1. Data points (x1, y1 ), (x2,y2),.......,(xn,yn) is regressed to y = 1/(ax+b)2. The constants of the model a and b are solved by data linearization. Find the formulas for calculating a and b?
Hint: Take the inverse and square-root of both sides.
2. It is desired to obtain a functional relationship between the mass density Ρ of air and the altitude h above the sea level for the dynamic analysis of bodies moving within earth's atmosphere. Use the approximation Ρ = k1e-k2h to fit the data given below by regression analysis.
Find the constants k1 and k2. You are allowed to linearize the data.
| Altitude (kilometers) |
Mass density (kg/m3) |
| 0.32 |
1.15 |
| 0.64 |
1.1 |
| 1.28 |
1.05 |
| 1.6 |
0.95 |
3. Fit W = at2 + bt + c to the following data to find W(360)
| t |
0
|
2
|
4
|
6
|
18
|
| W |
7.5
|
11.25
|
14.3
|
16
|
26
|
The data given above is actually the weight (lbs) of a baby as a function of the age (months) of the baby. We expect that the weight of the baby to saturate as the baby reaches adulthood. Suggest a different model and estimate W(360).