Members of our research team:

Tremayne Mikalauski

Rebekah Skinner

Jared Mackay

Edinson Navarro

Statistical Question to Answer:

Is there a correlation between height and shoe size?

Our Hypothesis:

It may be assumed that the taller a person is means the larger the shoe size they will have. The X data is the height in centimeters and the Y data

is the size of shoe. There is in fact a correlation between the height of a person and their shoe size. The shoe size of the person is dependent on the

persons height.

Data was collected from 40 students to see if their height correlated with their shoe size.

In order to get the most accurate calculation for this study, only people who were over the age of sixteen were used.

The Table to the right displays the data that was collected from each number of students for their height and shoe size.

# of Students Height (cm) Shoe Size (US) # of Students Height (cm) Shoe Size (US)

1 153 5 21 170 8.5

2 154 6 22 171 9

3 154 6 23 173 10

4 155 6 24 174 8

5 158 5 25 174 10

6 159 7 26 174 9

7 160 6 27 175 12

8 161 5 28 175 11

9 163 6 29 176 9

10 164 7 30 177 10

11 165 7 31 178 11

12 165 6 32 178 11

13 165 7 33 178 12

14 166 10 34 179 10.5

15 167 9.5 35 179 11.5

16 167 10 36 179 11

17 168 10 37 180 13

18 168 9 38 180 12

19 170 10.5 39 183 12.5

20 170 9.5 40 185 13

Mean 169.75 9.0375

Standard Deviation 8.6135 2.3949

Height Versus Shoe Size

The scatter plot to the right shows the

data Height (X) and Shoe Size (Y) data

inputted into a simple scatter plot.

With the several tables and charts below

summarized in different ways we will

be able to determine if there is in fact

a correlation between height and shoe

size.

Scatter Plot of Data obtained

Column N Mean Variance Std.

Dev. Std. Err.

Median Range Min Max Q1 Q3

Height 40 169.75 74.192308 8.6135 1.36191 170 32 153 185 164.5 177.5

Shoe Size

40 9.04 5.7357372 2.39494 0.37867 9.5 8 5 13 7 11

Summary Statistics

Data Analysis/Mathematical Process.

First lets look at a scatter plot of the collected data.

The Graph to the right shows the height vs. shoe size; and indicates that there is a strong correlation.

And when comparing the Table II Critical Values for Correlation Coefficient with our calculated r value of 0.8991 it appears that a significant correlation exists in our data set.

y = 0.25x - 33.4 R² = 0.8084

r/Corr = 0.8991

4

5

6

7

8

9

10

11

12

13

14

150 155 160 165 170 175 180 185 190S

ho

e S

ize (

US

)

Height (cm.)

Correlation of Height and Shoe Size

Series1

Linear (Series1)

Next we calculate the predicted y values using our best-fit line equation of (y = 0.25 x – 33.4).

We can then calculate the residuals using the formula (observed y – predicted y).

The Table to the right displays the residual vs. x data.

# of Students X Observed Y Predicted Y Residual # of Students X Observed Y Predicted Y Residual

1 153 5 4.85 0.15 21 170 8.5 9.1 -0.6

2 154 6 5.1 0.9 22 171 9 9.35 -0.35

3 154 6 5.1 0.9 23 173 10 9.85 0.15

4 155 6 5.35 0.65 24 174 8 10.1 -2.1

5 158 5 6.1 -1.1 25 174 10 10.1 -0.1

6 159 7 6.35 0.65 26 174 9 10.1 -1.1

7 160 6 6.6 -0.6 27 175 12 10.35 1.65

8 161 5 6.85 -1.85 28 175 11 10.35 0.65

9 163 6 7.35 -1.35 29 176 9 10.6 -1.6

10 164 7 7.6 -0.6 30 177 10 10.85 -0.85

11 165 7 7.85 -0.85 31 178 11 11.1 -0.1

12 165 6 7.85 -1.85 32 178 11 11.1 -0.1

13 165 7 7.85 -0.85 33 178 12 11.1 0.9

14 166 10 8.1 1.9 34 179 10.5 11.35 -0.85

15 167 9.5 8.35 1.15 35 179 11.5 11.35 0.15

16 167 10 8.35 1.65 36 179 11 11.35 -0.35

17 168 10 8.6 1.4 37 180 13 11.6 1.4

18 168 9 8.6 0.4 38 180 12 11.6 0.4

19 170 10.5 9.1 1.4 39 183 12.5 12.35 0.15

20 170 9.5 9.1 0.4 40 185 13 12.85 0.15

Residual - Predicted y is calculated (y = 0.25x - 33.4)

Next we plot the residual (observed y – predicted y) vs. x.

The Graph to the right shows that there is no discreet pattern in the data, nor does the spread of the residuals increase or decrease, therefore we can conclusively say that the data are linearly correlated.

y = -5E-18x - 6E-16 R² = 2E-33

-4

-3

-2

-1

0

1

2

3

4

150 155 160 165 170 175 180 185 190

Resi

du

al

(Ob

serv

ed

y -

Pre

dic

ted

y)

Height (cm.)

Residuals Versus Height

Series1

Linear (Series1)

Predictions: Now we can predict y by using various x values in our best-fit line equation of :

(y = 0.25 x – 33.4) or

(Shoe Size = 0.25 Height – 33.4) to test.

The Graph to the right illustrates the existing data and the tested values.

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5

6

7

8

9

10

11

12

13

14

150 155 160 165 170 175 180 185 190

Sh

oe S

ize (

US

)

Height (cm.)

Correlation of Height and Shoe Size

Series1

Series2

Linear (Series1)

Afterthought:

The data shows that the two variables, height and shoe size, have a strong correlation .Our r value of .8991 shows a strong linear correlation. Our evidence supports that in regards to most circumstance

the larger your shoe size the taller you are. The data we had collected was from another student working on a similar project. The data consists of height and shoe size from 40 people which include

students and/or teachers over the age of 16.

The data however was not accounting for the world population. A larger range of race and ancestry inheritances could alter some of the data. The limitations our data could possibly face is the fact that

male and female genders continue to grow until a certain age. This may be until early to middle 20’s.

Work Cited/Data Source:

Deloti. Slideshare.net. N.p., n.d. Web. 11 July 2013. <http://www.slideshare.net/deloti/correlation-of-height-and-shoe-size>.

Sullivan III, M. Statistics informed decisions using data. III. Table II. Upper Saddle River, New Jersey: Pearson Education Inc., 2010. Print.