Scientists have found a strong correlation between shoe size and reading level of school children. One way to measure reading level is to use a scale from 1.0 to 12.9 (5.7 is the level of reading which one would have in the 5^th grade at the end of the 7^th month). In Table 1 is sample data for 8 people.

Table 1

2.  Enter this data into a Fathom document and reorganize the data to illustrate your answer to the question above.

3.  Describe patterns you observe in the reorganized data.

4.  Graph the data and relate features of the graph to the patterns you described above.

Note: When you move the mouse on the graph window, the coordinates of the tip of the arrow will show up in the status bar at the bottom left of the Fathom window.

5.  What type of function would best fit this data? Manually fit an approximate line (Movable Line) to this data.

6.  Click on graph window to activate it. Choose Graph, then Show Squares. Discuss what the length of each square represents. 

7.  Compare the magnitude of the squares for Scott and Paula. According to your data, whose reading score is closer to that of a typical person who wears a size six shoe? Explain your reasoning.

12. Compare the equations of the Movable Line and the least-squares regression line. Turn off the      Movable Line.

Part 2: Interpreting Outliers. 

1.  Look at the scatterplot and decide which data point least fits the general trend of the data. Make a note of this point. Interpret the meaning of this data point in terms of the variables.

2.  Come up with a statement describing Paula’s coordinates. Write it down. We refer to that point as an outlier. How would you define an outlier? Compare your definition to one in a dictionary. Discuss how the formal definition could be interpreted.

3.  Write down the coordinates of the outlier. Predict the effect on the least-squares regression line when the outlier is moved closer to or farther from the line. Explain your prediction. Drag the point of the outlier to fit the line. See the change of the residual. Discuss the influence of an outlier on a regression line.

4.  Place your outlier back to its original position by typing the initial coordinates in the table (Those were Paula’s shoe size and reading score).

Part 3: Prediction and Causality. 

1.  Explain why this mathematical model makes sense with this population. Is this model applicable to the general population?

2.  Tammy’s shoe size is 5.5. Predict her reading score. How did you arrive at this prediction?  Discuss the appropriateness of this prediction.

3.  Would your prediction change if you know that Tammy is a college student?

4.  Which of the following statements are appropriate according to our model:

·        People with big feet read better than people with small feet;

·        There is a strong correlation between reading level of school children and their shoe size; and 

·        School children with larger shoe size read better than school children with smaller shoe sizes.