FlashcardsRegression Analysis and OLS Flashcards
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This 726-card comprehensive study set covers regression analysis, ordinary least squares (OLS), and applied statistics for business and data analysis. Topics include linear and logistic regression, correlation and R-squared, multiple regression, hypothesis testing, decision trees, time series analysis, break-even analysis, and linear programming. Ideal for professionals preparing for advanced statistics exams, data analysis certification, or self-study in quantitative business methods.
Terms in This Set
- Ordinary Least Squares (OLS) Regression
- Purpose of OLS Regression
- Dependent Variable (Y)
- Independent Variable (X)
- Coefficient
- Intercept (b₀)
- Slope (b₁)
- OLS Regression Equation
- Residual
- Residual Formula
- Meaning of Small Residual
- Meaning of Large Residual
- Why Residuals Cannot Be Added Directly
- Sum of Squared Residuals (SSR)
- SSR Formula
- Least Squares Principle
- Best-Fit Line
- Why Residuals Are Squared
- OLS Process
- Multiple Regression (OLS Extension)
- Multiple Regression Equation
- OLS Advantage
- OLS Advantage
- OLS Advantage
- OLS Advantage
- What OLS Minimizes
- Residual Meaning in Simple Terms
- Coefficient Meaning
- Best-Fit Line Definition
- OLS Memory Rule
- What Regression Is
- Linear Regression
- Multiple Regression
- Logistic Regression
- Linear Regression Assumptions (LINE)
- R² (R-Squared)
- R² Meaning Example (0.29)
- R² Interpretation
- Important OA Rule
- Goodness of Fit (R²)
- OLS Key Idea
- Regression Purpose
- OLS Goal
- Residual vs Coefficient
- Regression Main Use Cases
- Correlation vs. R²
- Correlation (r)
- Range of Correlation (r)
- Positive Correlation
- Negative Correlation
- No Correlation
- R² (Coefficient of Determination)
- Range of R²
- Difference Between Correlation and R²
- r = +0.90 Means
- r = -0.90 Means
- r = 0 Means
- R² = 0.80 Means
- R² = 0.25 Means
- P-value
- Decision Rule (p-value < 0.05)
- Decision Rule (p-value ≥ 0.05)
- Scientific Notation (8.36E-05)
- What does p = 0.0000836 mean?
- Multiple Regression
- Purpose of Multiple Regression
- Multiple Regression Equation
- Ŷ (Y-hat)
- β₀ (Intercept)
- β (Coefficient)
- Error Term (e)
- Simple Regression vs. Multiple Regression
- Benefit of Multiple Regression
- Positive Coefficient
- Negative Coefficient
- Coefficient
- Demand Equation
- Price Coefficient (-6.88)
- Advertising Coefficient (+0.115)
- Multicollinearity
- Problem with Multicollinearity
- OA Clue for Multicollinearity
- Multicollinearity
- Problem with Multicollinearity
- OA Clue for Multicollinearity
- r = 0
- r ≈ 0.5
- r = +1
- r = -1
- How to Determine Positive or Negative Correlation in Excel
- Upward Slope
- Downward Slope
- r = 0
- r ≈ 0.5
- r = +1
- r = -1
- How to Determine Positive or Negative Correlation in Excel
- Upward Slope
- Downward Slope
- Logistic Regression
- Purpose of Logistic Regression
- Dependent Variable in Logistic Regression
- Output of Logistic Regression
- Common Cutoff Threshold
- Probability ≥ 0.50
- Probability < 0.50
- Sigmoid Curve
- Maximum Likelihood Estimation (MLE)
- Binomial Logistic Regression
- Multinomial Logistic Regression
- Ordinal Logistic Regression
- Linear Regression
- Logistic Regression
- Linear Regression Uses
- Logistic Regression Uses
- Linear Regression Model Shape
- Logistic Regression Model Shape
- Dependent Variable in Linear Regression
- Dependent Variable in Logistic Regression
- OLS
- Residual
- R²
- Correlation (r)
- Multiple R
- Regression
- p-value < 0.05
- Logistic Regression
- What is OLS (Ordinary Least Squares) Regression?
- Purpose of OLS Regression
- Dependent Variable (Y)
- Independent Variable (X)
- Coefficient (β)
- Intercept (β₀)
- OLS Regression Equation
- Residual
- Residual Formula
- Small Residual
- Large Residual
- Why are residuals squared?
