Pregunta
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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

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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.

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