Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 57.87% per annum.
- LIN price at the close of December 8, 2025 was $389.38 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.18% per annum.
- LIN price at the close of December 8, 2025 was lower than the bottom border of the secondary price channel by $0.24 (0.06%).
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of LIN price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: September 11, 2025
End date: December 8, 2025
a = 10.3021
b = -0.0024
s = 0.0151
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0024) – 1
= -57.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0151) – 1
= 6.23%
September 11, 2025 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,737 + 2 × s)
= Exp(10.3021 + -0.0024 × 1,737 + 2 × 0.0151)
= Exp(6.2189)
= $502.14
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,737 – 2 × s)
= Exp(10.3021 + -0.0024 × 1,737 – 2 × 0.0151)
= Exp(6.1584)
= $472.68
December 8, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(10.3021 + -0.0024 × 1,825 + 2 × 0.0151)
= Exp(6.0105)
= $407.68
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(10.3021 + -0.0024 × 1,825 – 2 × 0.0151)
= Exp(5.9500)
= $383.76
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 57.87% per annum.
- LIN price at the close of December 8, 2025 was $389.38 and was inside the primary price channel.
Secondary Trend
Start date: October 30, 2025
End date: December 8, 2025
a = 8.6468
b = -0.0015
s = 0.0141
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0015) – 1
= -41.18%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0141) – 1
= 5.82%
October 30, 2025 calculations
Top border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 + 2 × s)
= Exp(a + b × 1,786 + 2 × s)
= Exp(8.6468 + -0.0015 × 1,786 + 2 × 0.0141)
= Exp(6.0785)
= $436.36
Bottom border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 – 2 × s)
= Exp(a + b × 1,786 – 2 × s)
= Exp(8.6468 + -0.0015 × 1,786 – 2 × 0.0141)
= Exp(6.0219)
= $412.35
December 8, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(8.6468 + -0.0015 × 1,825 + 2 × 0.0141)
= Exp(6.0218)
= $412.31
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(8.6468 + -0.0015 × 1,825 – 2 × 0.0141)
= Exp(5.9652)
= $389.62
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.18% per annum.
- LIN price at the close of December 8, 2025 was lower than the bottom border of the secondary price channel by $0.24 (0.06%).
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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