Sales prediction
- Input
- X = investimento em publicidade (R$), Y = vendas
- Expected output
- Ŷ = 500 + 3.2 × X
Each additional R$1 in advertising generates R$3.20 in predicted sales.
linear regression for prediction with OLS
Linear Regression for Prediction — OLS
OLS minimizes the sum of squared residuals. The resulting equation Ŷ = β₀ + β₁X lets you predict Y for any X in the sampled domain.
How to interpret OLS coefficients
- β₁ (slope): each additional unit of X increases/decreases Y by β₁ units. β₀ (intercept): expected value of Y when X = 0.
- Standard error measures the typical spread of points around the line. r² measures the portion of Y's variance explained by the model.
Examples
Height vs weight
- Input
- X = altura (cm), Y = peso (kg)
- Expected output
- Ŷ = −105 + 1.0 × X
For 175cm: Ŷ = −105 + 175 = 70kg expected.
Full tool FAQ
Simple linear regression is a statistical model that describes the linear relationship between an independent variable (X) and a dependent variable (Y) as a line: Ŷ = β₀ + β₁X.
Frequently asked questions
Can I predict values far beyond the observed data?
Not recommended. Extrapolation beyond the sampled range assumes the linear relationship continues, which is often invalid. The model is only reliable within the observed domain.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.