Linearized Equation Calculator

For multiple regression enter the rows one after another: x1, x2 for observation 1, then x1, x2 for observation 2, and so on.
For multiple regression, list one value per predictor in "Predictor values to predict at".
Fitted equation
y = 2.197121 e^(0.183258x)
Linear Regression Calculator
Slope (b)
0.183258
Intercept (a)
2.197121
Number of observations
5
Correlation r
0.769035
R squared
0.591415
Adjusted R squared
0.45522
Standard error of the estimate
0.278098
Standard error of the slope
0.087942
Standard error of the intercept
0.291672
t statistic for the slope
2.083844
p value for the slope
0.12853
Lower confidence limit for the slope
-0.096614
Upper confidence limit for the slope
0.46313
F statistic for the model
4.342407
p value for the model
0.12853
Residual degrees of freedom
3
Total sum of squares (SST)
0.567851
Regression sum of squares (SSR)
0.335835
Residual sum of squares (SSE)
0.232016
Sxx
10
Syy
6
Sxy
6
Mean of X
3
Mean of Y
4
Predicted y
6.59754
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.
A linearised fit minimises the squared error on the transformed scale, so it is not identical to a nonlinear least-squares fit of the original curve.
x = 6 lies outside the fitted range [1, 5], so the prediction extrapolates beyond the data.

How this is worked out

7 steps
  1. n = 5 observations.
  2. Taking logs turns y = a e^(bx) into ln y = ln a + b x, a straight line fitted by ordinary least squares.
  3. Fitted parameters: a = 2.19712109, b = 0.18325815.
  4. Fitted model: y = 2.197121 e^(0.183258x)
  5. SST = 0.56785112 splits into SSR = 0.33583548 explained and SSE = 0.23201564 unexplained, so R^2 = 0.59141467.
  6. Standard error of the estimate s = sqrt(SSE / 3) = 0.27809809.
  7. Prediction at 6: 6.59753955.
All coefficientstable
2.197121, 0.183258
Fitted valuestable
2.639016, 3.169786, 3.807308, 4.573051, 5.492803
Residualstable
-0.639016, 0.830214, 1.192692, -0.573051, -0.492803
Scatter points with the fittable
xyfittedresidual
122.639016-0.639016
243.1697860.830214
353.8073081.192692
444.573051-0.573051
555.492803-0.492803

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