Shoe-Size Lab

Summary:  It seems obvious that taller adults have bigger feet, but is it true? What “everybody knows” isn’t always true. Statistics uses numerical arguments, not intuition.

Data Collection

Pick 25 adults (18 or older) of the same sex as yourself, and ask them their height in inches (or cm, if you prefer) and their shoe size. You can be one of the 25. Record the answers using separate paper or this form:

Need graph paper? Here’s a sheet you can download and print (127 KB PDF).

Data Analysis

General directions:

Show all your work and answers on separate paper; you must show your work for full credit. Whenever possible, use TI calculator commands instead of formulas. Your “work” includes the commands, not the keystrokes.

Do all the graphs on graph paper or in Excel. (If it’s Excel, write down the formula or analysis tool that you used.)

Also hand in your data, either the table above or the separate sheet where you recorded your data. I cannot accept the lab without your raw data. And check your data entry! It’s pretty bad if your answers don’t match your data.

Staple all pages neatly before you come to class; loose sheets and insecure fasteners cost a 10% penalty.

Question 1 (4 points):  Make a scatter plot of your data. Label axes with titles and show the scales. Plot points as boxes or circles, not small dots. Either way, start the x and y axes at sensible numbers (not 0) and scale the plot to take up most of a sheet. This will show the relationship (if any) better than bunching all the points close together.

Question 2 (3 points):  Compute the correlation coefficient, using Excel or your TI calculator. Write it down with its proper symbol.

Question 3 (3 points): Your sample is not random, but just for this problem let’s assume it is. From your sample, can you infer a linear relation between height and shoe size for all men or all women, and if so, what direction? No hand-waving, please: use the numerical argument that you learned in class.

Question 4 (3 points):  Compute the equation of the line of best fit, and write it down with its proper symbol. Round coefficients to four decimal places.

Question 5 (3 points):  Give the coefficient of determination with its proper symbol, and interpret the number in non-technical English.

Question 6 (3 points):  Plot the line of best fit on your scatter diagram.

Question 7 (3 points):  State the numerical value of the y intercept and interpret it.

Question 8 (3 points):  State the numerical value of the slope and interpret it.

Question 9 (3 points):  Use your regression line to predict the shoe size for a woman of height 65″ or a man of height 70″, and write a short English interpretation.

Question 10 (2 points): Find the residual(s) for x=65 (women) or x=70 (men).