Exponential regression using Ti 83 is used to calculate an equation which best fits the connection between the collections of indiscriminate variables.
The variables a and b denotes the coefficients for the exponential.
Calculate Exponential Regression Equation(y) for the given data points in L1 and L2. The numbers under the L1 heading are times in minutes. The numbers under the L2 heading are temperatures in degrees Fahrenheit.
| L1 | L2 |
|---|---|
| 0 | 140 |
| 5 | 129 |
| 10 | 119 |
| 15 | 112 |
Calculate a,b coefficients for the exponential Regression.
First, let us calculate the value of a, b.
b = e (n x Σ L1log(L2) - Σ (L1) x Σ log(L2) ) / (n x Σ (L1)2 - Σ (L1) x Σ (L1) ) n-Total no of samples. ΣL1 log(L2) = 0 x log(140) + 5 x log(129) + 10 x log(119) + 15 x log(112) = 62.0466 Σ log(L2) = log(140) + log(129) + log(119) + log(112) = 8.3814 Σ L1 = (0 + 5 + 10 + 15) = 30 Σ L12 = (0 2 + 5 2 + 10 2 + 15 2) = 350 b= e(4 x 62.0466 - 30 x 8.3814) / (4 x 350 - 30 x 30) b= e-0.0065112 b= 0.9935
a = eΣ log(L2) - Σ (L1) x log(b) / n a = e(8.3814 - 30 x log(0.9935) ) / 4 a = e2.116590964 a = 8.3028
Now, substitute the values of a, b in the formula, Exponential Regression Equation(y) = a x b x = 8.3028 x 0.9935x
