Chapter 11 The RMS for Regression Error

RMS for Regression Error says how far typical points are above or below the regression line.

It works like the SD line to the average.

For example about 68% will be within one RMS error of the regression line. 

95% will be within two RMS error of the regression line

the Baseline method ingores the x-values and uses the average value of y to predict y.

It fall along a horizontal line for y- values (pg 183)

The RMS error for baseline method is just the SD of Y.

It says how far typical points are above or below a horizontal line through the average of Y

Error = actual-predicted(ave)

The  rms error for the regression line of y on x 

 

• Note:
• If you are predicting the (weight-y) from the the (height-x), use the SD of (weight-y)

The correlation coefficient (r) measures the spread relative to the SD.

The r.m.s error measures spread around the regression line.

1. r discribes the cluster of the points around a line, relative to the SD, (chapter 8)

2. r says how the average of value y depends on x-associated with each one- SD increase in x there is an increase of only r sd in y, on the average. (Chapter 10)

3. r determines the accuracy of the regression predictions, through the formula for rms error. (Chapter 11)

Prediction error are often called residuals. 

Residuals plots are useful diagnostics in multiple regression.

Residuals are graphed on a separate diagram. Each point of the scatter diagram is transferred to a second diagram called the residual plot. 

The x coordinate is left alone but the Y -coordinate is replaced by the residual at the point-the distant below (+) or below (-) the regression line.

The residual average out to 0; and the regression line for the residual plot is horizontal (There is no trend or pattern in the residuals)

When a vertical strip in a scatter diagram show similar amounts of spread, the diagram is to be Homoscedastic (football shaped)

When graphs are football shaped the prediction errors are similar along the regression line.

Heteroscedastic Diagram

When a scatter diagram is heteroscedastic the the regression method is off by different amounts in different parts of the scatter diagrams.

This method only works on football shaped diagrams

example: 1 a law school finds the following relations between lsat scores and first year scores.

• ave LSAT scores = 162, SD = 6
• ave 1st year scores = 68, sd =10