Line Regression Equation Calculator

X values (predictor)For multiple regression enter the rows one after another: x1, x2 for observation 1, then x1, x2 for observation 2, and so on.

Y values (response)

Model

Number of predictorsOnly used by multiple regression; the X list is read row by row in this many columns.

WeightsOne weight per observation for weighted least squares. Leave blank for equal weights.

Predict y at x =For multiple regression, list one value per predictor in "Predictor values to predict at".

Predictor values to predict atMultiple regression only: one value per predictor.

Confidence level (%)

Fitted equation

y = 2.2 + 0.6x

Linear Regression Calculator

Slope (b)

0.6

Intercept (a)

2.2

Number of observations

Correlation r

0.774597

R squared

0.6

Adjusted R squared

0.466667

Standard error of the estimate

0.894427

Standard error of the slope

0.282843

Standard error of the intercept

0.938083

t statistic for the slope

2.12132

p value for the slope

0.124027

Lower confidence limit for the slope

-0.300132

Upper confidence limit for the slope

1.500132

F statistic for the model

4.5

p value for the model

0.124027

Residual degrees of freedom

Total sum of squares (SST)

Regression sum of squares (SSR)

3.6

Residual sum of squares (SSE)

2.4

Sxx

Syy

Sxy

Mean of X

Mean of Y

Predicted y

5.8

Minimum mean-square error of the estimator

0.48

Worked out from NIST/SEMATECH e-Handbook of Statistical Methods, 4.1 Introduction to Process Modeling and 1.3.5.11 Linear Regression and 3 other sources.

x = 6 lies outside the fitted range [1, 5], so the prediction extrapolates beyond the data.

How this is worked out

8 steps

n = 5 observations.
Sxx = 10, Sxy = 6, Syy = 6.
Slope b = Sxy / Sxx = 6 / 10 = 0.6
Intercept a = ybar - b xbar = 4 - 0.6 x 3 = 2.2
Fitted model: y = 2.2 + 0.6x
SST = 6 splits into SSR = 3.6 explained and SSE = 2.4 unexplained, so R^2 = 0.6.
Standard error of the estimate s = sqrt(SSE / 3) = 0.89442719.
Prediction at 6: 5.8.

All coefficientstable

2.2, 0.6

Fitted valuestable

2.8, 3.4, 4, 4.6, 5.2

Residualstable

-0.8, 0.6, 1, -0.6, -0.2

Scatter points with the fittable

x	y	fitted	residual
1	2	2.8	-0.8
2	4	3.4	0.6
3	5	4	1
4	4	4.6	-0.6
5	5	5.2	-0.2

Results are general information, not financial, tax, legal, medical or engineering advice.