Question

Visually compare the scatter plots shown below. If a least squares line were determined for each data set, which do you think would have the smallest variance ${\mathit{s}}^{\mathbf{2}}$? Explain.

Short answer

Graph (c)

Step-by-step solution

Introduction

The Least Squares Regression Line is a line that tries to minimize the vertical distance between the data points and the regression line. The best line of fit minimizes variance, which is why it's called "least squares."

Scatterplot

Scatter plots demonstrate how much one factor influences the other by plotting pieces of data on a horizontal anda vertical axis. A scatter plot is a collection of dots drawn on horizontal and vertical axes. Scatter plots are useful in statistics since they illustrate the amount, if any, of correlation between the numbers of observable quantities as well as events (called variables). The points on a Scatter (XY) Plot represent the connection among data sets.

Smallest variance

If a minor square line fits the provided scatter graph, the points must lie on the straight line for the perfect match. The points in the figure in the plot (a) form a straight line. The points in figure (b) exhibit a declining tendency, although they do not form a straight-line pattern. The points in figure (c) depart from the straight-line shape as well as form a curvilinear design. As a result, the chart in figure (a) has the most negligible variation since the points are near minor square lines. Because the points are close to the shortest squares line, the chart in figure (c) has the lowest variation.