1. BA 275 Quantitative Business Methods
Agenda
Quiz #6
Multiple Linear Regression
Adjusted R-squared
Prediction

2. Simple Linear Regression Model
population
True effect of X on Y
Estimated effect of X on Y
sample
Key questions:
1. Does X have any effect on Y?
2. If yes, how large is the effect?
3. Given X, what is the estimated Y?

3. Key Q1: Does X have any effect on Y. Key Q2: How large is the effect
Key Q1: Does X have any effect on Y? Key Q2: How large is the effect? Key Q3: Predict Y for a given X. b0 b1
SEb1
SEb0

4. Prediction and Confidence Intervals
Prediction interval
Confidence interval

5. Model Comparison: A Good Fit?
SS = Sum of Squares = ???

6. Residual Analysis
The three conditions required for the validity of the regression analysis are:
the error variable is normally distributed.
the error variance is constant for all values of x.
the errors are independent of each other.
How can we diagnose violations of these conditions?
Residual:

7. Residuals, Standardized Residuals, and Studentized Residuals

8. Multiple Regression Model

9. Correlations

10. Fitted Model Q: Effect of AGE? H0: bAGE = 0 Ha: bAGE ≠ 0
Multiple Regression Analysis
Dependent variable: Price
Standard T
Parameter Estimate Error Statistic P-Value
CONSTANT
Age
Bidder ? ? ? ?
Q: Effect of AGE?
H0: bAGE = 0
Ha: bAGE ≠ 0
Q: Effect of BIDDER?
H0: bBIDDER = 0
Ha: bBIDDER ≠ 0
Degrees of freedom = ?

11. Fitted Model Fitted Model:
Multiple Regression Analysis
Dependent variable: Price
Standard T
Parameter Estimate Error Statistic P-Value
CONSTANT
Age
Bidder
Fitted Model:
Estimated price = AGE BIDDER

12. Prediction and Confidence Intervals
Fitted Model:
Estimated price = AGE BIDDER
Statgraphics demo

13. Analysis of Variance ? ?

14. Model Selection

15. Using Dummy Variables

16. Dummy Variable for LOCATION

17. Fitted Model

18. Questions Write down the fitted model.
Is the assumed model reliable? Why?
What is the value of R2? the adjusted R2? To select a model, why do we prefer adj-R2 to R2?
Predict the amount of money withdrawn from a neighborhood in which the median value of homes is $200,000 for an ATM that is located in a shopping center.
If the median value of homes increases by $2,000, then the amount of money withdrawn from an ATM located in a shopping center is expected to increase by
If the median value of homes is $200,000, then the amount of money withdrawn from an ATM located in a shopping center is ???; and the amount of money withdrawn from an ATM located outside a shopping center is ???. What is the difference?

19. Two Lines with the Same Slopes but Different Intercepts

20. Two Lines with Different Intercepts and Slopes