# Shoe-Size Lab (Due on 6 Oct)

Copyright © 2007–2015 by Stan Brown

Copyright © 2007–2015 by Stan Brown

**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.

Pick 24 adults (18 or older)
**of the same sex as yourself**.
Ask them their height
(to the nearest half inch)
and their shoe size.
(Show heights in the original feet and inches, then in inches.)

In the interests of time,
**you can take a convenience sample**, and add yourself as the 25th data
point.
Record the data on the form at the end of this lab, or use
separate paper laid out the same way.

- On separate paper, show your work and then your answer for the
first question, your work and then your answer for the second
question, and so on.
**You must show your work for full credit.**I recommend you use your calculator for calculations, but you may use Excel instead if you wish. **Check the numbers you enter in your calculator!**It’s pretty bad if your answers don’t match your data. When you can, use TI calculator commands instead of formulas.**Show calculator commands**, not keystrokes.- Do all the graphs on
**graph paper**or in Excel. Need graph paper? Here’s a sheet you can download and print (9 KB PDF), adapted from Kevin MacLeod’s Plain Graph Paper PDF Generator. - Use all or most of the page for the graph. Know when an axis must start at zero and when it should not.
- Do a professional job:
**Write neatly and legibly**, remove any “decorative fringe” from the paper, and so forth. I recommend pencil and eraser because correcting mistakes in ink is a bear. Word processing is also acceptable. **Hand in your data sheet**. I can’t accept the lab without the full set of raw data.- Don’t hand in the questions.
**Staple all pages**neatly before you come to class, because loose sheets and insecure fasteners cost a 10% penalty. You don’t need a report cover.

**Question 1** (4 points): Make a *scatterplot* of your data with x=height,
y=shoe size.
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): Compute the equation of the line of best fit, and write it
down with its proper symbol. Round coefficients to four decimal
places.

**Question 4** (3 points): Give the coefficient of determination with its proper symbol,
and interpret the number in terms of heights and
shoe sizes.

**Question 5** (3 points): Plot the line of best fit on your scatter diagram.
If you’re plotting by hand (not using
Excel or a similar computer program), show the
three x,ŷ pairs that you used to plot the line.

**Question 6** (3 points): State the numerical value of the y intercept and interpret
the number in terms of heights and shoe sizes.

**Question 7** (3 points): State the numerical value of the slope and interpret the
number in terms of heights and shoe sizes.

**Question 8** (3 points): Your sample is not random, but just for this problem
let’s assume it is. From your sample, what can you say about a
relation between height and shoe size for *all men* or *all
women*?
**No hand-waving**, please: use the numerical argument that you
learned in class.
Use plain English — no city-slicker words like
“correlated” or “associated”. Just talk about
heights and shoe sizes for *all* men or women.

**Question 9** (3 points): Use your regression line to predict the average shoe size for
women of height 65″ or men 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). If you don’t
have data with that x, pick the nearest x you do have.

Data Collected from 25 Men Women (circle one) | ||||
---|---|---|---|---|

Height (x) in the form 5′6½″ = 66.5″ | Shoe size (y) (include half sizes) |
Height (x) in the form 5′6½″ = 66.5″ | Shoe size (y) (include half sizes) | |

YOU ⇒ |

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