- Sum of Squared Residuals (SSR/RSS)
- Least Squares Principle
- OLS Goal
- OLS Process
- Advantages of OLS
- Business Uses of Regression
- Linear Regression
- Multiple Regression
- Logistic Regression
- Regression Assumptions (LINE)
- R² (R-Squared)
- Higher R² Means
- Correlation (r)
- Correlation Range
- R² Range
- Difference Between Correlation and R²
- Positive Correlation
- Negative Correlation
- No Correlation
- Correlation Does NOT Imply
- P-value
- Decision Rule for P-value
- Scientific Notation Example
- Multiple Regression Formula
- Error Term (e)
- Coefficient Interpretation
- Positive Coefficient
- Negative Coefficient
- Multiple Regression Advantage
- Purpose of Multiple Regression
- Best-Fit Line
- Best-Fit Plane (Hyperplane)
- Demand Equation Example
- Interpretation of Price Coefficient (-6.88)
- Interpretation of Advertising Coefficient (+0.115)
- Multicollinearity
- Problem with Multicollinearity
- Purpose of Regression
- Linearity
- How to Check Linearity
- Normality
- How to Check Normality
- Independence
- How to Check Independence
- Homoscedasticity
- How to Check Homoscedasticity
- Heteroscedasticity
- Outlier
- Invalid Outlier
- True Outlier
- Best Graph for Identifying Outliers
- IQR Formula
- Outlier Rule
- Cook's Distance
- Autocorrelation
- Problem with Autocorrelation
- Durbin-Watson Statistic
- Most Important Regression Assumption
- Exogeneity
- Least Important Assumption
- What is Logistic Regression?
- Logistic Regression Predicts
- Common Cutoff Threshold
- Probability ≥ 0.50
- Probability < 0.50
- Shape of Logistic Regression
- Method Used by Logistic Regression
- Binomial Logistic Regression
- Multinomial Logistic Regression
- Ordinal Logistic Regression
- Linear Regression vs. Logistic Regression
- Decision Tree
- Purpose of a Decision Tree
- Decision Under Certainty
- Decision Under Risk
- Decision Under Uncertainty
- Expected Value (EV)
- Expected Value Formula
- Best Decision in a Decision Tree
- Decision Tree Process
- Descriptive Analytics in Decision Trees
- Predictive Analytics in Decision Trees
- Prescriptive Analytics in Decision Trees
- Why Businesses Use Decision Trees
- OLS
- Residual
- R²
- r
- p < 0.05
- Linear Regression
- Logistic Regression
- Multiple Regression
- Decision Trees
- Correlation ≠ Causation
- What is Regression?
- Main Business Uses of Regression
- What does Linear Regression predict?
- What does Multiple Regression predict?
- What does Logistic Regression predict?
- Simple Linear Regression
- Multiple Regression
- Logistic Regression
- Dependent Variable (Y)
- Independent Variable (X)
- Coefficient (β)
- Intercept (β₀)
- Error Term (e)
- Purpose of a Coefficient
- Positive Coefficient (+)
- Negative Coefficient (−)
- Regression Equation (Simple)
- Regression Equation (Multiple)
- Ordinary Least Squares (OLS)
- What does OLS minimize?
- Residual
- Residual Formula
- Why are residuals squared?
- Least Squares Principle
- Best-Fit Line
- Steps of OLS Regression
- Advantages of OLS
- Linear Regression Assumptions (LINE)
- Correlation (r)
- Range of Correlation (r)
- R-Squared (R²)
- Range of R²
- Multiple R
- Range of Multiple R
- Difference Between Correlation and R²
- r = +1
- r = -1
- r = 0
- R² = 0.80
- Higher R² Means
- Goodness of Fit
- P-value
- Decision Rule for Significance
- p < 0.05
- p ≥ 0.05
- Scientific Notation Example
- Relationship vs. Causation
- Correlation Does Not Imply Causation
- Simple Regression Visualization
- Multiple Regression Visualization
- Purpose of Multiple Regression
- Why use Multiple Regression?
- Multicollinearity
- Problem with Multicollinearity
- How to Identify Positive Relationship
- How to Identify Negative Relationship
- Demand Equation Example
- Interpretation of a Negative Coefficient
- Interpretation of a Positive Coefficient
- Example of Price Coefficient (-6.88)
- Example of Advertising Coefficient (+0.115)
- What does R² = 0.64 mean?
- Purpose of Logistic Regression
- Dependent Variable in Logistic Regression
- Output of Logistic Regression
- Common Cutoff Threshold
- Probability ≥ 0.50
- Probability < 0.50
- Curve Used in Logistic Regression
- Method Used in Logistic Regression
- Purpose of MLE
- Binomial Logistic Regression
- Multinomial Logistic Regression
- Ordinal Logistic Regression
- Linear Regression vs. Logistic Regression
- What is a Chi-Square Test?
