Marketing Research - Correlation & Regression Analysis PDF

3/23/2024 Marketing Research By Kevin Barrera, M.Sc. MBA Correlation & Regression...

3/23/2024 Marketing Research By Kevin Barrera, M.Sc. MBA Correlation & Regression Analysis Chapter 19 © Mr. Kevin Giang Barrera Marketing Research 2 2 Part I Chapter 19 Correlation Analysis © Mr. Kevin Giang Barrera Marketing Research 4 4 1  3/23/2024 Learning Objectives Discuss the use of correlation as a measure of association Discuss the objectives and applications of regression analysis © Mr. Kevin Giang Barrera Marketing Research 5 5 Chi Square – Chi Square – Hypothesis independence Goodness of fit Chapter 17 Testing TODAY Frequency T test – single mean Correlation Associated Regression – simple Relationship Test Mean T test – unrelated samples Statistical Regression – T test – Tests multiple related samples Variance Chapter 19 Chapter 18 ANOVA © Mr. Kevin Giang Barrera Marketing Research 6 6 2  3/23/2024 What test and when? Type of Tests Number of Two variables or Single variable Variables groups Nature of Comparing Comparing Association the test means means TODAY Type of Continuous Continuous Continuous Categorical variables variables variables variables variables Single mean Related Unrelated Correlation & Chi-square Test  T-test sample T-test sample T-test Regression test © Mr. Kevin Giang Barrera Marketing Research 7 7 What test and when? Type of Tests Number of Two variables or Single variable Variables groups Nature of Comparing Comparing Association the test means means Type of Continuous Continuous Continuous Categorical variables variables variables variables variables Single mean Related Unrelated Correlation & Chi-square Test  T-test sample T-test sample T-test Regression test © Mr. Kevin Giang Barrera Marketing Research 8 8 3  3/23/2024 Identifying Relationships between variables Purchase Intention Customer Customer Purchase Experience Satisfaction Behavior WOM Correlation does not imply Causation!!! © Mr. Kevin Giang Barrera Marketing Research 9 9 Correlation Analysis © Mr. Kevin Giang Barrera Marketing Research 10 10 4  3/23/2024 Correlation Correlation Analysis Measures the strength of the relationship between two variables Pearson Correlation Coefficient (r) Measure of the degree of linear association between two continuous variables (X and Y) Population correlation (ρ) or Sample Correlation (r) lies between -1 and 1 ρ or r = 0 ----> absence of linear association © Mr. Kevin Giang Barrera Marketing Research 11 11 Scatter Plots Negative strong correlation Positive strong correlation Perfect positive correlation No correlation What is considered a weak or strong correlation effect size? Weak correlation effect ± 0.1 Moderate correlation effect ± 0.3 Strong correlation effect ± 0.5 © Mr. Kevin Giang Barrera Marketing Research 12 12 5  3/23/2024 Pizza Hut wants to know if customer satisfaction is related to customer’s likelihood to recommend Correlation Hypothesis? Analysis Ho: There is no correlation between Pizza Hut’s customers satisfaction and their likelihood to recommend Example HA: There is a positive correlation between Pizza Hut’s customers satisfaction and their likelihood to recommend Which are the IV and the DV? Both can be IV or DV If the correlation coefficient is 0.91, what can you conclude? Customer satisfaction of Pizza Hut’s customers and their likelihood of recommendation are positively correlated. © Mr. Kevin Giang Barrera Marketing Research 13 13 Pizza Hut wants to know if customer satisfaction is related to customer’s likelihood to recommend Correlation Analysis 1. Testing the hypothesis Ho: ρ = 0 Example HA: ρ ≠ 0 Let’s assume six customers (n=6) were surveyed… Hence, 2. Computing the test statistic 𝑡=𝑟 =𝑟 = 0.91 = 0.91 = 4.39.. © Mr. Kevin Giang Barrera Marketing Research 14 14 6  3/23/2024 Student’s t Probability Distribution Table 1-α or 1-α/2 Note: DF 0.9 0.95 0.975 0.99 0.995 A student’s t-test can be a one-tail or a 1 3.078 6.314 12.706 31.821 63.657 2 1.886 2.920 4.303 6.965 9.925 two-tail test. 3 1.638 2.353 3.182 4.541 5.841 Steps: 4 5 1.533 1.476 2.132 2.015 2.776 2.571 3.747 3.365 4.604 4.032 1. Identify the level of significance 6 1.440 1.943 2.447 3.143 3.707 2. Identify if two-tail or one-tail 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355  Two-tail  Enter with 1-α/2 and 9 1.383 