In this lesson, a scatterplot and quadratic regression will be used to solve the following problem.
The Problem |
In
one study the efficiency of photosynthesis in an Antarctic species
of grass was investigated. Table 1 below lists results for various
temperatures. The temperature x is in degrees Celcius
and the efficiency y is given as a percent. The purpose
of the research was to determine the temperature at which photosynthesis
is most efficient. (Source: D. Brown and P. Rothery, Models in Biology:
Mathematics, Statistics and Computing.) |
x |
-1.5 |
0 |
2.5 |
5 |
7 |
10 |
12 |
15 |
17 |
20 |
22 |
25 |
27 |
30 |
y(%) |
33 |
46 |
55 |
80 |
87 |
93 |
95 |
91 |
89 |
77 |
72 |
54 |
46 |
34 |
The following steps are needed to solve this problem:
a). Make a scatterplot of the data.
b). Find the least-squares function f of the form
c). Graph f and the data in [-5, 35, 5] by [20, 110, 10].
d). Determine the temperature at which f predicts that photosynthesis is most efficient.
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