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
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![### Hick's Law and Decision Time Analysis
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 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 \( b \approx 5.830 \).
#### Tasks
a) 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdff7b543-7c53-4567-b2e2-82ba64a4a215%2Fbbedb816-01de-49aa-b1a9-481b436a9cb2%2Fxj05df_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
