Marketing Research Chapter 14 Quiz
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Questions and Answers

What does the slope (b) represent in the linear equation Y = a + bX?

  • The total value of the dependent variable when the independent variable is zero
  • The amount by which the dependent variable changes for each unit increase in the independent variable (correct)
  • The total number of units sold
  • The starting point of the dependent variable

Which of the following is true about bivariate regression analysis?

  • It can be used with multiple dependent variables
  • It determines causation between the variables
  • It requires more than one independent variable
  • It analyzes the relationship between one independent variable and one dependent variable (correct)

What is the primary purpose of multiple regression analysis?

  • To analyze the relationship between independent and dependent variables with only one independent variable
  • To provide a correlation coefficient between a single independent variable and a dependent variable
  • To establish a linear relationship between two variables only
  • To analyze the relationship between two or more independent variables and a single dependent variable (correct)

What does regression analysis NOT imply about the relationship between X and Y?

<p>X is certainly the cause of Y (B)</p> Signup and view all the answers

In the regression line derived from least-squares estimation, what does the intercept (a) indicate?

<p>The value of Y when all independent variables are zero (B)</p> Signup and view all the answers

What does the coefficient of price indicate in the energy drink sales regression analysis?

<p>Sales decrease with an increase in price. (A)</p> Signup and view all the answers

What does an adjusted R-squared value of 0.59 represent in the regression analysis?

<p>Only 41% of the variance in sales remains unexplained. (A), 59% of the variance in sales is explained by price and advertising. (C)</p> Signup and view all the answers

In the regression equation for FastTransport Company, what does a coefficient of 21.46 for weight of the cargo (X2) signify?

<p>Each additional unit of weight increases transportation costs by $21.46. (B)</p> Signup and view all the answers

What is indicated by the p-value of 0.0001 for price in the energy drink sales regression?

<p>Price has a statistically significant effect on sales. (D)</p> Signup and view all the answers

What is the intercept in the FastTransport regression equation indicative of?

<p>It represents the cost when both independent variables are equal to zero. (A)</p> Signup and view all the answers

What does the estimated intercept ($a$) represent in the multiple regression equation?

<p>The baseline value of the dependent variable when all independent variables are zero (C)</p> Signup and view all the answers

Which of the following statements regarding the effect of advertising on sales is true?

<p>Sales increase with an increase in advertising. (B)</p> Signup and view all the answers

What is indicated by a p-value of $b_1 = 0.08$ in the context of hypothesis testing?

<p>There is insufficient evidence to reject the null hypothesis at a 95% significance level. (B)</p> Signup and view all the answers

What does an Adjusted $R^2$ value of 0.09 imply about the model's explanatory power?

<p>The model explains 9% of the variance in the dependent variable. (C)</p> Signup and view all the answers

Why does the coefficient of advertising in the energy drink sales analysis make sense?

<p>More advertising generally leads to more awareness and potential sales. (C)</p> Signup and view all the answers

What does the step of face validity in regression analysis assess?

<p>The logical relationship and reasonableness of results. (A)</p> Signup and view all the answers

What is indicated by the hypothesis $H_a$: at least one $b_i ≠ 0$?

<p>At least one independent variable influences the dependent variable. (C)</p> Signup and view all the answers

In the given multiple regression model, if airtime increases by 1 unit, what change in the monthly phone bill is expected, holding data usage constant?

<p>An increase of 0.09 units in the monthly bill (A)</p> Signup and view all the answers

What does a significant p-value for $b_2$ (< 0.000) suggest about data usage in the regression model?

<p>Data usage significantly increases the monthly phone bill. (D)</p> Signup and view all the answers

What should be considered about the face validity of the estimated coefficients?

<p>They should logically align with expectations based on real-world scenarios. (C)</p> Signup and view all the answers

Why is multiple regression analysis favored for modeling complex phenomena?

<p>It allows for the examination of the combined effects of more than one independent variable. (B)</p> Signup and view all the answers

What does the estimated intercept (𝑎ො) represent in the regression equation?

