesment means no discussion at all. Any talking will result in a 0. If you missed a quiz/test, you are responsible to come to office hours to retake it. Come see me right after class or office hours to discuss your copy, do not bring it up inside class. Any copy written in pencil cannot be considered for re- grading, use a pen.