Multiple Regression Combining Regressions and Model Choice Combining
Multiple Regression Combining Regressions and Model Choice
Combining Regressions n Combining Dummy Variable Regression with Simple Linear Regression n Dummy Variable Regression – Categories n Simple Linear Regression – Continuous Variables
Combining Regressions n Widget Co. Sales: Advertising Example n Two Different Sales Displays for Widget Co. ’s new ‘Crunchy Munchy’ grab bag. n Eye level Bugs Bunny Display
B. Bunny Display Catch the Wave, grab a bag of Crunchy Munchy
Combining Regressions n Widget Co. Sales: Advertising Example n Two Different Sales Displays for Widget Co. ’s new ‘Crunchy Munchy’ grab bag. n Eye level Bugs Bunny Display n Musical, Smiley Face Display
Smiley Display Smile all the While, grab a bag of Crunchy Munchy
Smiley Display Smile all the While, grab a bag of Crunchy Munchy
Smiley Web Site http: //www. funlaugh. com/newsmile. html
Combining Regressions n Widget Co. Sales: Advertising Example n Two Different Sales Displays for Widget Co. ’s new ‘Crunchy Munchy’ grab bag. n n Eye level Bugs Bunny Display Musical, Smiley Face Display
Combining Regressions n Widget Co. Sales: Advertising Example n Two Different Sales Displays for Widget Co. ’s new ‘Crunchy Munchy’ grab bag. n n n Eye level Bugs Bunny Display Musical, Smiley Face Display Considering four different price levels n n $0. 90 $1. 00 $1. 20 $1. 50
Simple Linear Regression n Basic Model (Place Displays in 48 randomly chosen stores, measure sales over a week, vary price).
Simple Linear Regression n Basic Model (Place Displays in 48 randomly chosen stores, measure sales over a week, vary price). n Sales:
Simple Linear Regression n Basic Model (Place Displays in 48 randomly chosen stores, measure sales over a week, vary price). n n Sales: Intercept (Sales Price = 0):
Simple Linear Regression n Basic Model (Place Displays in 48 randomly chosen stores, measure sales over a week, vary price). n n n Sales: Intercept (Sales Price = 0): Slope (Effect of Price):
Simple Linear Regression n Basic Model (Place Displays in 48 randomly chosen stores, measure sales over a week, vary price). n n Sales: Intercept (Sales Price = 0): Slope (Effect of Price): Price:
Dummy Variable Regression n Basic Model (Place 24 Bugs Bunny displays and 24 Smiley Face displays in randomly chosen stores, measure sales over a week, no price information).
Dummy Variable Regression n Basic Model (Place 24 Bugs Bunny displays and 24 Smiley Face displays in randomly chosen stores, measure sales over a week, no price information). n Sales:
Dummy Variable Regression n Basic Model (Place 24 Bugs Bunny displays and 24 Smiley Face displays in randomly chosen stores, measure sales over a week, no price information). n n Sales: Intercept (Sales using B. Bunny Display):
Dummy Variable Regression n Basic Model (Place 24 Bugs Bunny displays and 24 Smiley Face displays in randomly chosen stores, measure sales over a week, no price information). n n n Sales: Intercept (Sales using B. Bunny Display): Slope (Adjustment for Smiley Face Display):
Dummy Variable Regression n Basic Model (Place 24 Bugs Bunny displays and 24 Smiley Face displays in randomly chosen stores, measure sales over a week, no price information). n Sales: Intercept (Sales using B. Bunny Display): Slope (Adjustment for Smiley Face Display): n Display Dummy Variable: n n
Simple Linear Regression Smiley Sales B. Bunny Sales
Simple Linear Regression SPSS Analysis Results Sales as a function of Price
Simple Linear Regression Smiley Sales B. Bunny Sales Regression Line
Conclusions n n Price Has a Negative Impact on Sales The Smiley Face Sales are Higher than the Bugs Bunny Sales
Dummy Variable Regression
Dummy Variable Regression SPSS Analysis Results Sales as a function of Smiley
Conclusions n n Smiley Face Sales are Higher than the Bugs Bunny Sales Is there a way to combine both price and the smiley dummy variable?
