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Ti 83 Exponential Regression is used to compute an equation which best fits the co-relation between sets of indisciriminate variables.
Formula
${ y = a times b^x}$
Where −
-
${a, b}$ = coefficients for the exponential.
Example
Problem Statement:
Calculate Exponential Regression Equation(y) for the following data points.
| Time (min), Ti | 0 | 5 | 10 | 15 |
|---|---|---|---|---|
| Temperature (°F), Te | 140 | 129 | 119 | 112 |
Solution:
Let consider a and b as coefficients for the exponential Regression.
Step 1
${ b = e^{ frac{n times sum Ti log(Te) – sum (Ti) times sum log(Te) } {n times sum (Ti)^2 – times (Ti) times sum (Ti) }} } $
Where −
-
${n}$ = total number of items.
${ sum Ti log(Te) = 0 times log(140) + 5 times log(129) + 10 times log(119) + 15 times log(112) = 62.0466 \[7pt]
sum log(L2) = log(140) + log(129) + log(119) + log(112) = 8.3814 \[7pt]
sum Ti = (0 + 5 + 10 + 15) = 30 \[7pt]
sum Ti^2 = (0^2 + 5^2 + 10^2 + 15^2) = 350 \[7pt]
implies b = e^{frac {4 times 62.0466 – 30 times 8.3814} {4 times 350 – 30 times 30}} \[7pt]
= e^{-0.0065112} \[7pt]
= 0.9935
} $
Step 2
${ a = e^{ frac{sum log(Te) – sum (Ti) times log(b)}{n} } \[7pt]
= e^{frac{8.3814 – 30 times log(0.9935)}{4}} \[7pt]
= e^2.116590964 \[7pt]
= 8.3028
} $
Step 3
Putting the value of a and b in Exponential Regression Equation(y), we get.
${ y = a times b^x \[7pt]
= 8.3028 times 0.9935^x
} $
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