Question

The following data are a result of an investigation as to the effect of reaction temperature $x$ on percent conversion of a chemical process $y$. (See Myers, Montgomery and Anderson-Cook, 2009.) Fit a simple linear regression, and use a lack-of-fit test to determine if the model is adequate. Discuss. $$ \begin{array}{ccc} & \text { Temperature } & \text { Conversion } \\ \text { Observation } & \left({ }^{\circ} \mathrm{C}\right), x & (\%), y \\ \hline 1 & 200 & 43 \\ 2 & 250 & 78 \\ 3 & 200 & 69 \\ 4 & 250 & 73 \\ 5 & 189.65 & 48 \\ 6 & 260.35 & 78 \\ 7 & 225 & 65 \\ 8 & 225 & 74 \\ 9 & 225 & 76 \\ 10 & 225 & 79 \\ 11 & 225 & 83 \\ 12 & 225 & 81 \end{array} $$

Name: Problem 35, Chapter 11: Probability and Statistics for Engineers and Scientists
Uploaded: 2022-09-27T05:44:30-08:00
Duration: 1 min 24 s
Channel: Khoobchandra Agrawal

   The following data are a result of an investigation as to the effect of reaction temperature $x$ on percent conversion of a chemical process $y$. (See Myers, Montgomery and Anderson-Cook, 2009.) Fit a simple linear regression, and use a lack-of-fit test to determine if the model is adequate. Discuss.
$$
\begin{array}{ccc} 
& \text { Temperature } & \text { Conversion } \\
\text { Observation } & \left({ }^{\circ} \mathrm{C}\right), x & (\%), y \\
\hline 1 & 200 & 43 \\
2 & 250 & 78 \\
3 & 200 & 69 \\
4 & 250 & 73 \\
5 & 189.65 & 48 \\
6 & 260.35 & 78 \\
7 & 225 & 65 \\
8 & 225 & 74 \\
9 & 225 & 76 \\
10 & 225 & 79 \\
11 & 225 & 83 \\
12 & 225 & 81
\end{array}
$$

Probability and Statistics for Engineers and Scientists

Ronald E. Walpole,… 10th Edition

Chapter 11, Problem 35

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Solved by Expert Khoobchandra Agrawal

09/27/2022

Step 1

The general form of a simple linear regression model is $y = \beta_0 + \beta_1x + \epsilon$, where $y$ is the dependent variable (percent conversion), $x$ is the independent variable (temperature), $\beta_0$ and $\beta_1$ are the parameters of the model, and Show more…

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The following data are a result of an investigation as to the effect of reaction temperature $x$ on percent conversion of a chemical process $y$. (See Myers, Montgomery and Anderson-Cook, 2009.) Fit a simple linear regression, and use a lack-of-fit test to determine if the model is adequate. Discuss. $$ \begin{array}{ccc} & \text { Temperature } & \text { Conversion } \\ \text { Observation } & \left({ }^{\circ} \mathrm{C}\right), x & (\%), y \\ \hline 1 & 200 & 43 \\ 2 & 250 & 78 \\ 3 & 200 & 69 \\ 4 & 250 & 73 \\ 5 & 189.65 & 48 \\ 6 & 260.35 & 78 \\ 7 & 225 & 65 \\ 8 & 225 & 74 \\ 9 & 225 & 76 \\ 10 & 225 & 79 \\ 11 & 225 & 83 \\ 12 & 225 & 81 \end{array} $$