Y Hat Dance

Metacarpal Bones
An archaeologist finds a third metacarpal bone (the middle green bone in the figure) at a burial site and wants to predict how tall the person was. She has a sample of ten skeletons for which metacarpal size (in cm) and height (cm) are recorded and makes a scatterplot of the data. She then uses the regression method is to produce estimates for the height of a skeleton for a given metacarpal bone size.

  1. In this situation the size of the metacarpal bone would be the variable and the skeleton's height would be the  variable.

  2.  Please answer question 1 to reveal this question.

    The ten individual skeleton heights in the data set are  values.

  3.  Please answer question 1 to reveal this question.

    The y-coordinates on the regression line corresponding to the ten metacarpal sizes in the data set are called the values.

    For example if the metacarpal is 4.3 cm long then the y-coordinate for that x on the regression line is 167.2 cm.
     Height vs Metalcarpal Size

  4.  Please answer question 1 to reveal this question.

    By errors (or residuals), we mean the distance from an observed point to the fitted lined on the scatterplot.

  5. The least squares regression line minimizes the of the errors.

  6. The assumptions of a linear regression are supported when a plot of the residuals versus the fits (or versus the x-values) looks .