Work
through the following problems to check whether you can do everything
that the outcomes at the beginning of this unit state.
To
reinforce your feeling for the value of the regression
coefficient, drag the points in this applet to simulate
the four situations in the previous activity.
Given
the three points (1, 3), (2, 5), (3, 6), what function best
describes the data?
If (6, c) is part of the data, find the best value for c.
Assume
the model is linear. Find the least squares error
regression line (line of best fit) for the three points
algebraically, then use the model to predict the
value of c.
Open
the Three points Excel tool below. Use the Trendline to
find a linear and a quadratic regression
equation and predict c in each case. Which is the most appropriate
model?
Carbon
14 is a radioactive element that is used by scientists
to date archaeological findings because of its long
half-life. The table shows the amounts of Carbon 14
at times recorded every 100 years.
Use
the scatterplot applet below – load the Carbon
data, linearise the data, deduce the equation of the
exponential model, and use the model to calculate
the half-life.
Time
(years)
Amount
(mg)
0
100
100
98,798
200
97,610
300
96,436
400
95,276
500
94,131
600
92,999
Use
this Carbon Excel tool to fit an exponential regression
model and compare your results.
