Regression Overview Quiz

Regression Overview

• Regression is a statistical technique used to predict relationships between multiple independent variables and a single dependent variable.
• It's a supervised learning approach, aiming to find the best-fitting curve, which can be linear or non-linear, for a dependent variable within a multi-dimensional space.
• The goodness of fit is measured by the correlation coefficient (r) and R-squared (R²), representing the proportion of variance explained by the model.

Learning Objectives

• Understanding the concept of regression.
• Performing regression analysis in Excel.
• Improving regression model prediction accuracy.
• Understanding logistic regression.
• Recognizing advantages and disadvantages of regression.
• Practicing regression in Excel using hands-on exercises.

What is Regression?

• A well-established statistical method for predicting the relationship between several independent variables and one dependent variable.
• A supervised learning technique to find the best-fitting curve in a multi-dimensional space.
• The chosen curve can be linear (a straight line) or non-linear.
• The quality of the fit is evaluated by the coefficient of correlation (r) and the proportion of variance explained by the curve (R²).

How much to produce? (Example)

• A pizza shop owner and a friend analyze daily dough needs based on weather conditions' effect on sales.
• Weather is a variable affecting the number of sales (e.g., cooler weather correlates with more sales).
• The factors affecting sales extend beyond temperature (e.g., rain, weather variation.)
• Collecting data across the summer season helps analyze variables and predict the quantity of dough needed.

Key Steps for Regression

• Gathering all relevant variables for creating the model.
• Defining a dependent variable (DV).
• Identifying relationships between variables (visually if possible).
• Developing a method to predict the DV using other variables.

Case Study: Data-Driven Prediction (Nate Silver)

• Nate Silver is a data-driven political forecaster, predicting election outcomes using big data analytics.
• He accurately predicted the 2012 presidential election results (Obama's victory) and Senate race results in several states.
• Illustrates the use of data-driven methods in political forecasting.

Correlations and Relationships

• Categorize variables that have relationships or are unrelated.
• Correlation measures the strength of the relationship.
• Correlation values vary from -1 to +1 (+1 representing a perfect positive relationship)
• A correlation of zero indicates no relationship.

Visual Look at Relationships

• Scatter plots visualize relationships between two variables graphically.
• Scatter plots show the arrangement of data points in a 2-dimensional space, providing insights into potential relationships.

Scatter Plots (Types)

• Scatter plots display different types of relationships between variables (linear, curvilinear, no relationship).

Regression Exercise (Linear)

• Regression models can be expressed as linear equations (y = β0 + β1x + ε).
• 'y' is the predicted variable (dependent variable).
• 'x' is the predictor variable (independent variable).
• Multiple predictor variables (x1, x2, ...) are possible, but only one dependent variable (y).
• Example: Predicting house price based on house size.

House Data (Example)

• Example of analyzing house prices based on house size.
• Visualizing using a scatter plot to assess the relationship between house prices and size.
• Observing a positive correlation between house price and size.
• Regression can provide a more refined model to understand this relationship.

Correlation and Regression (House Data)

• High correlation coefficient calculated.
• A high R² value indicating a strong relationship.
• Example equation to predict house value given house size.
• Explaining that 70-80% variance of house price is explained through variable "size".

House Data (Correlation & Regression - Multiple Var)

• Regression analysis using multiple variables (Size and # of Rooms).
• High correlation coefficient and R² value with the addition of more variables indicate a stronger, more reliable model.

Predict the House Price (Example)

• Using regression coefficients to create a predictive equation for future transactions.
• Emphasizing the importance of comparing predicted values with actual values to gauge model accuracy.
• Implying that more data and improvement is possible.

Non-Linear Regression Exercise (Example)

• Analyzing the relationship between temperature and electricity consumption may not be linear.
• Visualizing using a scatter plot showing a non-linear relationship.
• Showing a poor fit for a linear model.
• Illustrating that a non-linear equation (e.g., Temp²,...) might be more suitable for fitting the data better.
• The R² value of model is typically low in non-linear models.

Predict Energy Consumption (Non-linear)

• Creating a non-linear predictive equation for energy consumption based on the temperature.
• Using modified variables in the equation to capture the non-linear relationship (e.g. Temp²).
• Illustrating the improvement in model accuracy with a non-linear model.
• Model accuracy is improved with variable modifications.

Logistic Regression

• Regression models typically deal with continuous numeric data, this model works with binary (yes/no) or categorical data.
• Measures the relationship between a categorical dependent variable and one or more independent variable.
• Example: Predicting if a loan application will be approved.

Logistic Regression (details)

• Logistic regression uses probability scores as the predicted values.
• Uses the natural logarithm of odds (logit) to create a continuous criterion.
• The dependent variable in logistic regression is binomial (having two possible values like 'yes' or 'no')..
• Logistic regression deals with categorical instead of a continuous variable.

Advantages of Regression Models

• Easy to understand based on basic statistical principles and correlation.
• Simple equations for use.
• Predictability parameters provide strong evaluation.
• Can include all variables relevant to the model.
• Relies on statistical packages, data mining tools, and spreadsheet software for usage.

Disadvantages of Regression Models

• Sensitive to data quality issues (missing values, non-normal distribution).
• Collinearity problems arise with strong linear correlations among variables.
• Becomes complex and unreliable with many variables (less predictable).
• May not capture non-linear relationships automatically.
• Requires user judgment (adding terms and adjusting models) for non-linear relationships and categorical variables.

Which Technique to Use?

• Choose Regression if predicting a continuous target variable (e.g., a precise value).
• Choose Classification if predicting a categorical target variable (e.g., "yes" or "no").

In-Class Exercise (Example)

• Creating a regression model to predict Test 2 based on Test 1 scores (example scenario).
• Predict a student's Test 2 score who scored 46 on Test 1.
• Defining the dependent and independent variables in the example scenario (Test 2 score is dependent variable).