Non-Linear Regression

1.  For each set of data use Excel to find the equation and the coefficient of determination for a curve of best fit.

x / y
.8 / 0.6
-3.5 / -5.8
-2 / 3
-1 / 6
0.2 / 4
1 / 1
-1.5 / 5
1.4 / 3.1
0.7 / 3
-0.3 / 6.1
-3.3 / -3.1
-4 / 7
2 / -5.7
x / y
-2.7 / 1.6
-3.5 / 3
-2.2 / 3
-0.5 / 0.5
0 / 1.3
0.6 / 4.7
1.8 / 1.7
-3.8 / 7
-1.3 / 0.6
0.8 / 7
0.5 / 2.7
1 / 1.5
3 / -1.1
x / y
1.1 / 2.5
3.5 / 11
2.8 / 8.6
2.3 / 7
0 / 1
3.8 / 14
1.4 / 4.2
-4 / 0.2
-1.3 / 0.6
3 / 12
4.1 / 17
2.2 / 5
-2.7 / 0.4

a) b) c)

2.  As a sample of radioactive element decays into more stable elements, the amount of radiation it gives off decreases. The level of radiation can be used to estimate how much of the original element remains. The following are measurements for a sample of radium-227.

Time (h) / 0 / 1 / 2 / 3 / 4 / 5 / 6
Radiation Level (%) / 100 / 37 / 14 / 5 / 1.8 / 0.7 / 0.3

a)  Create a scatter plot.

b)  Use an exponential regression to find the equation for the curve of best fit.

c)  Is this equation a good model for the radioactive decay of this element? Explain why or why not.

d)  Use the equation to predict how much radiation there would be after 2.5 hours.

3. An engineer is testing the transmitter of a new radio station. She measures the

radiated power at various distances from the transmitter. The engineer’s readings

are in microwatts per m2.

Distance (km) / 2 / 5 / 8 / 10 / 12 / 15 / 20
Power Level / 510 / 78 / 32 / 19 / 14 / 9 / 5

a) Find an equation for a curve of best fit for these data that has an r2 value of at least 0.98.

b) Use the equation for this curve of best fit to estimate the power level 50 km away.

4. Complete text page 56 #16,18.