Statistics 350 Lecture 1

Today Course outline Stuff Section

Stuff Course webpage: 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

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)

Stuff How to do well in this course?

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

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)?

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?

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)

Apartment Example

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

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 +  1 x 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)

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

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

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.

Simple Linear Regression Model: Where:

Simple Linear Regression Data:

Simple Linear Regression Features of the model:

Simple Linear Regression Consider the following picture to visualize these properties