1.833 2.262 2.821 3.250 DF 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106  One-tail  Enter with 1-α and DF 12 1.356 1.782 2.179 2.681 3.055 3. Match your 1-α or 1-α/2 in the top row 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 4. Look for the DF in the first column 15 1.341 1.753 2.131 2.602 2.947 5. Look for the t score value at the intersection Identify t score for α=0.05 and DF=n- 2=6-2=4, two-tail 1-α/2 =1-0.05/2 = 0.975 From the Table: t score(4,0.05) = 2.776 © Mr. Kevin Giang Barrera Marketing Research 15 15 Pizza Hut wants to know if customer satisfaction is related to customer’s likelihood to recommend Correlation Analysis 1. Testing the hypothesis Ho: ρ = 0 Example HA: ρ ≠ 0 Let’s assume six customers (n=6) were surveyed… Hence, 2. Computing the test statistic 𝑡=𝑟 =𝑟 = 0.91 = 0.91 = 4.39.. If we assume α=0.05, then tcritic (1-α/2)= 2.78 3. Decision 𝑡 = 4.39 > 𝑡 = 2.78 There is enough evidence to reject Ho. © Mr. Kevin Giang Barrera Marketing Research 16 16 7  3/23/2024 Part II Chapter 19 Regression Analysis © Mr. Kevin Giang Barrera Marketing Research 20 20 Correlation and Causation Conditions for Causation  Association between IV and DV (Correlation must exist)  Time precedence  IV has to happen before the DV  Elimination of extraneous variables (confounders) Likelihood to Customer Satisfaction recommend © Mr. Kevin Giang Barrera Marketing Research 21 21 8  3/23/2024 Correlation and Causation The correlation coefficient (r) provides a measure of association between two variables, but it does not imply a causal relationship between them. Even a Regression Analysis can measure only the nature and degree of association (or covariation) between variables To establish causation, along with mathematical models (e.g., regression), one needs underlying knowledge, theories and accounting for confounders © Mr. Kevin Giang Barrera Marketing Research 22 22 Regression Analysis © Mr. Kevin Giang Barrera Marketing Research 23 23 9  3/23/2024 Regression Analysis Statistical technique used to relate two or more variables The goal is to create a regression model that relates one or more independent variables (IV) to the effect or change of the dependent variable (DV) The IVs can be either continuous or categorical, BUT the DV can only be a continuous variable. It is used to explain and predict the variable of interest (DV) © Mr. Kevin Giang Barrera Marketing Research 24 This Photo by Unknown Author is licensed under CC BY-SA 24 Applications of Regression Analysis How does word-of-mouth impact the sales of boxed wine? Whether and how do cross-promotions and pricing impact the use of Amazon’s videos streaming service? Is the effect of advertising on brand equity for Costco different for traditional vs digital media? © Mr. Kevin Giang Barrera Marketing Research 25 25 10  3/23/2024 Regression Equation  Simple linear regression – only ONE X variable Y: the dependent variable i: each individual ε: error term observation X1…n: set of βo: the intercept β1…n: coefficients predictors (IVs) related to the set of observations IVs  Multiple linear regression – more than ONE X variables © Mr. Kevin Giang Barrera Marketing Research 26 26 Interpreting the Regression Parameters The intercept Model parameter that represents the mean value of the “Y” variable when the independent variables (Xs) are equal to zero The coefficients Model parameters that represent the average change in the “Y” when Xi is changed by 1 unit and all other Xs are kept constant. “A change of 1 unit in Xi leads to an increase/decrease of βi units in Y when everything else is kept constant.” The error term Error term that describes the unexplained effects on 𝑌𝑖 © Mr. Kevin Giang Barrera Marketing Research 27 27 11  3/23/2024 Testing Significance of Regression Parameters  Simple linear regression model 𝑌 =𝛽 +𝛽 𝑋 +𝜀 𝐻 : 𝛽 =0 𝐻 : 𝛽 ≠0 reject H if p-value < α  Multiple linear regression model 𝑌 = 𝛽 +𝛽 𝑋 + 𝛽 𝑋 + ⋯+𝛽 𝑋 + 𝜀 𝐻 : 𝛽 =⋯=𝛽 =0 𝐻 : 𝑁𝑜𝑡 𝐴𝑙𝑙 𝛽 = 0 (𝑗 = 1 𝑡𝑜 𝑛) reject H if p-value < α © Mr. Kevin Giang Barrera Marketing Research 28 28 Coding Categorical Variables Dummy-Variable Coding Process Category of interest is coded as “1” and all other categories are coded as “0” We code n-1 categories… where n is the total number of categories Gender Original Code Dummy 1 Dummy 2 Dummy 3 Dummy 4 Male 1 1 NA NA NA Binary Case