#linear regression

📖 One of the simplest yet most powerful algorithms, Linear Regression forms the foundation of predictive analytics in AI.

1️⃣ The Foundations

Models the relationship between independent variables (inputs) and a dependent variable (output).

Predicts continuous outcomes such as prices, sales, or temperature.

Expressed through the equation Y = a + bX, where a is intercept and b is slope.

2️⃣ Where It’s Used

Finance: Forecasting stock prices and revenue trends.

Marketing: Predicting campaign performance.

Business Analytics: Estimating sales or customer spending.

3️⃣ Strengths vs Limitations

Strengths

Easy to understand and interpret.

Works well for linearly related data.

Fast to train and implement.

Limitations

Performs poorly on non-linear data.

Sensitive to outliers and multicollinearity.

Limited accuracy for complex patterns.

4️⃣ Pro Tips

Always visualize your data to confirm linearity.

Use regularized versions (Ridge, Lasso) to prevent overfitting.

Normalize features for better performance.

💡 Final Note Linear Regression remains a classic model every data professional should master. Its simplicity offers clarity and forms the base for many advanced AI algorithms.

📌 Series Continuation This is Day 2 of the AI Models Explained series 🎉. Next up: Logistic Regression – The Core of Classification.

This image explains the two main types of linear regression: simple linear regression, which uses one independent variable, and multiple linear regression, which uses two or more. Both are used to predict outcomes based on input data. https://iabac.org/blog/linear-regression

This article was written as a practice exercise with reference to the information provided in the COURSERA course, specifically the Mars Crater Study.

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My program,

import pandas as pd

import statsmodels.formula.api as smf

# Set display format

pd.set_option('display.float_format', lambda x: '%.2f' % x)

# Read dataset

data = pd.read_csv('marscrater_pds.csv')

# Convert necessary variables to numeric format

data['DIAM_CIRCLE_IMAGE'] = pd.to_numeric(data['DIAM_CIRCLE_IMAGE'], errors='coerce')

data['DEPTH_RIMFLOOR_TOPOG'] = pd.to_numeric(data['DEPTH_RIMFLOOR_TOPOG'], errors='coerce')

# Perform basic linear regression analysis

print("OLS regression model for the association between crater diameter and depth")

reg1 = smf.ols('DEPTH_RIMFLOOR_TOPOG ~ DIAM_CIRCLE_IMAGE', data=data).fit()

print(reg1.summary())

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Output results,

Dep. Variable:     DEPTH_RIMFLOOR_TOPOG

R-squared:0.344

Model: OLS

Adj. R-squared:0.344

Method:Least Squares  

F-statistic:2.018e+05

Date:Thu, 27 Mar 2025

Prob (F-statistic):0.00

Time:14:58:20

Log-Likelihood:1.1503e+05

No. Observations:384343

AIC:-2.301e+05

Df Residuals:384341

BIC:-2.300e+05

Df Model: 1                                        

Covariance Type:nonrobust                                        

                  coef    std err        t      P>|t|      [0.025      0.975]

Intercept   0.0220   0.000     70.370     0.000     0.021       0.023

DIAM_CIRCLE_IMAGE    

0.0151   3.37e-05   449.169    0.000    0.015    0.015

Omnibus:390327.615

Durbin-Watson:1.276

Prob(Omnibus):0.000  

Jarque-Bera (JB):4086668077.223

Skew: -3.506

Prob(JB):0.00

Kurtosis:508.113

Cond. No.10.1

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Results Summary:

Regression Model Results:

R-squared: 0.344, indicating that the model explains approximately 34.4% of the variability in crater depth.

Regression Coefficient (DIAMCIRCLEIMAGE): 0.0151, meaning that for each unit increase in crater diameter, the depth increases by an average of 0.0151 units.

p-value: 0.000, indicating that the effect of diameter on depth is statistically significant.

Intercept: 0.0220, which is the predicted crater depth when the diameter is zero.

Conclusion:

Enhance your understanding of linear regression and learn about the working, applications, and basic challenges of this machine learning algorithm.

Read more: https://shorturl.at/EW7mj

  Maths and Evolutionary Biology Mathematics is often utilised across many fields – lets look at an example from biology, evolutionary biology and paleontology, in trying to understand the development of homo-sapiens.  We can start with a large data set which gives us the data for mammal body mass and brain size in grams (downloaded from here).  I then tidied up this to remove the rows with NA…

En esta entrada, exploraremos el coeficiente de correlación de Pearson, centrándonos en la relación entre el ingreso total anual y el consumo total anual estimado de alcohol.

Análisis de los Datos

Comenzamos creando una copia de nuestro conjunto de datos y eliminando las filas con entradas NaN, ya que el coeficiente de correlación no puede calcularse con datos faltantes.

Luego, procedimos a realizar un diagrama de dispersión de estas variables.

Observamos que el comportamiento de las variables no es lineal; de hecho, parece más apropiado considerar un ajuste logarítmico para establecer una regresión entre ellas. Este será un tema que exploraremos en futuras entradas del blog.

Resultados del Análisis

Tras la realización del diagrama de dispersión, calculamos el coeficiente de correlación de Pearson.

El resultado obtenido fue un coeficiente de aproximadamente -0.015 (-0.014984230083466107), con un valor p significativo de 0.022912246058339945.

Además, el coeficiente de determinación asociado fue de 0.0002245271511942507, indicando que una fracción extremadamente baja de la variabilidad del consumo total anual de alcohol puede explicarse por el ingreso total anual.

Conclusión