ECO221_LECTURE4

Lecture Overview

• Course: ECO 221 Economic Statistics

• Instructor: Professor Jose Xilau

• Lecture: 4

Deadlines & Assignments

• Homework 1: Due today at 11:59 PM on Gradescope

• Homework 2: Due Monday at 11:59 PM on Gradescope

• Reading Assignments:

  • Read TH Chapter 4

  • Complete reading comprehension questions for TH Chapter 4

  • Optional reading of Moore & McCabe 1.2, 2.2

Previous Lecture Recap

• Data Definition:

  • Overview of data and exploratory data analysis.

• Methods of Displaying Data:

  • Line graphs, bar graphs, histograms.

Current Lecture Focus

Relationships Between Two Variables

• Importance of understanding how two variables interact and relate to each other.

• Key methods to display relationships, such as scatterplots and using Stata for graphical representation.

Critical Questions Before Analyzing Data

• Purpose of Data Collection:

  • Why was the data collected?

• Identification of Subject:

  • Who or what do the data describe?

• Definitions and Measurements:

  • What is the definition of variables? What are the units of measurement?

• Data Collector Insights:

  • Who collected the data and what were their motivations?

• Context:

  • In what context was the information provided? Did respondents know they were being studied?

• Subject Knowledge:

  • Consider what you already know about the topic being studied.

Importance of Analyzing Multiple Variables

• Often, the interest lies in the relationships between multiple variables, leading to insightful statistics.

• Measurement should be conducted for both variables using the same observational units.

Examples of Variable Relationships

Case Study: Beer Consumption vs. Blood Alcohol Levels

• Conducted at Ohio State University where student volunteers drank varying amounts of beer.

• Findings: Higher beer consumption correlates with higher blood alcohol content.

Case Study: Dog Breed vs. Lifespan

• Researchers at University of Adelaide studied 164 dog breeds to determine lifespan influences.

• Conclusion: Larger breeds had a higher likelihood of dying from cancer at a younger age, attributed to selective breeding practices.

Understanding Association Between Variables

• Definition of Association:

  • Two variables are associated if knowledge of one provides informative insights about the other.

• Examples of associations:

  • Number of beers affects blood alcohol content; dog breed correlates with lifespan.

Strength and Nature of Associations

• Associations can range from strong to weak, with some showing undeniable trends while others exhibit exceptions.

  • Example: Smokers generally have shorter lifespans, yet some may outlive non-smokers.

Response vs. Explanatory Variables

• Response Variable: Measures the outcome of a study.

• Explanatory Variable: Accounts for changes in the response variable.

• Example:

  • Blood Alcohol Content (Response) and Number of Beers (Explanatory).

Scatterplots

• Definition:

  • Graphical representation to show relationships between two quantitative variables.

• Axes Setup:

  • Y-Axis: typically the response variable.

  • X-Axis: typically the explanatory variable.

• Each observation is represented as a point based on the values of both variables.

Best Practices in Scatterplots

• Causality Note:

  • A scatter plot indicates correlation but does not imply causation; a causal mechanism must be identified to argue for causation.

Analyzed Example: Crime and Ice Cream Sales

• Article link discusses correlation between rising ice cream sales and increasing crime rates.

Key Observations in Scatterplots

1. Patterns/Shapes

2. Strength of Relationship

3. Direction of Relationship: Positive or negative.

4. Outliers: Values significantly differing from the pattern.

Patterns and Strength in Scatterplots

• Linear Relationships:

  • Confirmed when dots follow a straight line (upward or downward sloping).

• Non-Linear Relationships:

  • Observed when data doesn't align with a straight trajectory, showing varied slopes.

• Directionality:

  • Upward slopes indicate positive relationships and downward indicate negative relationships.

Outliers

• Defined as individual values outside the main pattern which may skew interpretations.

Closing Remarks

• Reminder about upcoming assignments and reading tasks to prepare for the next lecture.