Statistics 350 Lecture 1

1
Statistics 350 Lecture 1
2
Today

• Course outline
• Stuff
• Section 1.1-1.3

3
Stuff

• Course webpage www.stat.sfu.ca/dbingham/Stat350
• Course assumes some background in Statistics
• Review material can be found in Appendix A of the
  text
• The course webpage has three review handouts
• Please go over this material!!!!!! Really!
• Check webpage for announcements and other fun
  stuff
• Lecture notes will be available online the night
  before class
• The notes (as you will see) require that you fill
  in the material

4
Stuff

• Homework
• About 7 assignments
• Homework to be handed in at the start of class on
  the assigned date
• Can work together, but hand in your own work!
• Computer packages for homework
• Use whatever you want
• SPSS, JMP are free to download from the
  microcomputer store
• Can get help in the Statistics drop-in lab for
  SPSS, JMP and minitab
• The Stats Lab is located in K9516 (inside K9510)

5
Stuff

• How to do well in this course?

6
Apartment Example

• So you want to find a new apartment
• You look up the apartment listings in the
  classified ads and two pieces of information
  (among others) are provided
• The size of the apartment in square feet
• The monthly rent

7
Apartment Example

• Questions of interest
• How much should you expect to spend on an
  apartment of a specified size?
• How much more would you have to spend for a
  larger apartment?
• How big an apartment can you get for C/month
  (i.e., C is the amount you actually want to
  spend)?

8
Comment

• This is an example of a regression problem
• Have numerical measurements on two variables and
  would like to investigate their relationship
• Form of the relationship
• Direction
• Does one variable appear to influence another?

9
Comment

• In simple linear regression, we will use a
  straight line to approximate whatever
  relationship exists between two variables
• Traditionally, if there is a cause and effect
  relationship between two variables, or one wishes
  to predict the outcome of one variable based on
  the other, the Cause variable (independent
  variable) is denoted as X and the Effect
  variable (dependent variable) is denoted by Y
• First step in simple linear regression is to plot
  the data (independent variable on the x-axis and
  dependent variable on the y-axis)

10
Apartment Example
11
Apartment Example

• Does a straight line appear to provide a
  reasonable approximation of the relationship
  between rent and apartment size?

12
Relationships Between Two Variables

• A functional relationship between two variables
  is given by a mathematical formula
• For example, the mathematical formula for a
  straight line is y?0?1x
• x denotes the independent variable
• y denotes the dependent variable
• ?0 is the intercept (the value of y when x is
  zero)
• ?1 is the slope (i.e., the amount y changes for
  each 1-unit increase in x)

13
Relationships Between Two Variables

• From a data analysis standpoint, what is the
  problem if you want to fit a straight line?
• The slope and intercept are both

14
Relationships Between Two Variables

• A statistical relation, is not a perfect
  one.have randomness (i.e., see scatter-plot)
• At the same value of x will not always observe
  the same y
• Will use data to estimate the model parameters to
  get estimated regression line

15
Simple Linear Regression

• Simple linear regression" - attempt to use a
  straight line to describe the relationship
  between the response Y and a single explanatory
  variable, X
• Later will learn about Multiple linear
  regression," where more than one variable is used
  to describe the response, making models which are
  linear combinations of the parameters
• Nonlinear regression" uses models which are not
  linear combinations of the parameters.

16
Simple Linear Regression

• Model
• Where

17
Simple Linear Regression

• Data

18
Simple Linear Regression

• Features of the model

19
Simple Linear Regression

• Consider the following picture to visualize these
  properties