- When to Use It Use Chi-Square when
- Regression
- Purpose of regression
- Dependent Variable (Y)
- Independent Variable (X)
- Simple Regression
- Multiple Regression
- Logistic Regression
- Coefficient (β)
- Intercept (β₀)
- Residual
- Regression Equation
- Slope (m)
- Purpose of the slope
- Purpose of the intercept
- Regression measures
- Regression does NOT prove
- Regression requires
- Regression is appropriate when
- OLS (Ordinary Least Squares)
- OLS
- OLS stands for
- Goal of OLS
- Least Squares Principle
- SSR
- RSS
- Residual
- Small residual
- Large residual
- Why square residuals?
- Another reason to square residuals
- Best-fit line
- OLS can be used with
- OLS is used for
- Correlation & R²
- Correlation (r)
- Range of correlation
- r = +1
- r = -1
- r = 0
- Positive correlation
- Negative correlation
- R² (R-Squared)
- Range of R²
- Higher R²
- Lower R²
- Correlation measures
- R² measures
- Multiple R
- Correlation does NOT imply
- Statistical Significance
- P-value
- Significant relationship
- Not significant
- Low p-value
- High p-value
- Statistically significant means
- Hypothesis Testing
- Null Hypothesis (H₀)
- Alternative Hypothesis (H₁)
- Regression H₀
- Regression H₁
- Reject H₀ when
- Fail to reject H₀ when
- Business Questions
- Good regression question
- Bad regression question
- Use the word
- Avoid the words
- A regression question should include
- A regression question should ask about
- Regression Output
- Coefficient
- Positive coefficient
- Negative coefficient
- Regression equation is used to
- Excel coefficient table provides
- Regression output includes
- Multiple Regression
- Purpose of multiple regression
- Benefit of multiple regression
- Coefficient in multiple regression
- Error term (e)
- Multicollinearity
- Problem with multicollinearity
- Multiple regression uses
- Logistic Regression
- Logistic regression
- Dependent variable in logistic regression
- Common logistic outcomes
- Logistic regression uses
- Logistic regression curve
- Probability output
- Default cutoff value
- Probability ≥ 0.50
- Probability < 0.50
- Binomial logistic regression
- Multinomial logistic regression
- Ordinal logistic regression
- Demand Analysis
- Demand equation
- Positive coefficient in demand analysis
- Negative coefficient in demand analysis
- Price coefficient is usually
- Advertising coefficient is usually
- Higher R² in demand analysis
- Application Questions
- A company wants to know if click-through rate is related to weekly sales. Is regression appropriate?
- A company asks if advertising increases sales. Is this a good regression question?
- A regression finds p = 0.03. What should you conclude?
- A regression finds p = 0.42. What should you conclude?
- A regression finds R² = 0.75. What does this mean?
- A regression finds R² = 0.28. What does this mean?
- A coefficient is positive. What does this mean?
- A coefficient is negative. What does this mean?
- Which regression predicts weekly sales?
- Which regression predicts customer purchase (Yes/No)?
- Which regression uses one predictor?
- Which regression uses multiple predictors?
- Which regression minimizes squared residuals?
- What does OLS minimize?
- What does R² measure?
- What does correlation measure?
- What does p-value measure?
- What happens if residuals are large?
- What happens if residuals are small?
- Can regression prove causation?
- Can regression predict future values?
- Which variable is plotted on the X-axis?
- Which variable is plotted on the Y-axis?
- What type of data is required for linear regression?
- What does the intercept represent?
- What does the slope represent?
- If two predictors are highly correlated, what is the problem?
- If p < 0.05 but R² is low, what does it mean?
- What is the purpose of the regression equation?
- Correlation between ice cream sales and drowning deaths is high. Does this prove one causes the other?
- OLS
- OLS stands for
- Goal of OLS
- Least Squares Principle
- SSR
- RSS
- Residual
- Small residual
- Large residual
- Why square residuals?
- Another reason to square residuals
- Best-fit line
- OLS can be used with
- OLS is used for
- OLS
- OLS stands for
- Goal of OLS
- Least Squares Principle
- SSR
- RSS
- Residual
- Small residual
- Large residual
- Why square residuals?
- Another reason to square residuals
- Best-fit line
- OLS can be used with
- OLS is used for
- OLS
- OLS stands for
- Goal of OLS
- Least Squares Principle
- SSR
- RSS
- Residual
- Small residual
- Large residual
- Why square residuals?
