Statistical
Exponential Regression Compound Growth Factor and Base Formula (LOGEST via LN & SLOPE)
Fit exponential curves y = a * b^x using log-transformed linear regression EXP(SLOPE(LN(y), x)) and EXP(INTERCEPT(LN(y), x)) to forecast compounding series.
How LOGEST fits y = a * b^x via natural logarithms
Taking the natural logarithm of both sides of y = a * b^x linearizes the model into ln(y) = ln(a) + x * ln(b). Excel's LOGEST(known_y's, known_x's) simply runs ordinary least squares on (x, ln(y)) and exponentiates the resulting slope and intercept.
Adding an explicit ln(y) column C2:C6 = LN(B2) makes the transformation transparent: EXP(SLOPE(C2:C6, A2:A6)) returns the per-period multiplicative factor b (so b - 1 is the compound growth rate), EXP(INTERCEPT(C2:C6, A2:A6)) returns the x = 0 base value a, and a * POWER(b, x_new) reproduces Excel's GROWTH forecast.
| Period (x) | ARR ($k) (y) | Log-Transformed LN(y) | Fitted Parameter |
|---|---|---|---|
| 0 | 100.00 | 4.6052 | Base a = 100.00 |
| 1 | 120.00 | 4.7875 | Growth factor b = 1.2000 (+20%/period) |
| 2 | 144.00 | 4.9698 | Log-space R^2 = 1.0000 |
| 3 | 172.80 | 5.1521 | Forecast at x = 5 -> 248.83 |
| 4 | 207.36 | 5.3345 | Doubling Series (b = 2) at x = 5 -> 3,200.00 |
Multiplicative Growth Factor b (LOGEST Slope Equivalent)
Exponentiates the OLS slope of LN(y) in C2:C6 against period index x in A2:A6.
=ROUND(EXP(SLOPE(C2:C6, A2:A6)), 4)Exponential Curve Forecast a * b^x (GROWTH Equivalent)
Projects y at target period E2 using fitted base a = EXP(INTERCEPT(C2:C6, A2:A6)) and factor b = EXP(SLOPE(C2:C6, A2:A6)).
=ROUND(EXP(INTERCEPT(C2:C6, A2:A6)) * POWER(EXP(SLOPE(C2:C6, A2:A6)), E2), 2)Try the example
Use the original values or change them to test your understanding.