This document contains notes from a statistics lesson on linear regression and residuals. It discusses defining a linear model, calculating residuals as the difference between predicted and actual values, interpreting residuals by squaring and summing them to find the line of best fit, and using residuals to measure prediction error from the linear model. It also notes that upcoming activities will include practicing computing, interpreting, and graphing residuals using an example about car fuel efficiency and curb weight data.

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.