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Owner: cpears93
Created: Mar 2, 2013
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Views: 117923
Tags: height, size
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Height Versus Shoe Size
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This data set shows us the differences between height and shoe size in a sample size of 199. The height will be our explanatory variable, and shoe size will be our dependent variable.

Data set 1. Height vs Foot/Shoe Size Data   [Info]
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Observed below, is a scatter plot of the data shown above. As signified in the scatter plot, the explanatory variable (height), and response variable (foot size) have a positive correlation. This is known because while one goes up, the other goes up as well at a constant rate. We can also see that there are some possible outliers in the data. It seems that as height increases, so does foot size for the most part. As well, the correlation value is higher than what the critical value is, also proving a positive association.

Result 1: Scatter Plot - Height vs Foot size   [Info]
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Result 2: Correlation height vs foot size   [Info]
Correlation between Height and Foot is:

Next we can see the simple linear regression summary. Here we can see a lot of different information. We are told that the linear correlation coefficient is r = 0.6222. Since r is closer to +1 we have stronger evidence that there is a positive association. We also find here that the least squares regression line is y-hat = -5.6680 + 0.2337. The R-sq value is 0.3871, which means only 38.71% of the variability is accounted for on the fitted line.

Result 3: Simple Linear Regression Summary - Height vs Foot size   [Info]
Simple linear regression results:
Dependent Variable: Foot
Independent Variable: Height
Foot = -5.6679645 + 0.23370141 Height
Sample size: 199
R (correlation coefficient) = 0.6222
R-sq = 0.38713068
Estimate of error standard deviation: 1.4213197

Parameter estimates:
Parameter Estimate Std. Err. Alternative DF T-Stat P-Value
Intercept -5.6679645 1.4216981 ≠ 0 197 -3.9867566 <0.0001
Slope 0.23370141 0.020949969 ≠ 0 197 11.155215 <0.0001

Analysis of variance table for regression model:
Source DF SS MS F-stat P-value
Model 1 251.38507 251.38507 124.438835 <0.0001
Error 197 397.96948 2.0201497
Total 198 649.35455

Predicted values:
X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new
0.1 -5.644594 1.4196084 (-8.444174, -2.8450143) (-9.606185, -1.6830032)

Residuals stored in new column, Residuals.

Result 4: Simple Linear Regression Fitted Line Plot - height vs foot size   [Info]
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In the residual scatter plot shown below it can be determined there is no real pattern. They data is a tad crowded, but that could be from the large sample number. Since there is no distinct pattern to the graph, it can be determined that a linear model is appropriate for this data.

Result 5: Simple Linear Regression Residuals plot - height   [Info]
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The histogram of residuals below shows some interesting information. The shape for the most part seems evenly distributed. There seems to be a slight tail to the right, but doesn’t seem to be of concern. For the most part, the shape seems to show a bell shape, which shows an even distribution of the data. From this graph stronger evidenced is provided that a linear model is appropriate.

Result 6: Simple Linear Regression residual histogram - height vs shoe size   [Info]
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Shown below is the boxplot of residuals. The boxplot shows that there are a few outliers in the data. But, the median for the most part is in the middle; slightly to the left of the box. Both tails seem to be the same size. The few outliers have made the data slightly skewed right.

Result 7: Boxplot of Residuals - Height vs Foot size   [Info]
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Courtney Pearson

HTML link:
<A href="">Height Versus Shoe Size</A>

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By msullivan13803
Mar 11, 2013

Well done.
By msoren77
Mar 3, 2013

Great report, Courtney! I was surprised to see the correlation was not closer to 1. I would have thought it'd be almost perfect! I, too, wonder if the data would change if the measurements were taken by a doctor. Many people estimate their heights. I do not see the source for your data. Does it say how it was obtained? - Miranda Sorensen
By jeremiah.bly
Mar 2, 2013

This data is pretty interesting. I would have assumed that the average person would have feet sized in proportion to their heights. I wonder how much the data would change if the data was collected throught measurement instead of through each person volunteering this information. I know that many people would likely falsify their heights, and if we were talking about weight that would be an even larger lurking variable.
-Jeremiah Bly

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