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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