Calcolatore Pendenza Regressione Lineare Avanzato
Calcola la pendenza della retta di regressione lineare con analisi avanzata dei dati.
Pendenza (b1)
0.8333
Slope (b1) vs Number of Data Points (n)
Formula
Linear Regression Slope
The slope of the least-squares regression line measures the average change in y for each one-unit increase in x.
Formula
b1 = (n × Σxy - Σx × Σy) / (n × Σx² - (Σx)²)
This is derived by minimizing the sum of squared residuals. A positive slope indicates a positive relationship; negative slope indicates an inverse relationship.
Esempio Risolto
Given n=10, Σxy=3500, Σx=150, Σy=200, Σx²=2850.
- 01Numerator = 10(3500) - 150(200) = 35000 - 30000 = 5000
- 02Denominator = 10(2850) - 150² = 28500 - 22500 = 6000
- 03b1 = 5000 / 6000 = 0.8333
Domande Frequenti
What does the slope represent?
The slope b1 represents the predicted change in the response variable y for a one-unit increase in the predictor x. It quantifies the strength and direction of the linear relationship.
Can the slope be zero?
Yes. A slope of zero means there is no linear relationship between x and y. This is tested with a t-test where t = b1 / SE(b1). If t is not significant, the slope is not distinguishable from zero.
How does sample size affect the slope estimate?
Larger samples give more precise slope estimates (smaller standard error). The slope itself does not systematically change with sample size, but confidence intervals narrow.
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