# Ch18 - Chapter 18 Multiple Regression 1 18.1 Introduction...

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1 Multiple Regression Chapter 18

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2 18.1 Introduction In this chapter we extend the simple linear regression model, and allow for any number of independent variables. We expect to build a model that fits the data better than the simple linear regression model.
3 We shall use computer printout to Assess the model How well it fits the data Is it useful Are any required conditions violated? Employ the model Interpreting the coefficients Predictions using the prediction equation Estimating the expected value of the dependent variable Introduction

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4 Coefficients Dependent variable Independent variables Random error variable 18.2 Model and Required Conditions We allow for k independent variables to potentially be related to the dependent variable y = β 0 + β 1 x 1 + β 2 x 2 + …+ β k x k + ε
5 Multiple Regression for k = 2, Graphical Demonstration - I y = β 0 + 1 x X y X 2 1 The simple linear regression model allows for one independent variable, “x” y = β 0 + β 1 x + ε The multiple linear regression model allows for more than one independent variable. Y = β 0 + β 1 x 1 + β 2 x 2 + ε Note how the straight line becomes a plain, and. .. 2

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6 Multiple Regression for k = 2, Graphical Demonstration - II Note how a parabola becomes a parabolic Surface. X y X 2 1 y= b 0 + b 1 x 2 y = b 0 + b 1 x 1 2 + b 2 x 2 b 0
7 The error ε is normally distributed. The mean is equal to zero and the standard deviation is constant ( σ ε 29 for all values of y. The errors are independent. Required conditions for the error variable

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8 If the model assessment indicates good fit to the data, use it to interpret the coefficients and generate predictions. Assess the model fit using statistics obtained from the sample. Diagnose violations of required conditions. Try to remedy problems when identified. 18.3 Estimating the Coefficients and Assessing the Model The procedure used to perform regression analysis: Obtain the model coefficients and statistics using a statistical software.
9 Example 18.1 Where to locate a new motor inn? La Quinta Motor Inns is planning an expansion. Management wishes to predict which sites are likely to be profitable. Several areas where predictors of profitability can be identified are: Competition Market awareness Demand generators Estimating the Coefficients and Assessing the Model, Example

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10 Profitabil ity Competition Market awareness Customers Community Physical Margin Rooms Nearest Office space College enrollment Income Disttwn Distance to downtown. Median household income. Distance to the nearest La Quinta inn. Number of hotels/motels rooms within 3 miles from the site.
11 Estimating the Coefficients and Assessing the Model, Example Profitabil ity Competition Market awareness Customers Community Physical Operating Margin Rooms Nearest Office space College enrollment Income Disttwn Distance to downtown.

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Ch18 - Chapter 18 Multiple Regression 1 18.1 Introduction...

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