Stock Price Trends
Stock price trends estimated using linear regression.
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- Statement of Comprehensive Income
 - Balance Sheet: Liabilities and Stockholders’ Equity
 - Cash Flow Statement
 - Analysis of Reportable Segments
 - Common Stock Valuation Ratios
 - Return on Equity (ROE) since 2005
 - Debt to Equity since 2005
 - Price to Operating Profit (P/OP) since 2005
 - Price to Sales (P/S) since 2005
 - Analysis of Debt
 
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Summary
Key facts
- The primary trend is increasing.
 - The growth rate of the primary trend is 52.15% per annum.
 - CTAS price at the close of January 8, 2025 was $192.28 and was lower than the bottom border of the primary price channel by $17.11 (8.17%). This indicates a possible reversal in the primary trend direction.
 - The secondary trend is decreasing.
 - The decline rate of the secondary trend is 88.06% per annum.
 - CTAS price at the close of January 8, 2025 was higher than the top border of the secondary price channel by $3.85 (2.04%). This indicates a possible reversal in the secondary trend direction.
 - The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
 
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 CTAS 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: 
                End date: 
a =
b =
s =
Annual growth rate:
Exp(365 × b) – 1
                = Exp(365 × ) – 1
                = 
            
Price channel spread:
Exp(4 × s) – 1
                = Exp(4 × ) – 1
                = 
            
February 21, 2023 calculations
Top border of price channel:
Exp(Y)
                = Exp(a + b × X + 2 × s)
                = Exp(a + b ×  + 2 × s)
                = Exp( +  ×  + 2 × )
                = Exp()
                = $
Bottom border of price channel:
Exp(Y)
                = Exp(a + b × X – 2 × s)
                = Exp(a + b ×  – 2 × s)
                = Exp( +  ×  – 2 × )
                = Exp()
                = $
December 17, 2024 calculations
Top border of price channel:
Exp(Y)
                = Exp(a + b × X + 2 × s)
                = Exp(a + b ×  + 2 × s)
                = Exp( +  ×  + 2 × )
                = Exp()
                = $
Bottom border of price channel:
Exp(Y)
                = Exp(a + b × X – 2 × s)
                = Exp(a + b ×  – 2 × s)
                = Exp( +  ×  – 2 × )
                = Exp()
                = $
Description
- The primary trend is increasing.
 - The growth rate of the primary trend is 52.15% per annum.
 - CTAS price at the close of January 8, 2025 was $192.28 and was lower than the bottom border of the primary price channel by $17.11 (8.17%). This indicates a possible reversal in the primary trend direction.
 
Secondary Trend
Start date: 
                End date: 
a =
b =
s =
Annual growth rate:
Exp(365 × b) – 1
                = Exp(365 × ) – 1
                = 
            
Price channel spread:
Exp(4 × s) – 1
                = Exp(4 × ) – 1
                = 
            
November 21, 2024 calculations
Top border of price channel:
Exp(Y)
                = Exp(a + b × X + 2 × s)
                = Exp(a + b ×  + 2 × s)
                = Exp( +  ×  + 2 × )
                = Exp()
                = $
Bottom border of price channel:
Exp(Y)
                = Exp(a + b × X – 2 × s)
                = Exp(a + b ×  – 2 × s)
                = Exp( +  ×  – 2 × )
                = Exp()
                = $
January 6, 2025 calculations
Top border of price channel:
Exp(Y)
                = Exp(a + b × X + 2 × s)
                = Exp(a + b ×  + 2 × s)
                = Exp( +  ×  + 2 × )
                = Exp()
                = $
Bottom border of price channel:
Exp(Y)
                = Exp(a + b × X – 2 × s)
                = Exp(a + b ×  – 2 × s)
                = Exp( +  ×  – 2 × )
                = Exp()
                = $
Description
- The secondary trend is decreasing.
 - The decline rate of the secondary trend is 88.06% per annum.
 - CTAS price at the close of January 8, 2025 was higher than the top border of the secondary price channel by $3.85 (2.04%). This indicates a possible reversal in the secondary trend direction.
 
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