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Created: Dec 6, 2017
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Week 14 StatCrunch- 14-1
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Introduction

There has always been speculation concerning a relationship between height and length of extremities. For this reason, we undertook a study to study the relationship between stature (height) and the length of hands and feet.

Methods

A sample of 155 people was collected. Their height (meters) and lengths of both their right hand and foot (centimeters) were measured and recorded. Gender was also recorded as male (1) or female (0). Multiple regression will be used to predict (with appropriate confidence) the heights of 5 subjects including both male and female subjects.

Data does qualify as interval-ratio so it is appropriate to move on to a regression analysis.

First, we must check our assumptions and assess correlation between our variables. Based on the p-values indicated below, there does appear to be evidence of correlation between the variables and height. Additionally, it appears that the variables are also correlated to each other indicating multicollinearity. However, as our goal is a predictive model, multicollinearity is not of great concern.

 

Result 1: Wk 14 Correlation Matrix   [Info]
Correlation matrix:
HeightHandLengthFootLength
HandLength0.87329538
(<0.0001)
FootLength0.88127952
(<0.0001)
0.78822431
(<0.0001)
Male0.80594839
(<0.0001)
0.72143003
(<0.0001)
0.75160459
(<0.0001)

Checking the assumptions:

Result 2: Wk 14 QQ Plot   [Info]
Right click to copy

Result 3: Wk 14 Residuals vs. Predicted   [Info]
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Based off the above plots we do not have any issues with normality or constant variability. We can now move on to choose our model. Based on our initial correlation matrix , there is evidence that all predictor variables may be individually useful in estimating average height, so we will use all 3 variables in our model leaving us with a full model.

Analysis.

Based on the p-value of <0.0001 in the ANOVA table, we have evidence that a model containing hand length, foot length, and gender (male) would be useful in estimating average height. Based on the p-values of <0.0001 in the parameter estimates table, we have evidence that hand length, foot length, and gender (male) are each individually useful in estimating average height.

 

Result 4: Wk 14 Multiple Linear Regression Results   [Info]
Multiple linear regression results:
Dependent Variable: Height
Independent Variable(s): HandLength, FootLength, Male
Height = 0.5821637 + 0.28134313 HandLength + 0.20620435 FootLength + 0.039614232 Male

Parameter estimates:
ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept0.58216370.060551033 ≠ 01519.6144306<0.0001
HandLength0.281343130.034229638 ≠ 01518.2192844<0.0001
FootLength0.206204350.025848756 ≠ 01517.9773413<0.0001
Male0.0396142320.0084984607 ≠ 01514.6613421<0.0001

Analysis of variance table for multiple regression model:
SourceDFSSMSF-statP-value
Model31.19310090.39770029363.6738<0.0001
Error1510.165128040.0010935632
Total1541.3582289

Summary of fit:
Root MSE: 0.033069067
R-squared: 0.8784
R-squared (adjusted): 0.876
Residuals stored in new column: Residuals

Next we will predict the average height for varying males and females. Predictions as follows:

We can predict with 95% confidence that the height for a male with a hand length of 2.2 cm and foot length of 2.7 cm is somewhere between 1.73 and 1.86 meters.

We can predict with 95% confidence that the height for a male with a hand length of 2.4cm and foot length of 2.9 cm is somewhere between 1.83 and 1.96 meters.

We can predict with 95% confidence that the height for a female with a hand length of 1.9 cm and foot length of 2.3 cm is somewhere between 1.52 and 1.66 meters.

We can predict with 95% confidence that the height of a male with hand length 1.6 cm and for length 2.6 cm is somewhere between 1.53 and 1.68 meters.

We can predict with 95% confidence that the height of a female with hand length 2.1 cm and foot length 2.7 cm is somewhere between 1.66 and 1.80 meters.

Discussion

Based on the results, there is evidence that gender, hand length, and foot length have predictive abilities of stature.

Conclusions/Further Study

The results of this study indicate that gender, hand length, and foot length can be used to predict height for individuals. Clinically this may be useful in the pediatric setting if there are any concerns of developmental issues. If a patient was not measuring at a height of what is expected based on prediction intervals, it would warrant diagnostic testing for certain diseases affecting growth and development. Further studies shou

 

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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=74190">Week 14 StatCrunch- 14-1</A>

Comments
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By sadouskasm
Dec 7, 2017

Good job on the revisions. I did the same report and had to make some of the same.
By danielle.hubbard85
Dec 7, 2017

Good job on making the updates to your report. I agree this would be important in the pediatrics when looking at issues affecting children's growth.
By nku.katie.waters
Dec 5, 2017

Hi Ashleigh,
Good job! A few comments:
1. It is not necessary to check for "nonlinear" form by looking at scatterplots. That is an assumption for simple linear regression involving two variables. Scatterplots are only useful when we are only looking at two variables.

2. When interpreting the correlation matrix, we might also note the presence of multicollinearity as most of these variables have a moderate correlation to each other. Since our goal is to find a predictive model, multicollinearity is not a big concern.

3. We can interpret the MLR results as followed: Based on the p-value in the ANOVA table, there is evidence that a model containing HandLength, FootLength, and Gender (Male) is useful in estimating average height. Based on the individual p-values in the parameter estimate table, all three predictors are individually useful in estimating average height.

4. You should omit the word "average" from the interpretation of the PIs. These give us estimates for individuals (not average).

Please let me know if you have any questions.
By ashleigh.eversole
Dec 5, 2017

Thanks guys! I tried to model after what I found in the text and researched other examples online. I wish I would have tried that in the beginning because it really did help! Good luck to all of us as we complete our last two weeks of work! Thanks for everyone's feedback this semester!
By ekilburn81
Dec 4, 2017

Great job on your report. Your were very detailed. I did the same study and I feel that you were on point with your interpretations. Good job.
By morgan.samad
Dec 2, 2017

Great job on your report! Very detailed and good interpretations.
By danielle.hubbard85
Dec 1, 2017

Great job on your report. I agree with making sure to rule out issues for not following in the predict height category when looking at other variables. But also feel this is looked at sometimes to closely, as everyone is unique and may not fall exactly into their predication. Good job!
By sadouskasm
Dec 1, 2017

Good job on your report. I never thought about this being used for certain diseases affecting growth and development. That would be a great application!

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