Ti 83 Exponential Regression is used to compute an equation which best fits the co-relation between sets of indisciriminate variables.
Formula
y=a×bxy=a×bx
Where −
· a,ba,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=en×∑Tilog(Te)−∑(Ti)×∑log(Te)n×∑(Ti)2−×(Ti)×∑(Ti)b=en×∑Tilog(Te)−∑(Ti)×∑log(Te)n×∑(Ti)2−×(Ti)×∑(Ti)
Where −
· nn = total number of items.
∑Tilog(Te)=0×log(140)+5×log(129)+10×log(119)+15×log(112)=62.0466∑log(L2)=log(140)+log(129)+log(119)+log(112)=8.3814∑Ti=(0+5+10+15)=30∑Ti2=(02+52+102+152)=350⟹b=e4×62.0466−30×8.38144×350−30×30=e−0.0065112=0.9935∑Tilog(Te)=0×log(140)+5×log(129)+10×log(119)+15×log(112)=62.0466∑log(L2)=log(140)+log(129)+log(119)+log(112)=8.3814∑Ti=(0+5+10+15)=30∑Ti2=(02+52+102+152)=350⟹b=e4×62.0466−30×8.38144×350−30×30=e−0.0065112=0.9935
Step 2
a=e∑log(Te)−∑(Ti)×log(b)n=e8.3814−30×log(0.9935)4=e2.116590964=8.3028a=e∑log(Te)−∑(Ti)×log(b)n=e8.3814−30×log(0.9935)4=e2.116590964=8.3028
Step 3
Putting the value of a and b in Exponential Regression Equation(y), we get.
y=a×bx=8.3028×0.9935x
