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?

X is certainly the cause of Y Signup and view all the answers

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

The value of Y when all independent variables are zero Signup and view all the answers

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

Sales decrease with an increase in price. Signup and view all the answers

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

Only 41% of the variance in sales remains unexplained. 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?

Each additional unit of weight increases transportation costs by $21.46. Signup and view all the answers

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

Price has a statistically significant effect on sales. Signup and view all the answers

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

It represents the cost when both independent variables are equal to zero. Signup and view all the answers

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

The baseline value of the dependent variable when all independent variables are zero Signup and view all the answers

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

Sales increase with an increase in advertising. Signup and view all the answers

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

There is insufficient evidence to reject the null hypothesis at a 95% significance level. Signup and view all the answers

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

The model explains 9% of the variance in the dependent variable. Signup and view all the answers

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

More advertising generally leads to more awareness and potential sales. Signup and view all the answers

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

The logical relationship and reasonableness of results. Signup and view all the answers

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

At least one independent variable influences the dependent variable. 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?

An increase of 0.09 units in the monthly bill 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?

Data usage significantly increases the monthly phone bill. Signup and view all the answers

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

They should logically align with expectations based on real-world scenarios. Signup and view all the answers

Why is multiple regression analysis favored for modeling complex phenomena?

It allows for the examination of the combined effects of more than one independent variable. Signup and view all the answers

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

The total salary when no units are sold Signup and view all the answers

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

The increase in total salary for each additional unit sold Signup and view all the answers

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

Fail to reject H0 at 95% confidence level Signup and view all the answers

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

A very small portion of variance in Y is explained by X 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)?

Total salary increases by $102.2 Signup and view all the answers

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

Error or residuals in the prediction Signup and view all the answers

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

There is no relationship between X and Y Signup and view all the answers

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

It assesses whether the analysis is reasonable based on intuition. Signup and view all the answers

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

For every unit sold, the salary increases by $102.2. Signup and view all the answers

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

The F-statistic evaluates the goodness of fit. Signup and view all the answers

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.