Suggested Questions for Classroom Activities

Activity Hand_Size: Is Hand Size A Good Predictor Of Height?

(1)  Describe the distribution of palm size and height. Are they approximately mound-shaped?

(2)  Is there any unusual data that needs to be discussed and/or discarded?  For example, 
      a height of 8 feet.

(3)  Describe palm length and height by numerical measures: mean, median, standard
      deviation, and range.  Is the difference between mean and median large enough to 
      notice a skewness in the distribution of palm length and height respectively?

(4)  Is there a noticeable difference in the distributions of  palm length and height between
      male and females?

(5)  Construct a scatter plot between height (Y) and palm length. Is there a clear pattern of
      the relationship?  Describe your observations.

(6)  Construct a scatter plot between height (Y) and palm length for males and females
      separately.  Is there a clear difference in the pattern of the relationship between males
      and females?

(7)  Compute the correlation coefficient between palm length and height.  Use this coefficient
      to justify your observations of the patterns in the scatter plot.

(8)  Compute the correlation coefficient between palm length and height for males and
      females separately. Use these correlation coefficients to justify your observations of the
      different patterns in the scatter plots between males and females.

(9)  Similarly to questions 1-8, questions can be asked to investigate the palm width and
      height or palm width and palm length.

(10) Discuss the least squares method using the palm length to predict height.  If you have
       Fathom, there is an interactive tool to demonstrate how the least square method works.

(11) Demonstrate how changing a case can influence the model fitting, and stress the
      importance of data integrity.  (Fathom can be used for this purpose.)

(12) Build the model and discuss the meaning of intercept and slope when using palm length
      to predict height.

(13) Give examples to illustrate the validity of the model when using a model to make a
      prediction. It is important to keep in mind one should not use the model to predict height
      for palm length being much smaller or much larger than the sample data.  For example:
      Suppose the model is height = 40 + 4(palm length)   (units in inches) and the data used
      for building the model ranges from 7" to 12".  Ask students to predict height for palm
      length equal to 3" or 15".  Then discuss the possible problem of using this model to
      predict height for a 3" palm length.  (The collected data is for the adult population.  
      A 3" palm length is for a little child which is from a different population.)

(14) Discuss residuals and stress the importance that a plot of the residuals vs. case id 
      should show a random pattern.

(15) An advanced model may be introduced by adding gender into the model. 
      height = b0 + b1(palm length) + b2(gender) where gender equals 0 for females and 
      1 for males. Discuss the measuring of b1 and b2.

(16) A model may be introduced by using both palm length and palm width as predictors for
      discussion of redundancy of highly correlated predictors and the issue of multicollinearity.