11th octoberalg2

1. Mr.Anas Lahrichi

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.