- Another reason to square residuals
- Best-fit line
- OLS can be used with
- OLS is used for
- P-value
- Significant relationship
- Not significant
- Low p-value
- High p-value
- Statistically significant means
- Good regression question
- Bad regression question
- Use the word
- Avoid the words
- A regression question should include
- A regression question should ask about
- Good regression question
- Bad regression question
- Use the word
- Avoid the words
- A regression question should include
- A regression question should ask about
- Coefficient
- Positive coefficient
- Negative coefficient
- Regression equation is used to
- Excel coefficient table provides
- Regression output includes
- Purpose of multiple regression
- Benefit of multiple regression
- Coefficient in multiple regression
- Error term (e)
- Multicollinearity
- Problem with multicollinearity
- Multiple regression uses
- Purpose of multiple regression
- Benefit of multiple regression
- Coefficient in multiple regression
- Error term (e)
- Multicollinearity
- Problem with multicollinearity
- Multiple regression uses
- Logistic regression
- Dependent variable in logistic regression
- Common logistic outcomes
- Logistic regression uses
- Logistic regression curve
- Probability output
- Default cutoff value
- Probability ≥ 0.50
- Probability < 0.50
- Binomial logistic regression
- Multinomial logistic regression
- Ordinal logistic regression
- Demand equation
- Positive coefficient in demand analysis
- Negative coefficient in demand analysis
- Price coefficient is usually
- Advertising coefficient is usually
- Higher R² in demand analysis
- Time Series Analysis
- Independent Variable (Time Series)
- Dependent Variable
- Forecasting
- Trend
- Cyclicality
- Seasonality
- Irregularity
- Random Variation
- TC SIR
- Regression (Time Series)
- Linear Regression
- Fixed Costs
- Variable Costs
- Break-Even Point (BEP)
- Break-Even Analysis
- Below BEP
- Above BEP
- Crossover Analysis
- Crossover Point
- After Crossover
- Linear Programming (LP)
- Objective Function
- Constraints
- Decision Variables
- Excel Solver
- Simplex LP
- Cluster Analysis
- Segmentation
- Purpose of Clustering
- Limitation of Clustering
- Regression Analysis
- Decision Analysis
- Decision Tree
- Monte Carlo Simulation
- Monte Carlo Idea
- Monte Carlo Use
- Monte Carlo Limitation
- Statistics (Managerial Tool)
- Probability
- High Probability
- Low Probability
- Statistics as a Managerial Tool
- What Statistics Helps Answer
- Key Idea
- Manager Use
- Probability
- High Probability
- Low Probability
- Risk Use
- Single Event Probability
- Complement Rule
- Conditional Probability
- Intersection (AND)
- Union (OR)
- Mutually Exclusive
- Permutations
- Combinations
- Bayes’ Theorem
- Central Tendency
- Mean
- Median
- Mode
- Outlier Effect
- Range
- Variance
- Standard Deviation
- IQR
- Empirical Rule
- Z-Score
- Z-Score Meaning
- Statistics (Managerial Use)
- Statistics as a Managerial Tool
- Statistics Purpose
- Key Questions
- Manager Use
- Data Types
- Descriptive Statistics
- Inferential Statistics
- Predictive Statistics
- Probability
- Risk
- High Probability
- Low Probability
- Expected Value
- Random Variable
- Discrete Variable
- Continuous Variable
- Single Event Probability
- Joint Probability
- Marginal Probability
- Complement Rule
- Conditional Probability
- Independence
- Dependence
- Intersection (AND)
- Union (OR)
- Mutually Exclusive
- Addition Rule
- Multiplication Rule
- Counting Principle
- Permutations
- Combinations
- Factorial (!)
- Bayes’ Theorem
- Posterior Probability
- Prior Probability
- Likelihood
- Normal Distribution
- Mean = Median = Mode
- Standard Normal Distribution
- Z-Score
- Z-Score Formula
- Positive Z
- Negative Z
- Empirical Rule
- Outlier
- Measures of Central Tendency
- Mean
- Median
- Mode
- Measures of Dispersion
- Range
- Variance
- Standard Deviation
- IQR
- Quartiles
- Q1
- Q2
- Q3
- Boxplot
- Skewness
- Right Skew
- Left Skew
- Outliers Impact
- Decision Analysis
- Decision Tree
- Expected Value
- Regression Analysis
- Linear Regression
- Independent Variable
- Dependent Variable
- Time Series Analysis
- Trend
- Seasonality
- Cyclicality
- Irregularity
- Random Variation
- TC SIR Model
- Break-Even Point
- Break-Even Analysis
- Fixed Costs
- Variable Costs
- Contribution Margin
- Profit Region
- Loss Region
- Crossover Analysis
- Crossover Point
- Cost Advantage
- Linear Programming
- Objective Function
- Constraints
- Decision Variables
- Feasible Region
- Optimal Solution
- Slack
- Binding Constraint
- Non-Binding Constraint
- Excel Solver
- Simplex Method
- Cluster Analysis
- Segmentation
- Cluster Purpose
- Cluster Limitation
- Decision-Making Tools
- Monte Carlo Simulation
- Simulation Runs
- Output Distribution
- Expected Outcome
- Risk Analysis
- Monte Carlo Limitation
- Statistics in Business
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