Combined Regression n Combined Model (Two Displays, Variable Prices). n Intercept 0 (For B. Bunny Display):
Combined Regression n Combined Model (Two Displays, Variable Prices). n Intercept 0 (For B. Bunny Display): Intercept 1 (Adjustment to Intercept for Smiley): n Display Dummy Variable: n
Combined Regression n Combined Model (Two Displays, Variable Prices). n Intercept 0 (For B. Bunny Display): Intercept 1 (Adjustment to Intercept for Smiley): n Display Dummy Variable: n n n Slope (Effect of Price): Price:
Combined Regression Smiley Sales Smiley Regression Line B. Bunny Sales B. Bunny Regression Line
Combined Regression SPSS Analysis Results Sales as a function of Price and Smiley
Multiple Regression n n Regression with more than one X – Independent – Variable. Multiple X variables raises some basic questions n n n Which variables should be included in the regression? Which strategies can be used to select variables? What tools can be used to help make these decisions?
Is Beef a Luxury? n The American Association of Beef Producers are considering two different advertising for beef. n n The first campaign tries to reinforce the idea that beef is the meat in the basic American meat and potatoes diet. (Beef is necessary. ) The second campaign tries to reinforce the idea that prime rib is a meal for Royalty and that everyone in America deserves the best. (Beef is a luxury. )
Is Beef a Luxury? n Data n National Meat Consumption over time (Index) n National Meet Prices over time (Index) n National Disposable Income over time (Index)
Beef Consumption Over Time
Meat Prices Over Time
Income Over Time
Multiple Regression Model n What influences Consumption of Beef? n Price of Beef:
Multiple Regression Model n What influences Consumption of Beef? n Price of Beef: n Price of Pork:
Multiple Regression Model n What influences Consumption of Beef? n Price of Beef: n Price of Pork: n Price of Other Meat:
Multiple Regression Model n What influences Consumption of Beef? n Price of Beef: n Price of Pork: n Price of Other Meat: n Income:
Variable Selection Strategies n n Backwards Strategy n Start Large and Remove Stepwise Strategy n Start Small and Build up
Backwards Strategies n Backwards Strategy n Start Large and Remove n Start with all of the Variables n Remove variables , one at a time, that are “unimportant” n n Remove variables that have the largest p-value Stop once all p-values are less than 0. 05
SPSS Backwards Regression Full Model
SPSS Backwards Regression Full Model Remove Variable: Price of Other Meats P-value Large Price of Other Meat has No Impact on Consumption
SPSS Backwards Regression Next Model Remove Variable: Price of Pork P-value Large Price of Pork has a Marginal Impact on Consumption
SPSS Backwards Regression Final Model Keep all of the Variables: p-values < 0. 05
Final Model
Managerial Insights n Increase in Price of Beef, Decrease Consumption n n Increase Price by 1 Unit Decrease Consumption by 0. 441 Units
Managerial Insights n Increase in Price of Beef, Less Consumption n Increase Price by 1 Unit Decrease Consumption by 0. 441 Units Increase in Income, Increase Consumption n n Income Increases by 1 Unit Consumption Increases by 4. 151 Units
Managerial Insights
Is Beef a Luxury? n Luxury Good n %Change Consumption/%Change Income > 1 n n Get more money spend more of it on Beef %Change Consumption = Change Consumption/Current Consumption n %Change Income = Change Income/Current Income
Is Beef a Luxury? n Luxury Good n %Change Consumption/%Change Income = (Change Consumption/Change Income) x (Current Income/Current Consumption) = 4. 151 x (19. 33/109. 48) = 4. 151 x (0. 176) = 0. 733
Managerial Insights n Beef is not a Luxury – Use the Meat and Potatoes Campaign n n The first campaign tries to reinforce the idea that beef is the meat in the basic American meat and potatoes diet. (Beef is necessary. ) The second campaign tries to reinforce the idea that prime rib is a meal for Royalty and that everyone in America deserves the best. (Beef is a luxury. )
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