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# EXAM 2 - Review of Linear & Non-Linear Relationships M346

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This 8 page Study Guide was uploaded by Elizabeth Frabotta on Sunday October 9, 2016. The Study Guide belongs to M346 at Indiana University taught by Niket Jindal in Fall 2016. Since its upload, it has received 5 views. For similar materials see M346 Analysis of Marketing Data in Business Marketing at Indiana University.

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Date Created: 10/09/16

Day 12: Linear and Non -linear Relationships Monday, October 3, 2016 11:25 AM Readiness Assessment 12 Questions 1-5: Use the following regression equation 1. To test whether Advertising moderates the impact of Coupons on Sales, check if _______ is significant. a. Sales = b0+b1(Coupons) + b2(Adv)+b3(CouponsxAdv) + E b. B3 --> advertising moderates the impact of coupons on sales c. Answer = B3 2. The coefficient estimate for b1gives the impact of Coupons on Sales. a. False b. Would be true but we added b3, another interaction c. Coupons on sales is b1+b3xAdv d. B1 is impact of coupons on sales when advertising is 0 (b1+b3(adv)) e. B2 is impact of advertiisng on sales when coupons is 0 (b2+b3(Coupons) 3. The regression analysis gives the following significant coefficient estimates: What is the impact of Coupons on Sales for Advertising = 20? Please round your answer to one decimal place a. 2 + .03(20)=2.6 b. Answer: 2.6 4. The coefficient estimates given in Question 3 indicate that the impact of Coupons on Sales is greater when there is _______ A dvertising. a. Just need to look at B3 b. B3 is positive, so the greter the Advertising, the greater the impact on Sales c. Answer = MORE d. If b3 was a negative number, then answer = less 5. Suppose the regression analysis gives the following significant coefficient estimates: These coefficient estimates ind Coupons on Sales is greater when there is _______ Advertising. a. B3 is positive, tells youMORE b. -2+.03xAdv 6. The coefficient estimates for the regression equation: are Day 12: Linear and Non -linear Relationships Monday, October 3, 2016 11:25 AM Readiness Assessment 12 Questions 1-5: Use the following regression equation 1. To test whether Advertising moderates the impact of Coupons on Sales, check if _______ is significant. a. Sales = b0+b1(Coupons) + b2(Adv)+b3(CouponsxAdv) + E b. B3 --> advertising moderates the impact of coupons on sales c. Answer = B3 2. The coefficient estimate for b1gives the impact of Coupons on Sales. a. False b. Would be true but we added b3, another interaction c. Coupons on sales is b1+b3xAdv d. B1 is impact of coupons on sales when advertising is 0 (b1+b3(adv)) e. B2 is impact of advertiisng on sales when coupons is 0 (b2+b3(Coupons) 3. The regression analysis gives the following significant coefficient estimates: What is the impact of Coupons on Sales for Advertising = 20? Please round your answer to one decimal place a. 2 + .03(20)=2.6 b. Answer: 2.6 4. The coefficient estimates given in Question 3 indicate that the impact of Coupons on Sales is greater when there is _______ A dvertising. a. Just need to look at B3 b. B3 is positive, so the greter the Advertising, the greater the impact on Sales c. Answer = MORE d. If b3 was a negative number, then answer = less 5. Suppose the regression analysis gives the following significant coefficient estimates: These coefficient estimates ind Coupons on Sales is greater when there is _______ Advertising. a. B3 is positive, tells youMORE b. -2+.03xAdv 6. The coefficient estimates for the regression equation: are a. B3 is positive, tells youMORE b. -2+.03xAdv 6. The coefficient estimates for the regression equation: are b0 = 3 (p = .001) b1 = 2 (p = .020) Which of the following are true? a. There is a positive linear relationship between Advertising and Sales b. B1 needs to be positive & needs to be advertising & significant c. If p value is .72, probably no