<p>The total salary when no units are sold (C)</p> Signup and view all the answers

What is the coefficient (𝑏෠) interpreting in the regression equation?

<p>The increase in total salary for each additional unit sold (B)</p> Signup and view all the answers

If the p-value is greater than 0.05, what conclusion can be drawn regarding H0?

<p>Fail to reject H0 at 95% confidence level (A)</p> Signup and view all the answers

What does an R² value of 0.015 indicate in this regression analysis?

<p>A very small portion of variance in Y is explained by X (C)</p> Signup and view all the answers

In the provided regression equation, what is the effect of an increase in X (units sold) on Y (total salary)?

<p>Total salary increases by $102.2 (A)</p> Signup and view all the answers

What does the term 'e' represent in the regression equation?

<p>Error or residuals in the prediction (B)</p> Signup and view all the answers

What does the hypothesis H0: 𝑏෠ = 0 signify in regression analysis?

<p>There is no relationship between X and Y (B)</p> Signup and view all the answers

In the context of the given regression analysis, which statement regarding face validity is true?

<p>It assesses whether the analysis is reasonable based on intuition. (B)</p> Signup and view all the answers

If the coefficient for units sold is reported as 102.2, what does this suggest about commission earnings?

<p>For every unit sold, the salary increases by $102.2. (B)</p> Signup and view all the answers

Which of the following is TRUE regarding the statistical test in regression analysis?

<p>The F-statistic evaluates the goodness of fit. (A)</p> Signup and view all the answers

Flashcards

Bivariate Regression

Analyzes the relationship between one independent variable and one dependent variable.

Multiple Regression

Analyzes the relationship between multiple independent variables and one dependent variable.

Regression Analysis

A method to determine if a linear relationship exists between variables.

Independent Variable

The variable that is manipulated or changed to see its effect on the dependent variable.

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Dependent Variable

The Variable that is measured to see the effect of the independent variable.

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Simple Linear Regression

A statistical method that models the relationship between two variables, one independent (X) and one dependent (Y).

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Dependent Variable (Y)

The variable that is being predicted or explained in a regression model.

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Independent Variable (X)

The variable used to predict or explain the dependent variable (Y).

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Intercept (a)

The value of the dependent variable (Y) when the independent variable (X) is zero.

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Slope (b)

The change in the dependent variable (Y) for every one-unit change in the independent variable (X).

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Hypothesis Testing (H0, Ha)

In regression, testing if there's a relationship between the variables (slope = 0).

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p-value

The probability of observing results as extreme as, or more extreme than, those observed, if the null hypothesis were true.

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R-squared (R²)

The proportion of variance in the dependent variable that is predictable from the independent variable(s).

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Error Term (e)

The difference between the actual value of the dependent variable and the predicted value.

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Regression Analysis

A statistical process for estimating the relationships among variables.

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Multiple Regression

Predicting a dependent variable using multiple independent variables.

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Dependent Variable

The variable being predicted (outcome).

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Independent Variable

Variables used to predict the outcome (inputs).

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Multiple Regression Equation

Y = a + b1X1 + b2X2 + ... + bnXn + e.

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F-test in Multiple Regression

Tests if any independent variables have a relationship with the dependent variable.

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Coefficient of Determination (R-squared)

Percentage of variance in Y explained by all Xs.

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Adjusted R-squared

R-squared adjusted for the number of independent variables.

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Interpreting Coefficients

Effect of a one-unit change in an independent variable on the dependent variable, holding other Xs constant.

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Regression Equation

Mathematical formula expressing the relationship between a dependent variable and one or more independent variables.

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Intercept (a)

The predicted value of the dependent variable when all independent variables are zero.

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Coefficient (b)

Numerical value representing the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant.

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Positive Coefficient

Indicates a positive relationship between variables; as the independent variable increases, the dependent variable also increases.

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Negative Coefficient

Indicates a negative relationship between variables; as the independent variable increases, the dependent variable decreases.

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Adjusted R-squared

A measure of the goodness of fit of a model that considers the number of predictors in the model.

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P-value (F-statistic)

Probability of obtaining results as extreme as observed if the model is true. A significance level of 0.01 (or less) often used for rejecting null hypothesis.

