Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.

ossidianaZ 2021-09-26 Answered

Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.

\(\begin{array}{|c|c|} \hline x&0&1&2&3&4\\ \hline y&10089&578&968&457&8\\ \hline \end{array}\)

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coffentw
Answered 2021-09-27 Author has 14785 answers

a) Check the 1st differences of the consecutive y-values. Since they are nearly constant, we can use a linear model.
y | 1st differences
\(100 |\)
\(89.5 | 89.5-100=-10.5\)
\(78.9 | 78.9-89.5=-10.6\)
\(68.4 | 68.4-78.9=-10.5\)
\(57.8 | 57.8-68.4=-10.6\)
b)At the WolframAlpha web site you can enter: fit linear \({{0,100},{1,89.5},{2,78.9},{3,68.4},{4,57.8}}\)
Which results i \(y=100.02-10.55x\)

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