Econometrics Analysis of Sales, Price and Advertising with OLS in Gretl
1.
- a) Econometrics Utility: Econometrics applies statistical and mathematical methods to quantify economic relationships, test theoretical models against real-world data, and forecast future trends.
- b) Data Type and Range: The dataset consists of monthly time series data spanning from January 2015 to April 2024.
- c) Variables: The endogenous (dependent) variable is the sales revenue (Sales). The explanatory (independent) variables are the product price (Price) and annual advertising expenditure (Advertising)
Ultimate AP Statistics Formula and Exam Cheat Sheet
Random:
everyone has an equal chance.
Systematic:
choose every kth person.
Stratified:
divide into groups, randomly sample from each group.
Cluster:
divide into groups, randomly select entire groups.
Convenience:
choose whoever is easiest to reach. Qualitative = Categories = Eye color, Quantitative = Numbers = Height, Discrete = Counted = Number of siblings, Continuous = Measured = Weight. Common bias:
Selection bias:
sample doesn’t represent population.
Voluntary response:
people choose whether
Read MoreStatistical Hypothesis Testing and Interpretation
Statistical Test Selection Matrix
- T-Test (1-Sample Mean): Testing a single group’s average (μ) against a single historical benchmark value.
- 1-Prop Z-Test (1-Sample Proportion): Testing a single group’s percentage or proportion (p) against a benchmark value.
- 2-Prop Z-Test (2 Independent Proportions): Comparing percentages or categorical success rates between two completely separate groups.
- 2-Sample T-Test (2 Independent Means): Comparing the average scores or numerical measurements between two separate
Key Concepts in Number Theory and Statistics
Number Theory and Modular Arithmetic
1. Define GCD (1 Mark)
GCD (Greatest Common Divisor) is the largest positive integer that divides two or more integers exactly.
2. Prime Factorization of 1330 (1 Mark)
1330 = 2 × 5 × 7 × 19
3. Define Residue (1 Mark)
A residue modulo m is any integer equivalent to another integer modulo m.
4. State the Chinese Remainder Theorem (1 Mark)
If the moduli are pairwise coprime, a system of congruences has a unique solution modulo the product of the moduli.
5. Define Fermat
Read MoreStatistical Analysis and APA Reporting Templates
Multiple Linear Regression Analysis
Purpose: Predict a continuous dependent variable using two or more predictors.
Assumptions: Linearity, independence, homoscedasticity, normality of residuals, and no multicollinearity.
How to Read:
- Model Summary: R²
- ANOVA: F and p
- Coefficients: B, β, t, and p
Interpretation Formula: F(df1, df2) = value, p = value, R² = value.
Effect Size: R² = .02 (small), .13 (medium), .26 (large).
APA Template for Reporting Model and Predictors:
ANOVA Table: Regression: F(2, 47) =
Read MoreEssential Probability and Statistics Principles
Counting Principles and Techniques
Fundamental Counting Principle
Fundamental Counting Principle: If a task or process is made up of stages with separate (distinct) choices at each stage, the total number of choices is m × n × p × …, where m is the number of choices at the first stage, n is the number of choices at the second stage, and so forth.
Tree Diagrams vs. Fundamental Counting Principle
Tree Diagrams: A tree diagram is a useful tool for organized counting that shows all possible outcomes
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