# Scatter diagram

I am trying to understand how the regression line "fits" into the scatter plot and how to extract and interpret the data being requested.

Statistical Problem

1.

The following scatterplot shows the miles per gallon for SUVs based on the horsepower of the engines.

a. Draw the least squares regression line (a straight line) on the scatterplot

using the eyeball approach. Use the edge of your calculator to insure

that you have a straight line.

b. In the space to the right of the graph, sketch the plot of the residuals versus HP.

Label the "Residuals" on the y-axis and "HP" on the x-axis. The horizontal line is at

"Residual = 0.0".

Do not plot all the points; just give a rough idea of what the pattern is.

Using your line as the estimate of the means, determine the values of

maximum positive residual and the maximum negative residual and scale

the y-axis accordingly. Your values can be approximate; just get in the ballpark.

c. Based on this plot, what transformation of the Y variable

would you recommend using for the next step of the analysis?

https://brainmass.com/statistics/scatter-plot/interpreting-scatter-plot-data-147422

## SOLUTION This solution is **FREE** courtesy of BrainMass!

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Statistical Problem

1. The following scatter plot shows the miles per gallon for SUVs based on the horsepower of the engines.

a). Draw the least squares regression line (a straight line) on the scatter plot using the eyeball approach. Use the edge of your calculator to insure that you have a straight line.

b. In the space to the right of the graph, sketch the plot of the residuals versus HP.

Label the "Residuals" on the y-axis and "HP" on the x-axis. The horizontal line is at

"Residual = 0.0".

Do not plot all the points; just give a rough idea of what the pattern is.

Using your line as the estimate of the means, determine the values of

maximum positive residual and the maximum negative residual and scale

the y-axis accordingly. Your values can be approximate; just get in the ballpark.

The maximum value of positive residual = 5

The maximum value of negative residual = -5

C). Based on this plot, what transformation of the Y variable would you recommend using for the next step of the analysis?

The shape of the residual plot is U shaped . The plot of residuals against HP suggests that there is a nonlinear relationship between HP and MPG. The logarithmic transformation Log(HP) can be used in regression .

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