Report Properties
Thumbnail:
Owner: amollo26
Created: Oct 7, 2013
Share: yes
Views: 134951
Tags:

Results in this report

Data sets in this report
None

Need help?
To copy selected text, right click to Copy or choose the Copy option under your browser's Edit menu. Text copied in this manner can be pasted directly into most documents with formatting maintained.
To copy selected graphs, right click on the graph to Copy. When pasting into a document, make sure to paste the graph content rather than a link to the graph. For example, to paste in MS Word choose Edit > Paste Special, and select the Device Independent Bitmap option.
You can now also Mail results and reports. The email may contain a simple link to the StatCrunch site or the complete output with data and graphics attached. In addition to being a great way to deliver output to someone else, this is also a great way to save your own hard copy. To try it out, simply click on the Mail link.
Correlation of Shoe Size and Height (Andy Mollo's StatCrunch Report #2)

Are people with big feet taller than people with small feet? My StatCrunch report attempts to see if there is a correlation between shoe size and height. The data I used came from the Sullivan Statistics Survey.

Scatterplot 1 shows a scatter diagram with shoe size as the explanatory variable and height (in inches) as the response variable. The shape of the scatterplot indicates that there is a positive linear correlation between the two variables. In general, as shoe size increases, height increases.

Result 1: Scatterplot 1: Correlation of Shoe Size and Height   [Info]

The Dataset confirms this linear correlation. The correlation coefficient (R) for these variables is 0.6222. While Table II from the Sullivan text doesn't give a critical correlation coefficient value for a scenario like this where n = 199, the critical correlation coefficient value for n = 30 is 0.361. Since 0.6222 is greater than 0.361 and since the critical correlation coefficient value decreases as n increases, we can assume that 0.6222 shows that there is indeed a linear correlation between shoe size and height.

The Dataset also shows that the R squared value is 0.3871. This means that 38.71% of the variability in height is explained by shoe size. The Dataset also shows the slope of the best fit line: y-hat = 50.874798 + 1.6565183x. So, for example, if someone's shoe size is 10, we would expect them to 67.44 inches tall.

Result 2: Dataset: Correlation of Shoe Size and Height   [Info]
Simple linear regression results:
Dependent Variable: Height
Independent Variable: Foot
Height = 50.874798 + 1.6565183 Foot
Sample size: 199
R (correlation coefficient) = 0.6222
R-sq = 0.38713068
Estimate of error standard deviation: 3.7840705

Parameter estimates:
 Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept 50.874798 1.5311509 ≠ 0 197 33.22651 <0.0001 Slope 1.6565183 0.14849721 ≠ 0 197 11.155215 <0.0001

Analysis of variance table for regression model:
 Source DF SS MS F-stat P-value Model 1 1781.8633 1781.8633 124.438835 <0.0001 Error 197 2820.8804 14.31919 Total 198 4602.7437

Predicted values:
 X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 10 67.43998 0.2691875 (66.90912, 67.97084) (59.958637, 74.921326)

Residuals stored in new column, Residuals.

Scatterplot 2 is a scatter diagram of the residuals. There is no pattern to the residuals. They are scattered at random. This suggests that the linear model can appropriately describe the correlation between shoe size and height.

Result 3: Scatterplot 2: Residuals v. Shoe Size   [Info]

The Boxplot shows that there are four residual outliers. Reviewing the raw data from the Sullivan Statistics Survey suggests that these outliers are not the result of data entry errors. All of the outliers, such as a 4'4" person having size 12 feet, are extreme but within the realm of possibility. Thus, it would not be appropriate to immediately discard them. Since there are outliers both above and below the boxplot, the outliers balance each other out to an extent and probably do not affect our analysis too much.

Result 4: Boxplot: Residuals   [Info]

This analysis shows that there is a linear correlation between foot size and height. We can expect people with large feet to be taller than people with small feet. However, there are a few sources of error in our analysis which could be addressed in future studies. For one, shoe size is not a perfect measure of foot size. Some people may not be wearing shoes which fit them properly. It might be better to directly measure foot size. Also, men and women have different shoe size scales. A size 10 for women is smaller than a size 10 for men. If shoe size, rather than foot size, must be used, it might be helpful to break women and men apart in future studies. Nevertheless, since such a strong linear correlation was found in this study, I would expect to still find one in any future study.