Final answer:
To find the equation for a linear model from a scatter plot, one uses two points closest to the line to calculate the slope and intercept, or employs a calculator's regression function to determine the least-squares regression line, which is typically the line of best fit for the data.
Step-by-step explanation:
Finding the Equation for a Linear Model from a Scatter Plot
To determine the equation for a linear model based on a scatter plot using two points closest to the line, we consider the options provided:
- y = -1.5x + 6
- y = 1.5x + 6
- y = 1.5x - 12
- y = 2x + 6
When constructing a scatter plot and applying linear regression, we use the regression function of a calculator to find the least-squares regression line. This line minimizes the sum of squared errors (distances between the actual y-values of data points and estimated y-values on the regression line). To find the best fitting equation manually, we can select two convenient points on the graph, calculate the slope (rise over run), and find the y-intercept (where the line crosses the y-axis).
The scatter plot pattern, the correlation coefficient (r² value), and whether the residuals consistently distribute around the regression line can all indicate how well the linear model fits our data. If the r² value is high (closer to 1), it suggests a strong linear relationship between the variables.