Some non-linear regressions can also be estimated using a linear regre

vakirnarhh

vakirnarhh

Answered question

2021-11-26

Some non-linear regressions can also be estimated using a linear regression model (using "linearization"). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression im the form y^=cdX to estimate parameters c and d from the data by linearizing the model through lny^=lnc+(lnd)x=b0+b1x.
xyxy163123538725697549732573454892
Using Excel ot other software, the non-linear regression model y^=cdX can be estimated as y^=?(?)X

Answer & Explanation

Warajected53

Warajected53

Beginner2021-11-27Added 12 answers

Step 1
The given data is:
x1y1163122569725734353875497354892
Using ln on this data we get:
x1y11ln(6312)2ln(5697)2ln(5734)3ln(5387)5ln(4973)5ln(4892)
Using a calculator the linear approximation is: y=8.77735+(0.0562864)x
Step 2
Comparing we get:
ln(c)=8.77735
ln(d)=0.0562864
This means c=e8.77735=6485.6674 and d=e0.0562864=0.9453
Answer: 6485.6674(0.9453)x

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