The Multiple Regression Model

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Presentation transcript:

The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (y) & 2 or more independent variables (xi) Population model: Y-intercept Population slopes Random Error Estimated multiple regression model: Estimated (or predicted) value of y Estimated intercept Estimated slope coefficients

Example A distributor of frozen desert pies wants to evaluate factors thought to influence demand Dependent variable: Pie sales (units per week) Independent variables: Price (in $) Advertising ($100’s) Data is collected for 15 weeks

Pie Sales Model Sales = b0 + b1 (Price) + b2 (Advertising) Week Pie Sales Price ($) Advertising ($100s) 1 350 5.50 3.3 2 460 7.50 3 8.00 3.0 4 430 4.5 5 6.80 6 380 4.0 7 4.50 8 470 6.40 3.7 9 450 7.00 3.5 10 490 5.00 11 340 7.20 12 300 7.90 3.2 13 440 5.90 14 15 2.7 Multiple regression model: Sales = b0 + b1 (Price) + b2 (Advertising)

TASK 1A: CALCULATE & INTERPRET COEFFICIENTS Slope (bi) y-intercept (b0)

TASK 1B: Write out tThe Multiple Regression Equation

TASK 1C: Using The Model to Make Predictions Predict sales for a week in which the selling price is $5.50 and advertising is $350: