Module 4: Correlation/Regression Analysis

What does correlation analysis measure?

The strength and direction of the relationship between two variables.

What is the range of the correlation coefficient (r)?

From -1 to +1.
+1 = perfect positive, -1 = perfect negative, 0 = no linear relationship.

Does correlation imply causation?

No, correlation shows association, not cause-and-effect.

Example of misleading correlation?

Ice cream sales and drowning incidents increase in summer — related to temperature, not each other.

What is regression analysis used for?

To predict the value of one variable (DV) based on another (IV).

Regression model example?

Predicting sunscreen sales (DV) based on temperature (IV).

Difference between correlation and regression?

• Correlation → checks if two things go together, how strong & direction.

• Regression → predicts how one variable changes with another.

Can regression prove causation?

No, it shows prediction or association, not definite causation.

Which study type is correlation and which is regression?

• Study A (grades drop 20% per hour of TV) → Regression

• Study B (grades tend to drop with more TV) → Correlation

What is simple linear regression?

One DV and one IV.
Example: Exam score (Y) predicted by study hours (X).

Write the simple linear regression model equation.

Yi = β₀ + β₁Xi + εi

What does β₁ represent?

The slope — how much DV changes for a one-unit change in IV.

What is εi in regression?

Error term — captures unmeasured influences on DV.

What is multiple regression analysis?

One DV and multiple IVs.
Example: Exam scores predicted by study time, health, and IQ.

What is logistic regression used for?

Binary outcomes (Yes/No, 0/1).
Example: Predict pass/fail based on hours studied.

What determines the type of regression model used?

The data type of the dependent variable (DV).

Which regression for continuous DV?

Linear regression.

Which regression for binary DV (Yes/No)?

Logistic regression.

Which regression for ordinal DV (ranked categories)?

Option 1: Linear regression (simple).
Option 2: Recode ordinal → binary, then logistic regression.

What is the typical significance level (α)?

0.05 — if p-value ≤ 0.05, reject the null hypothesis.

Example of regression hypothesis testing?

Income = b₀ + b₁East + b₂South + b₃North + ε
Reject null for regions where p ≤ 0.05.

Two ways to access Tableau Public?

• Web Authoring (online)

• Desktop Edition (downloaded)

How to import Excel data into Tableau Public (Web)?

Go to CREATE → Web Authoring → Connect Excel Data.

What are Measures in Tableau?

Quantitative fields used for aggregation (e.g., sum of income).

What are Dimensions in Tableau?

Qualitative or individual-level data (e.g., gender, city).

When to use “Dimension” instead of “Measure”?

When adding up values doesn’t make sense (e.g., age, weight).

Difference between continuous and discrete data in Tableau?

• Continuous → numeric range with continuous axes.

• Discrete → categorical, plotted as separate categories.

How to make a histogram in Tableau?

• Right-click variable → Create → Bins

• Set bin size = 1

• Place Bin variable on Columns and variable on Rows → Measure > Count

How to save a plot from Tableau Public Web?

Click the download image button or take a screenshot.

Why is saving from Tableau Desktop more complex?

You must publish the workbook first before downloading.