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Face Validity

Assess if the variables included in the regression make logical sense in describing the target phenomenon. Does it match real world observations?

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Study Notes

Course Information

  • Course: Marketing Research
  • Section: B
  • Instructor: Dr. Yuyan Wei
  • Term: Fall 2024
  • Course Code: MARK 302

Chapter 14: Regression Analysis

  • Topic: More powerful statistical methods
  • Topic: Week 9
  • Topic: Tests for relational hypothesis
  • Topic: Regression analysis is used to analyze the relationship between variables
  • Topic: Bivariate regression analyzes the relationship between one independent (predictor) and one dependent variable
  • Topic: Multiple regression analyzes the relationship between two or more independent (predictor) variables and one dependent variable
  • Topic: Regression analysis does not prove causation but can show correlation and relationships

Linear Relationship

  • Description: A linear relationship exists when there's a consistent relationship between variables and they have a linear pattern
  • Example: Salesperson's monthly salary = base salary + commission per unit sold, e.g., $2,500 + $100 x units sold
  • Equation: Y = a + bX
    • Y: dependent variable
    • X: independent variable
    • a: intercept (base salary)
    • b: slope (commission)

Regression Line

  • Description: The regression line is a straight line that best represents the relationship between independent and dependent variable in a scatterplot
  • Equation: Y = a + bX + e
    • Y: dependent variable
    • â: estimated intercept
    • b: estimated slope / coefficient
    • X: independent variable
    • e: error (difference between actual and predicted value)

Regression Analysis - Interpret Results

  • Assumptions: b = 0 (no relationship vs. b ≠ 0 (relationship exists between variables)
  • The simple regression statistical test produces p-value based on F-statistic for the hypothesis and estimates and intercepts
  • R² / adjusted R²: measures percentage of variance in the dependent variable explained by the independent variable
  • Significance level α (e.g., 0.1, 0.05, 0.01); if p-value ≤ α, reject null hypothesis

Interpreting Results – Face Validity

  • Examine if the intercept and coefficients make sense in practice; are positive or negative coefficients meaningful for that context

In-Class Exercise #1

  • Topic: Regression Analysis of Price and Advertising on Energy Drink Sales
  • Steps to interpret Results
  • Step 1: Use statistical equations to illustrate the relationship between variables
  • Step 2: Check the P-value of F-stats
  • Step 3: Check the P-value of t-stats
  • Step 4: Interpret Adjusted R² (e.g., how much variation can be explained with the independent variables)

In-Class Exercise #2

  • Topic: Regression Analysis of Transportation Costs for a Company
  • Variables
    • X₁: number of cargos per shipment
    • X₂: weight of cargo
    • Y: transportation costs
  • Interpret a,b₁ and b₂
  • Evaluate face validity in context (e.g. negative coefficient may seem counterintuitive; consider cost model elements that might cause regression to seem invalid)

Multiple Regression Analysis

  • Equation: Y = a + b₁X₁ + b₂X₂ + … + bₙXₙ + e
    • Y = dependent variable
    • â = estimated intercept
    • bᵢ= estimated slope / coefficient of
    • Xᵢ = independent variables
    • e = error term
  • Hypotheses:
  • H₀: No relationship between independent and dependent variables (b₁ = b₂= … = bₙ = 0)
  • H₁: At least one independent variable affects the dependent variable (at least one bᵢ ≠ 0)

Multiple Regression Analysis - Interpret Results

  • Describe how to interpret information from Excel outputs
  • Step 1: Equation
  • Step 2: Verify P-value (F-Stats). Verify statistical significance
  • Step 3: Verify P-value of t-stats (individual variables). Determine whether a variable has a relationship with the dependent variable
  • Step 4: Verify Adjusted R²
  • Step 5: Check Face Validity (Examine the findings to make sense of the coefficients)

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Description

Test your knowledge on Regression Analysis from Marketing Research. This quiz covers bivariate and multiple regression, how to interpret linear relationships, and the distinction between correlation and causation. Prepare to analyze various statistical methods with practical examples.

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