### Hick's Law and Decision Time AnalysisHick's law states that the time $ T $ for a person to choose between $ n $ choices is given by the equation:\[ T = b \log(n+1) \]where $ b $ is a constant estimated from data. The following table shows data for a particular person:| $ n $ (choices) | 2 | 4 | 8 | 16 | 32 | 64 ||-------------------|------|------|------|------|------|------|| $ T $ (seconds) | 2.51 | 3.9 | 5.57 | 7.49 | 8.44 | 10.83 |Using nonlinear regression, it was found that $ b \approx 5.830 $.#### Tasksa) Upload a picture of the scatterplot of $ T $ against $ n $. This scatterplot should also include the fitted model on the same axes.b) Find the residuals for each point.| $ n $ (choices) | 2 | 4 | 8 | 16 | 32 | 64 ||-------------------|------|------|------|------|------|------|| $ T $ (seconds) | 2.51 | 3.9 | 5.57 | 7.49 | 8.44 | 10.83 || Residuals | | | | | | |c) Calculate the $ SS_{res} $ for the model.### Explanation- **Scatterplot:** You are required to create a scatterplot of the data points comparing the number of choices $ n $ with the time $ T $ in seconds. Alongside, plot the fitted model curve using $ b \approx 5.830 $.- **Residuals:** Calculate the difference (residuals) between the observed $ T $ values and the predicted $ T $ values from the model for each value of $ n $.- **Sum of Squared Residuals ($ SS_{res} $):** Compute the sum of the squares of the residuals to assess the goodness of fit for the model.

a) From the given information, n T 5.83*log(n+1) 2 2.51 2.781616915 4 3.9 4.074995125 8…

Hick's law states that the time T for a person to choose between n choices is given by the equation: data for a particular person: T = blog(n+1) where b is a constant estimated from data. The table shows n (choices) T (seconds) 2 4 8 16 32 64 2.51 3.9 5.57 7.49 8.44 10.83 Using nonlinear regression, it was found that bz 5.830 a) Upload a picture of the scatterplot of T against n. This scatterplot should also include

Hick's law states that the time T for a person to choose between n choices is given by the equation: data for a particular person: T = blog(n+1) where b is a constant estimated from data. The table shows n (choices) T (seconds) 2 4 8 16 32 64 2.51 3.9 5.57 7.49 8.44 10.83 Using nonlinear regression, it was found that bz 5.830 a) Upload a picture of the scatterplot of T against n. This scatterplot should also include

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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