Shoe-Size Lab

Summary:  It seems intuitively 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 and their shoe size. (You can be one of the 25.) Record the answers using separate paper or this form, and be sure to note whether it’s men or women:

Data Analysis

You’ll see numbered questions and problems below, with point values. Write your answers on separate paper and hand them in. 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.

Staple all pages neatly. Loose sheets and insecure fasteners are not acceptable.

Question 1 (0 points):  What number do you guess the correlation coefficient will be? There’s no right or wrong answer here — just think a little about what you expect. At the end of the analysis you can compare your expectation to what you actually found.

Question 2 (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. Use graph paper, or graph in Excel. If you use graph paper, scale your graph so that it takes up most of the sheet. If you use Excel, use “Print to fit” so that the graph is a whole sheet.

For the remaining problems, use your TI calculator or Excel, whichever you prefer. Show your work or you will not receive full credit. For the calculator, that means showing the commands not the keystrokes. For Excel, it means writing down the Excel formula or the analysis tool that you used.

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

Did the value turn out to be pretty much what you expected, or were you surprised?

Question 4 (3 points): Your sample is not random, but just for this problem let’s assume it is. Is there a linear relation between height and shoe size for all (wo)men, and if so, what direction? No hand-waving, please: use the numerical argument that we learned in class.

Question 5 (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 6 (3 points):  Give the coefficient of determination with its proper symbol, and interpret it in English.

Question 7 (3 points):  Plot the line on your scatter diagram.

Question 8 (2 points):  State the numerical value of the y intercept and interpret it.

Question 9 (4 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. Probably your value isn’t a whole size or half size — explain why this is or isn’t okay. (Hint: when we predict from a regression line, what are we predicting?)