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