Types, Steps & Interpretation Guide

Assumptions Of Regression Analysis

To get accurate and trustworthy results, regression analysis relies on a few key assumptions. These assumptions make sure your results are valid.

Linearity

The relationship between the independent and dependent variable should be a straight line. If the relationship is curved, simple linear regression will not work well.

Independence of Errors

The errors (residuals) should be independent of each other. This means one error should not influence another.

Why it matters: If errors are related, your predictions may be biased (example: time-series data with trends).

Homoscedasticity

This means the spread of residuals should be consistent across all values of the independent variable.

In simple terms:

• The variance of errors should stay the same.
• If errors get bigger at higher values, your model becomes unreliable.

Normality of Residuals

Residuals should follow a normal distribution.
This helps your regression coefficients and p-values remain accurate.

How to check:

• Histogram
• Q-Q plot
• Shapiro-Wilk test

No Multicollinearity

Multicollinearity happens when two predictors are highly correlated with each other.
This makes it hard to know which variable is actually influencing the outcome.

Why it matters:

• It inflates standard errors
• It makes coefficients unstable
• It weakens model reliability

How to detect: VIF (Variance Inflation Factor)

How To Perform Regression Analysis

Running a regression analysis becomes much easier when you break it down into clear steps. 

Step 1: Define Your Research Question

Start by asking what you want to find out. For example:

• Does marketing spend affect sales?
• Do hours of sleep influence productivity?
• Which factors predict patient recovery time?

Step 2: Choose Your Variables

You need two types of variables:

• Dependent Variable (Outcome): The variable you want to predict or explain.
• Independent Variables (Predictors): Factors that influence the dependent variable.

Example: If your question is “Does exercise affect weight loss?”

• Dependent variable: weight loss
• Independent variable: hours of exercise per week

Step 3: Collect and Clean Your Data

Good data leads to good results. Make sure your dataset is:

• Complete (no major missing values)
• Clean (correct formats, no duplicates)
• Accurate (no outliers unless justified)
• Suitable for regression (numeric values for predictors and outcomes)

How to clean your data?

• Removing extreme outliers
• Replacing missing values
• Converting categories into numbers
• Checking consistency in units (e.g., cm vs inches)

Step 4: Check Assumptions

Before running regression, ensure that your data meets key assumptions:

• Linearity
• Independence of errors
• Homoscedasticity
• Normal distribution of residuals
• No multicollinearity

How to check assumptions?

• Scatterplots
• Q–Q plots
• VIF values
• Residual vs fitted plots
• Statistical tests (Shapiro–Wilk, Durbin–Watson, etc.)

Step 5: Run the Regression (SPSS, R, Python, Excel)

You can run regression using many tools:

SPSS	Go to Analyse → Regression → Linear/Logistic
R	Use functions like lm() for linear and glm() for logistic regression.
Python	Use libraries like statsmodels or scikit-learn.
Excel	Use the Data Analysis Toolpak to run simple and multiple regression.

Step 6: Interpret the Results

Interpretation helps you understand what your numbers actually mean. Key elements to interpret:

• Coefficients: Tell you how much the dependent variable changes when the predictor changes.
• P-values: Show whether the relationship is statistically significant.
• R-squared: Explains how much of the outcome is predicted by your model.
• Standard error & confidence intervals: Show how stable and reliable your estimates are.
• F-statistic: Shows whether your overall model is significant.

Step 7: Validate the Model

Model validation checks whether your regression works well on new data.

How to validate:

• Use train–test split
• Check adjusted R-squared
• Examine residual plots
• Remove unnecessary predictors
• Look for overfitting
• Run cross-validation (in R or Python)

How To Interpret Regression Output

Once you run a regression, you will see a table full of numbers with coefficients, p-values, R², and more. Below is a breakdown of each key output.

Coefficients (β values)

Coefficients show how much the dependent variable changes when one independent variable increases by one unit, while keeping all other variables constant.

How to interpret a coefficient

• Positive coefficient: the dependent variable increases
• Negative coefficient: the dependent variable decreases
• Zero or very small coefficient: little or no relationship
  

Example: If β = 2.5 for hours studied, it means: 

For every additional hour studied, the exam score increases by 2.5 points (on average).

P-values

P-values show whether a predictor has a statistically significant effect on the outcome.

How to interpret p-values

• p < 0.05 → statistically significant
• p ≥ 0.05 → not statistically significant
  

This means:

• If p < 0.05, the predictor meaningfully contributes to the model.
• If p ≥ 0.05, the predictor likely has little or no effect.
  

Example: If “sleep hours” has p = 0.002, it significantly affects the outcome. If “coffee intake” has p = 0.45, it does not significantly affect the outcome.

R-squared & Adjusted R-squared

These values tell you how well your model explains the variation in your dependent variable.

R-squared (R²)

Shows the percentage of variance explained by your predictors.

Example: R² = 0.70 → your model explains 70% of the variation.

Adjusted R-squared

More reliable for multiple regression. It adjusts for the number of variables and penalises unnecessary predictors. Use it when:

• You have more than one independent variable
• You want a realistic measure of model performance

Standard Error

Standard error shows how accurately the coefficient is estimated.

Lower standard error → more reliable coefficient

Higher standard error → coefficient may be unstable or noisy

If the standard error is large compared to the coefficient, you may need:

• More data
• Fewer predictors
• Better model specification

Confidence Intervals

Confidence intervals (often 95%) show the range where the true coefficient value is likely to fall.

How to interpret

If the CI does not include zero, the variable is usually significant. If the CI includes zero, the effect may be weak or questionable.

Example: Coefficient for exercise = 1.2

CI = [0.5, 1.8] → does not include zero → significant effect.

F-statistic

The F-statistic tells you whether your entire model is statistically significant.

High F-statistic + p < 0.05 → your overall model works

Low F-statistic + p ≥ 0.05 → your model does not explain the outcome well

Frequently Asked Questions