Fitting Exponential Models to Data

Regression Analysis

• Modeling technique to find a curve that models data. Includes exponential, logarithmic, and logistic regressions.

Exponential Regression

• Equation: y = a ^x
• Models growth that starts slowly and accelerates, or decay that rapidly slows down.
• Calculator function: EXP reg
• Steps:
  • Enter data into L1 and L2 (x and y values) using the STAT > EDIT menu.
  • Turn on stat plot.
  • Adjust the window to fit the data range.
  • Use STAT > CALC > EXP reg to find the regression equation.

Logarithmic Regression

• Equation: y = a + b \ln x
• Models growth or decay that accelerates rapidly and then slows over time.
• Calculator function: LN reg
• Steps:
  • Enter data into L1 and L2.
  • Turn Stat Plot on.
  • Adjust window.
  • Use STAT > CALC > LN reg to find the regression equation.

Logistic Regression

• Equation: y = c / (1 + a e^{-bx})
• Models growth that accelerates rapidly and then slows to an upper limit.
• Calculator function: Logistic
• Steps:
  • Enter data into L1 and L2.
  • Turn Stat Plot on.
  • Adjust window.
  • Use STAT > CALC > Logistic to find the regression equation.