Answer all questions with all work **Understanding Hick's Law through Nonlinear Regression**Hick'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 table below shows the 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 \(b \approx 5.830\).**b) Finding the Residuals for Each Point**To evaluate the fit of the nonlinear regression model, we compute the residuals for each data point:| n (choices) | 2 | 4 | 8 | 16 | 32 | 64 ||-------------|------|-----|-----|-----|-----|-----|| T (seconds) | 2.51 | 3.9 | 5.57 | 7.49 | 8.44 | 10.83 || residuals | | | | | | |*(Note: Residuals must be calculated using the formula \( \text{residual} = T_{\text{observed}} - T_{\text{predicted}} \).)***c) Calculating the Sum of Squares of the Residuals (\(SS_{\text{res}}\))**The sum of squares of the residuals measures how well the model fits the data. It is calculated using the residuals obtained from the model predictions.**d) Commenting on Model Fit**The fit of the model can be assessed by examining the magnitude of the residuals and the \(SS_{\text{res}}\). A lower \(SS_{\text{res}}\) implies a better fit, indicating that the model's predictions are closer to the observed values. Further statistical tests or graphical analyses may be necessary for a comprehensive evaluation.

Name: Answer all questions with all work **Understanding Hick's Law through
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Answer all questions with all work **Understanding Hick's Law through Nonlinear Regression**Hick'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 esti