Final answer:
The best-fitting line in determining closeness is identified using the least-squares regression method. This statistical process finds the line with the minimal sum of squared differences (SSE) between actual data points and predicted values. The slope of this line is used to interpret the change in the dependent variable for each unit increase in the independent variable.
Step-by-step explanation:
The method that identifies the best-fitting line when determining closeness is called linear regression, specifically the least-squares regression method. This statistical process finds a straight line that minimizes the sum of the squared differences between the actual data points and the predicted values on the line, known as the sum of squared errors (SSE). The least-squares criteria ensure that any other line would have a higher SSE, thus confirming that the chosen line has the best fit for the data provided.
Steps for Drawing the Best-Fit Line
- Plot your data points on a scatter plot.
- Determine if a line would be an appropriate fit by examining the scatter plot and checking for any outliers that might skew the regression line.
- Use statistical software, a spreadsheet, or a calculator to calculate the best-fit line, or draw it by hand using a straight edge to approximate the line that fits the data best.
The slope of the least-squares line, represented by the letter 'm' in the line equation y = mx + b, helps in interpreting the rate of change in the dependent variable for each unit increase in the independent variable. When employing the best-fit line for predictions, it's important to consider whether the line is valid for the entire range of data, such as predicting the cost of a 300 oz. size laundry detergent if such a size hasn't been observed in the data set.
Ultimately, whether using computers or manual calculations like the median-median approach, identifying the least-squares line is crucial for making predictions. This line serves as an estimate for the population's best-fit line, based on sample data. The presence of a strong correlation coefficient further justifies using the regression line for prediction purposes.