Pregunta
b. Use technology to find the equation of the line of best fit, \( y=m x+b \), and the coefficient of determination and interpret the slope, the vertical intercept, and the coefficient of determination. (Round the answers to 3 decimal places.) i. \( m=\square \) Selecl an answer \( v \) is the Select an answer ii. \( b=\square \) Select an answer \( v \) is the Select an answer 2 of 3 , iii. \( r^{2}=\square \) Nence there is a Select an answer \( v \) linear relation. Next Part
Ask by Boone Hamilton. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
To find the equation of the line of best fit \( y = mx + b \) and the coefficient of determination \( r^2 \), follow these steps:
1. **Collect Data Points**: Gather paired data points \((x_i, y_i)\).
2. **Use Technology**: Utilize software like Excel or Python to perform linear regression.
3. **Interpret Results**:
- **Slope \( m \)**: Shows the change in \( y \) per unit increase in \( x \).
- **Y-Intercept \( b \)**: The value of \( y \) when \( x = 0 \).
- **\( r^2 \)**: Indicates the strength of the linear relationship (close to 1 is strong).
Provide your data points for specific calculations.
Solución
To find the equation of the line of best fit \( y = mx + b \) and the coefficient of determination \( r^2 \), we need a set of data points. Since you haven't provided specific data, I will outline the steps to find these values using technology, and then I can perform calculations if you provide the data.
### Steps to Find the Line of Best Fit and Coefficient of Determination
1. **Collect Data Points**: You need a set of paired data points \((x_i, y_i)\).
2. **Use Technology**: You can use software like Excel, Python, or a graphing calculator to perform a linear regression analysis. This will yield the slope \( m \), the y-intercept \( b \), and the coefficient of determination \( r^2 \).
3. **Interpret the Results**:
- **Slope \( m \)**: This indicates the change in \( y \) for a one-unit increase in \( x \). A positive slope means that as \( x \) increases, \( y \) also increases, while a negative slope indicates the opposite.
- **Y-Intercept \( b \)**: This is the value of \( y \) when \( x = 0 \). It represents the starting point of the line on the y-axis.
- **Coefficient of Determination \( r^2 \)**: This value indicates how well the data fits the linear model. An \( r^2 \) value close to 1 suggests a strong linear relationship, while a value close to 0 suggests a weak relationship.
### Example Calculation
If you provide a set of data points, I can perform the calculations to find \( m \), \( b \), and \( r^2 \). Please provide the data points for further assistance.
Respondido por UpStudy AI y revisado por un tutor profesional
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