What is the relationship between a regression line and a scatter plot?

The relationship between a regression line and a scatter plot is fundamentally about how the regression line represents the trend in the data. Specifically, a regression line is fitted to the data points in a scatter plot to capture the underlying pattern of the relationship between the variables being analyzed. The key aspect of this relationship is that the regression line minimizes the sum of squared distances between the data points and the line itself.

This method, known as least squares regression, aims to produce a line that best approximates the data by ensuring that the total of the squared vertical distances from each data point to the line is as small as possible. This fitting process ensures that the line is positioned in such a way that it reflects the trend in the data points effectively, thereby making it easier to interpret and predict outcomes based on the variables in question.

In terms of the other options, the first choice does not apply because a regression line does not limit the number of data points; it is constructed using all available points. The third choice about central tendency does not directly relate to the regression line, as it deals more with measures like mean or median rather than trends indicated by regression. Lastly, while the regression line may show patterns related to variance, its primary role is not to show variance directly