Rekenmachine lineaire regressie (best passende lijn)
Deze rekenmachine berekent de kleinste-kwadratenlijn y = mx + b voor gepaarde gegevens. Hij toont de gemiddelden, de gebruikte sommen, de helling en het snijpunt met de y-as, en de correlatiecoëfficiënt r en r², die aangeven hoe goed de lijn past.
Resultaat
Vul waarden in en tik op Berekenen om het resultaat te zien.
Formule
The least-squares slope and intercept. The line always passes through the point of means (x̄, ȳ).
r is between −1 and 1: near ±1 means the points lie close to a line; near 0 means no linear pattern.
Zo gebruik je deze rekenmachine
- Enter the x values and the matching y values in the same order.
- Press Calculate to see the equation of the line, the slope, the intercept, r and r².
Uitgewerkte voorbeelden
x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5
x̄ = 3 and ȳ = 4. Sxx = 10 and Sxy = 6, so m = 6/10 = 0.6.
b = 4 − 0.6 × 3 = 2.2, so the line is y = 0.6x + 2.2.
Syy = 6, so r = 6/√60 ≈ 0.7746 and r² = 0.6.
A perfect line: y = 2x + 1
Every point lies on y = 2x + 1, so r = 1 and r² = 1.
A downward trend
x̄ = 2.5, ȳ = 7, Sxx = 5 and Sxy = −11, so m = −2.2 and b = 7 + 2.2 × 2.5 = 12.5.
Syy = 26, so r = −11/√130 ≈ −0.9648: a strong downward trend.
Veelgemaakte fouten
- Entering x and y values in different orders, which pairs the wrong points.
- Reading r² as the slope: r² is how much of the variation the line explains.
- Using the line far outside the range of the data (extrapolation).
Veelgestelde vragen
How do you calculate the line of best fit?
Find the means of x and y, then m = Sxy/Sxx and b = ȳ − m·x̄. The calculator shows each of these sums.
What does the correlation coefficient r mean?
r measures how close the points are to a straight line: 1 is a perfect upward line, −1 a perfect downward line, 0 no linear relationship.
What is r²?
The share of the variation in y that the line explains. r² = 0.6 means the line explains 60% of it.