Female 2 0 NA NA NA The variable coded as zero is defined as the baseline Consumer Type Original Code Dummy 1 Dummy 2 Dummy 3 Dummy 4 Light user 1 1 0 NA NA Multinomial Moderate user 2 0 1 NA NA Case Heavy user 3 0 0 NA NA The variable that is not coded is defined as the baseline © Mr. Kevin Giang Barrera Marketing Research 29 29 12  3/23/2024 Simple Regression Analysis © Mr. Kevin Giang Barrera Marketing Research 30 30 Pizza Hut wants to know if customer satisfaction affects customer’s likelihood to recommend Simple Regression Hypothesis? Ho: The level of satisfaction of Pizza Hut’s customers does not affect their Analysis likelihood to recommend HA: The level of satisfaction of Pizza Hut’s customers affects their likelihood Example to recommend Which are the IV and the DV? Satisfaction is the IV and Likelihood to recommend is the DV How to write the regression equation? 𝑅𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑 = 𝛽 + 𝛽 ∗ 𝑆𝑎𝑡𝑖𝑠𝑓𝑎𝑐𝑡𝑖𝑜𝑛 + 𝜀 © Mr. Kevin Giang Barrera Marketing Research 31 31 13  3/23/2024 Pizza Hut wants to know if customer satisfaction affects customer’s likelihood to recommend Simple Regression After estimating the model. How to interpret the coefficients? Analysis Example 1 𝛽o =2.5 When customer satisfaction is zero, the average likelihood to recommend is 2.5 Example 𝑌 = 2.5 + 1.5𝑋 𝛽1 =1.5 For every unit increase of satisfaction, the average likelihood to recommend will increase by 1.5 units 𝛽o =0.6 When customer satisfaction is zero, the average Example 2 likelihood to recommend is 0.6 𝑌 = 0.6 − 0.5𝑋 𝛽1 =-0.5 For every unit increase of satisfaction, the average likelihood to recommend will decrease by 0.5 units © Mr. Kevin Giang Barrera Marketing Research 32 32 Regression Equation  Simple linear regression – only ONE X variable Y: the dependent variable i: each individual ε: error term observation X1…n: set of βo: the intercept β1…n: coefficients predictors (IVs) related to the set of observations IVs  Multiple linear regression – more than ONE X variables © Mr. Kevin Giang Barrera Marketing Research 33 33 14  3/23/2024 Multiple Regression Analysis © Mr. Kevin Giang Barrera Marketing Research 34 34 Pizza Hut wants to know if location, prices, promotion, variety and service affect customer satisfaction Multiple Regression Hypothesis? Ho: None of the independent variables affect customer satisfaction Analysis HA: Some of the independent variables affect their customer satisfaction Which are the IV and the DV? Example Satisfaction is the DV and Location, Prices, Promotion, Variety and Service are the IVs How to write the regression equation? 𝑠𝑎𝑡𝑖𝑠𝑓𝑎𝑐𝑡𝑖𝑜𝑛 = 𝛽 + 𝛽 ∗ 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 + 𝛽 ∗ 𝑃𝑟𝑖𝑐𝑒 + 𝛽 ∗ 𝑃𝑟𝑜𝑚𝑜𝑡𝑖𝑜𝑛 + 𝛽 ∗ 𝑉𝑎𝑟𝑖𝑒𝑡𝑦 + 𝛽 ∗ 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 + 𝜀 © Mr. Kevin Giang Barrera Marketing Research 35 35 15  3/23/2024 Pizza Hut wants to know if location, prices, promotion, variety and service affect customer satisfaction Multiple Regression After estimating the model. How to interpret the coefficients? Example 1: 𝑌 = 2.5 + 1.5𝐿𝑜 + 0.5𝑃𝑟 + 1.2𝑃𝑟𝑜 − 0.65𝑉𝑎 + 2.5𝑆𝑒𝑟 Analysis 𝛽o= 2.5 When all the IVs are zero, the average satisfaction is 2.5 𝛽5 =2.5 “Customer Satisfaction” increases by 2.5 units on average when Example “Service” increases by 1 unit, controlling for all other independent variables in the model Example 2: Let’s assume “Service” is a categorical variable with two levels (0=Bad; 1=Good) 𝑌 = 2.5 + 1.5𝐿𝑜 + 0.5𝑃𝑟 + 1.2𝑃𝑟𝑜 − 0.65𝑉𝑎 + 2.5𝑆𝑒𝑟 𝛽5 =2.5 “Customer Satisfaction” increases by 2.5 units on average when “Service” is good (compared to being bad), controlling for all other independent variables in the model © Mr. Kevin Giang Barrera Marketing Research 36 36 Interpreting a Regression Output R2 and Adjusted R2 : Measure of Model Fit. That is, how well the model fits the data SUMMARY OUTPUT They range between 0 and 1. The closer to 1 the better the fitting of the model R2 = 0.94 means that 94% of the variance in the DV (“Y”) is explained by the IVs (Xs) Regression Statistics For multiple regression, adjusted R2 is a better metric as it accounts for shared variance Multiple R 0.971806283 R Square 0.944407452 F-statistic tests whether having a regression model (HA) is better Adjusted R Square 0.939465892 than a null model (Ho). Standard Error 5.183661779 As p-value related to F test is