Final answer:
To find the equation that best fits a scatterplot, one must input the data into a calculator, calculate the least-squares regression line, draw the line of best fit, and interpret the line's slope, y-intercept, and correlation coefficient to understand the relationship between the variables.
Step-by-step explanation:
To identify the linear equation that best fits the data in a scatterplot, the following steps are typically taken:
- Enter the data into a calculator to make a scatter plot, determining the independent variable (generally the x-value) and the dependent variable (generally the y-value).
- Use the calculator's regression function to calculate the least-squares regression line.
- Draw the line of best fit on the scatter plot to visually assess the fit.
- Calculate the slope (b) of the least-squares line, which represents the rate of change between the variables.
- Identify the y-intercept (a) of the line, which represents the value of the dependent variable when the independent variable is zero.
- Determine the correlation coefficient (r value), with an r value of zero indicating no linear relationship between the variables.
- Discuss the significance of the correlation coefficient to assess if there is a meaningful linear relationship.
If relevant, additional contexts such as the estimated average height for a specific age can be calculated based on the best-fit line's equation.