relationship; MUST BE SIGNIFICANT (.05) just b1 needs to be significant AND positive d. If significant & negative, negative relationship e. SIGNIFICANCE: Null Hypothesis is b1=0; when p is less than .05 we're saying yes there is a relationship 7. The coefficient estimates for the regression equation: are b0 = 2.8 (p = .001) b1 = 1.0 (p = .120) b2 = -3.5 (p = .030) Which of the following are true? a. B1 is not significant but b2 is b. Anything that talks about a linear relationship is incorrect c. For NEGATIVE non linear, b2 needs to be significant d. If want to test for cubic relationship, need this term, square term & cubed term (as long as b3 is significant, there is a cubic relationship) e. Always need lower ordered terms in equation, not coefficient estimates for all (Just for the highest one) f. Answer = There is a Negative Non Linear Relationship between Advertising and Sales 8. As Advertising increases, the impact of an increase in Advertising on Sales _______. a. Becomes Smaller b. Why: b2 is negative so it becomes smaller c. Ex. y=x^2 (positive slope);=x^2 (negative slope) d. Look at highest order Interpreting Linear and Non-linear relationships • Zip code w/ most negative relationships has most retail potential a. B3 is positive, tells youMORE b. -2+.03xAdv 6. The coefficient estimates for the regression equation: are b0 = 3 (p = .001) b1 = 2 (p = .020) Which of the following are true? a. There is a positive linear relationship between Advertising and Sales b. B1 needs to be positive & needs to be advertising & significant c. If p value is .72, probably no relationship; MUST BE SIGNIFICANT (.05) just b1 needs to be significant AND positive d. If significant & negative, negative relationship e. SIGNIFICANCE: Null Hypothesis is b1=0; when p is less than .05 we're saying yes there is a relationship 7. The coefficient estimates for the regression equation: are b0 = 2.8 (p = .001) b1 = 1.0 (p = .120) b2 = -3.5 (p = .030) Which of the following are true? a. B1 is not significant but b2 is b. Anything that talks about a linear relationship is incorrect c. For NEGATIVE non linear, b2 needs to be significant d. If want to test for cubic relationship, need this term, square term & cubed term (as long as b3 is significant, there is a cubic relationship) e. Always need lower ordered terms in equation, not coefficient estimates for all (Just for the highest one) f. Answer = There is a Negative Non Linear Relationship between Advertising and Sales 8. As Advertising increases, the impact of an increase in Advertising on Sales _______. a. Becomes Smaller b. Why: b2 is negative so it becomes smaller c. Ex. y=x^2 (positive slope);=x^2 (negative slope) d. Look at highest order Interpreting Linear and Non-linear relationships • Zip code w/ most negative relationships has most retail potential c. Ex. y=x^2 (positive slope);=x^2 (negative slope) d. Look at highest order Interpreting Linear and Non-linear relationships • Zip code w/ most negative relationships has most retail potential • Add and interpret interaction terms in a linear regression model • Add and interpret non -linear teams in a linear regression (Relationship) model ○ SPSS --> Linear Regression • y=b0+b1(x1)+b2(x2)+ • We're going to focus on POLYNOMIALS for no -linear relationships ○ Starts on question 6 in readiness ○ Curvature to relationship; not straight slope • Sales = b0+b1(Adv)+E ○ B1=2 Sales go up by 2 for every 1 increase in Adv ○ ○ Positive slope of value 2; straight line w/ slope of 2; sales on vertical axis, adv on horizontal Group Exercise 1 • Retail Analysts Exercise 2, pg. 31 ○ Does the % of females moderate the effect of Pop2000 on automobile dealerships? Add a term for the interaction between Pop2000 and of females to regression model § from Ex 1 § R & R2 we never use § Transform >> Compute >> New Variable >> Pop2000*%Females □ Dependents: Number of Automobile Dealerships □ Ivs: New variable, pop 2000, area, % of females, % of people married □ Method - Enter □ Statistics - Descriptives □ Save - Unstandardized Residuals ○ Question 1: Does adding interaction term improve performance of model? § Auto = b0+ b1(Area)+b2(Pop)+b3(%Females)+b4(%married)+b5(Pop*%Females)+E § Ex. 1 Adjusted R squared of .383 § .390 in Ex2, so yes IMPROVES ○ Question2: Which hvariables have a significant coefficient estimate? § Area, population, and interaction ○ Question 3: For every 10,000 increase in population, how many more automobile dealerships can be supported in a zip code with 50% females? ○ c. Ex. y=x^2 (positive slope);=x^2 (negative slope) d. Look at highest order Interpreting Linear and Non-linear relationships • Zip code w/ most negative relationships has most retail potential • Add and interpret interaction terms in a linear regression model • Add and interpret non -linear teams in a linear regression (Relationship) model ○ SPSS --> Linear Regression • y=b0+b1(x1)+b2(x2)+ • We're going to focus on POLYNOMIALS for no -linear relationships ○ Starts on question 6 in readiness ○ Curvature to relationship; not straight slope • Sales = b0+b1(Adv)+E ○ B1=2 Sales go up by 2 for every 1 increase in Adv ○ ○ Positive slope of value 2; straight line w/ slope of 2; sales on vertical axis, adv on horizontal Group Exercise 1 • Retail Analysts Exercise 2, pg. 31 ○ Does the % of females moderate the effect of Pop2000 on automobile dealerships? Add a term for the interaction between Pop2000 and of females to regression model § from Ex 1 § R & R2 we never use § Transform >> Compute >> New Variable >> Pop2000*%Females □ Dependents: Number of Automobile Dealerships □ Ivs: New variable, pop 2000, area, % of females, % of people married □ Method - Enter □ Statistics - Descriptives □ Save - Unstandardized Residuals ○ Question 1: Does adding interaction term improve performance of model? § Auto = b0+ b1(Area)+b2(Pop)+b3(%Females)+b4(%married)+b5(Pop*%Females)+E § Ex. 1 Adjusted R squared of .383 § .390 in Ex2, so yes IMPROVES ○ Question2: Which hvariables have a significant coefficient estimate? § Area, population, and interaction ○ Question 3: For every 10,000 increase in population, how many more automobile dealerships can be supported in a zip code with 50% females? ○ ○ § B2(Pop)+B5(Pop&%Females) § -33.5(10,000)+.001(10,000*0.5) § ANSWER = 1.65 ○ Question 4: Is the impact of population on the number of automobile dealerships significantly greater for zip codes with a large percentage of females than for zip codes with a small percentage of females? Why? § Significant & Positive § B5 is positive & significant =YES GROUP EXERCISE 2 • Using the regression equation in Ex 1 of case study, ○ Run a regressio to test if Area has a cubic relationship. If it does sketch & interpret § Start with this regression & add b5(Area^2)+b6(area^3) § All you look for is b6 significant? If it is it has a cubic relationship § .095 is greater than .05, NO not significant, does not have cubic relationship ○ Run a regression to test if Population has a quadratic relationship. If it does, sketch & interpret § =b5(Pop^2)+E .011, YES significant quadratic § ○ § B2(Pop)+B5(Pop&%Females) § -33.5(10,000)+.001(10,000*0.5) § ANSWER = 1.65 ○ Question 4: Is the impact of population on the number of automobile dealerships significantly greater for zip codes with a large percentage of females than for zip codes with a small percentage of females? Why? § Significant & Positive § B5 is positive & significant =YES GROUP EXERCISE 2 • Using the regression equation in Ex 1 of case study, ○ Run a regressio to test if Area has a cubic relationship. If it does sketch & interpret § Start with this regression & add b5(Area^2)+b6(area^3) § All you look for is b6 significant? If it is it has a cubic relationship § .095 is greater than .05, NO not significant, does not have cubic relationship ○ Run a regression to test if Population has a quadratic relationship. If it does, sketch & interpret § =b5(Pop^2)+E .011, YES significant quadratic §

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