Regression - PowerPoint PPT Presentation

Slide1 l.jpg
Download
1 / 26

  • 228 Views
  • Uploaded on
  • Presentation posted in: Sports / Games

Regression. The basic problem Regression and Correlation Accuracy of prediction in regression Hypothesis testing Regression with multiple predictors. The Basic Problem. How do we predict one variable from another? How does one variable change as the other changes?

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Presentation

Regression

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Slide1 l.jpg

Regression

  • The basic problem

  • Regression and Correlation

  • Accuracy of prediction in regression

  • Hypothesis testing

  • Regression with multiple predictors


The basic problem l.jpg

The Basic Problem

  • How do we predict one variable from another?

  • How does one variable change as the other changes?

  • Cause and effect (can only be inferred if it makes theoretical sense)


An example l.jpg

An Example

  • Effect of Dow Jones Performance on Darts performance (to what degree can Dow Jones predict Dart performance)


Slide4 l.jpg

The Data


Slide5 l.jpg

Relationship can be represented by line of best fit


Why use regression l.jpg

Why use regression?

  • We may want to make a prediction.

  • More likely, we want to understand the relationship.

    • How fast does Darts rise with one unit rise in Dow Jones?


Regression line l.jpg

Regression Line

  • Formula

    • = the predicted value of Y (Darts)

    • X = Dow value


Regression coefficients l.jpg

Regression Coefficients

  • “Coefficients” are a and b

  • b = slope (also called rate of change)

    • Change in predicted Y for one unit change in X

  • a = intercept

    • value of when X = 0


Calculation l.jpg

Calculation

  • Slope

  • Intercept


For our data l.jpg

For Our Data

  • b = 11.13/5.43 = 2.04

  • a = 14.52 - 2.04*5.95 = 2.37

  • See SPSS printout on next slide


Spss printout for one predictor l.jpg

SPSS Printout for one Predictor

R2, Percentage of Variance


Spss printout cont l.jpg

SPSS printout cont.

Error of prediction

Is regression

Significant?

Intercept

Slope


Slide13 l.jpg

Note:

  • The values we obtained are shown on printout.

  • The intercept is labeled “constant.”

  • Slope is labeled by name of predictor variable.


Making a prediction l.jpg

Making a Prediction

  • Suppose that we want to predict Darts score for a new Dow Score of 200

  • We predict that Darts will be at 23.65 when Dow is at 25

  • Check with data: what is real value of Darts when Dow is 25


Slide15 l.jpg

Prediction

Residual


Errors of prediction l.jpg

Errors of Prediction

  • Residual variance

    • The variability of predicted values

  • Standard error of estimate

    • The standard deviation of predicted values


Standard error of estimate l.jpg

Standard Error of Estimate

  • A common measure of the accuracy of our predictions

    • We want it to be as small as possible.


R 2 as predictable variability l.jpg

r 2 as % Predictable Variability

  • Define Sum of Squares


Major points l.jpg

Major Points

  • Predicting one dependent variable from multiple predictor variables

  • Example with Product Advisor Data

  • Multiple correlation

  • Regression equation

  • Predictions


The problem l.jpg

The Problem

  • In the product advisor study, we asked participants to rate the system on a number of aspects: e.g, usefulness, ease of use, trust, kind of product information, number of ratings etc.

  • Lets think of overall usefulness as our dependent variable. Which of the above factors can predict overall usefulness?

  • What percentage variance do they explain in the usefulness overall?

  • What factors play the more important role?


Product advisor data l.jpg

Product Advisor Data


Correlational matrix l.jpg

Correlational Matrix


Regression results using simple linear regression using method enter l.jpg

Regression Results(using simple linear regression using method “enter”

R2, Percentage of Variance


Slide24 l.jpg

Regression is significant

Importance of each variable

Is contribution significant?


Regression coefficients25 l.jpg

Regression Coefficients

  • Slopes and an intercept.

  • Each variable adjusted for all others in the model.

  • Just an extension of slope and intercept in simple regression

  • SPSS output on next slide


Regression equation l.jpg

Regression Equation

  • A separate coefficient for each variable

    • These are slopes

  • An intercept (here called b0 instead of a)


  • Login