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Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
Chapter 4
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Chapter 4

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Transcript

  • 1. Chapter 4 Basic Estimation Techniques
  • 2. Simple Linear Regression 4-
    • Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X
      • Slope parameter ( b ) gives the change in Y associated with a one-unit change in X ,
  • 3. Method of Least Squares 4-
    • The sample regression line is an estimate of the true regression line
    • •
  • 4. Sample Regression Line (Figure 4.2) 4- A 0 8,000 2,000 10,000 4,000 6,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Advertising expenditures (dollars) Sales (dollars) S • • • • • • • e i
  • 5.
    • 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
    Unbiased Estimators 4- • •
  • 6. Relative Frequency Distribution* (Figure 4.3) 4- 0 8 2 10 4 6 1 1 3 5 7 9 *Also called a probability density function (pdf)
  • 7.
    • Must determine if there is sufficient statistical evidence to indicate that Y is truly related to X (i.e., b  0)
    Statistical Significance 4-
    • Test for statistical significance using t -tests or p -values
  • 8.
    • 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 -Test 4-
  • 9. 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
    4- •
  • 10. Performing a t -Test
    • If absolute value of t -ratio is greater than the critical t , the parameter estimate is statistically significant
    4-
  • 11. 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
    4-
  • 12. Coefficient of Determination
    • R 2 measures the percentage of total variation in the dependent variable that is explained by the regression equation
      • Ranges from 0 to 1
      • High R 2 indicates Y and X are highly correlated
    4-
  • 13. 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
    4-
  • 14. 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
    4-
  • 15.
    • Use when curve fitting scatter plot
    Quadratic Regression Models 4- • • • is U -shaped or U -shaped
  • 16. Log-Linear Regression Models 4- • • • • •

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