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**BA 275 Quantitative Business Methods**

Agenda Quiz #6 Multiple Linear Regression Adjusted R-squared Prediction

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**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?

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**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

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**Prediction and Confidence Intervals**

Prediction interval Confidence interval

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**Model Comparison: A Good Fit?**

SS = Sum of Squares = ???

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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:

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**Residuals, Standardized Residuals, and Studentized Residuals**

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**Multiple Regression Model**

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Correlations

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**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 = ?

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**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

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**Prediction and Confidence Intervals**

Fitted Model: Estimated price = AGE BIDDER Statgraphics demo

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Analysis of Variance ? ?

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Model Selection

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Using Dummy Variables

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**Dummy Variable for LOCATION**

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Fitted Model

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**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?

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**Two Lines with the Same Slopes but Different Intercepts**

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**Two Lines with Different Intercepts and Slopes**

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OPIM 303-Lecture #8 Jose M. Cruz Assistant Professor.

OPIM 303-Lecture #8 Jose M. Cruz Assistant Professor.

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