Exercise 1.2.27 (27-28)

Question

For each scatter plot, decide what type of function you might choose as a model for the data. Explain your choices.

Khagan Gulusoy · Accepted Answer

\begin{enumerate}
    \item [27.] \begin{enumerate}
        \item Since the data looks periodic, a good choice for a model would be a cosine function of the type
        $$f:X	o\mathbb{R}, \quad f(x)=a\cos(rx)+c$$
        for some constants $b, \ a, \ r\in \mathbb{R},$ where $X$ is an interval in $\mathbb{R}.$
        \item Since the data looks linear, a good choice for a model would be a linear function of the type
        $$f:X	o\mathbb{R}, \quad f(x)=kx+b$$
        for some constants $k\in \mathbb{R}_-, \ b\in \mathbb{R}_+,$ where $X$ is an interval in $\mathbb{R}.$%\forall x\in X:\quad f(x)=kx+b$ for some $k,b\in \mathbb{R},$ where $X$ is the domain of $f.$
    \end{enumerate}
    \item [28.] \begin{enumerate}
        \item Since the data is a parabola, a good choice for a model would be an even power function of the type
        $$f:X	o\mathbb{R}, \quad f(x)=ax^{2n}+c$$
        for some constants $n\in \mathbb{N}, \ a, \ c\in \mathbb{R},$ where $X$ is an interval in $\mathbb{R}.$
        \item Since the data is a hyperbola, a good choice for a model would be an even power function of the type
        $$f:X	o\mathbb{R}, \quad f(x)=ax^{-1}+c$$
        for some constants $r, \ a, \ c\in \mathbb{R},$ where $X$ is an interval in $\mathbb{R}.$
    \end{enumerate}
\end{enumerate}

Exercise 1.2.27 (27-28)

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Exercise 1.2.27 (27-28)

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