Consider the following scatterplot and line of best fit A Us

Consider the following scatterplot and line of best fit:

A. Use the following diagram to explain what is meant by line of best fit.

B.Does the point in the box have a positive or a negative residual? Explain.

C. Is the point in the box an outlier or an influential point? Explain.

Solution

A ) Line of best fit  is a straight line that best represents the data on a scatter plot.  
This line may pass through some of the points, none of the points, or all of the points.

B)The residual of each point is the distance from the point to the line, calculated as follows: Resid = Ypt - Yline. Calculated in this way, points above the line have positive residuals, those below have negative residuals.

As here ypt < yline {y axis point for point and y axis point for line}

Hence it will be negative.

c)An influential point is an outlier that greatly affects the slope of the regression line. One way to test the influence of an outlier is to compute the regression equation with and without the outlier.

This point is too far from other points in above graph. Hence we may say that this is  influential point. This may affect slope of regression line.