Chapter 4
This presentation is the property of its rightful owner.
Sponsored Links
1 / 16

Chapter 4 PowerPoint PPT Presentation


  • 92 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 4. Basic Estimation Techniques. •. Slope parameter ( b ) gives the change in Y associated with a one-unit change in X ,. Simple Linear Regression. Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X.

Download Presentation

Chapter 4

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


Chapter 4

Chapter 4

Basic Estimation Techniques


Simple linear regression

  • Slope parameter (b) gives the change in Y associated with a one-unit change in X,

Simple Linear Regression

  • Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X


Method of least squares

Method of Least Squares

  • The sample regression line is an estimate of the true regression line


Sample regression line figure 4 2

ei

Sample Regression Line (Figure 4.2)

S

70,000

Sales (dollars)

60,000

50,000

40,000

30,000

20,000

10,000

A

10,000

4,000

2,000

8,000

6,000

0

Advertising expenditures (dollars)


Unbiased estimators

Unbiased Estimators

  • The distribution of values the estimates might take is centered around the true value of the parameter

  • An estimator is unbiased if its average value (or expected value) is equal to the true value of the parameter


Relative frequency distribution figure 4 3

Relative Frequency Distribution (Figure 4.3)

1

4

2

3

8

9

10

5

6

7

0

1


Statistical significance

Statistical Significance

  • Must determine if there is sufficient statistical evidence to indicate that Y is truly related to X (i.e., b 0)

  • Test for statistical significance using t-tests orp-values


Performing a t test

Performing a t-Test

  • First determine the level of significance

    • Probability of finding a parameter estimate to be statistically different from zero when, in fact, it is zero

    • Probability of a Type I Error

  • 1 – level of significance = level of confidence


Performing a t test1

Performing a t-Test

  • Use t-table to choose critical t-value with n – k degrees of freedom for the chosen level of significance

    • n = number of observations

    • k = number of parameters estimated


Performing a t test2

Performing a t-Test

  • If absolute value of t-ratio is greater than the critical t, the parameter estimate is statistically significant


Using p values

Using p-Values

  • Treat as statistically significant only those parameter estimates with p-values smaller than the maximum acceptable significance level

  • p-value gives exact level of significance

    • Also the probability of finding significance when none exists


Coefficient of determination

Coefficient of Determination

  • R2 measures the percentage of total variation in the dependent variable that is explained by the regression equation

    • Ranges from 0 to 1

    • High R2indicates Y and X are highly correlated


F test

F-Test

  • Used to test for significance of overall regression equation

  • Compare F-statistic to critical F-value from F-table

    • Two degrees of freedom, n – k & k – 1

    • Level of significance

  • If F-statistic exceeds the critical F, the regression equation overall is statistically significant


Multiple regression

Multiple Regression

  • Uses more than one explanatory variable

  • Coefficient for each explanatory variable measures the change in the dependent variable associated with a one-unit change in that explanatory variable


Quadratic regression models

Quadratic Regression Models

  • Use when curve fitting scatter plot is -shaped or -shaped


Log linear regression models

Log-Linear Regression Models


  • Login