Simple linear regression results:Dependent Variable: LengthIndependent Variable: Width Length = 12.325859 + 1.5597885 WidthSample size: 29R (correlation coefficient) = 0.85807111R-sq = 0.73628603Estimate of error standard deviation: 1.2631656Parameter estimates:Parameter Estimate Std. Err. Alternative DF T-Stat P-valueIntercept 12.325859 1.8283346 ≠ 0 27 6.741577 <0.0001Slope 1.5597885 0.17964996 ≠ 0 27 8.6823761 <0.0001Analysis of variance table for regression model:Source DF SS MS F-stat P-valueModel 1 120.28121 120.28121 75.383655 <0.0001Error 27 43.08086 1.5955874 Total 28 163.36207

R and R^2 are moderately strong, showing that the data is linear

There is a strong positive association in both the fitted line and the scatter plot, however the residual scatter plot has no patterns that are glaringly obvious.

I am going to try to straighten the data and see if I can strengthen the residual

Squaring the data resulted in this:

It’s identical to the original.

Finding the log of the lengths gave me these results:

The log of the lengths gave the smallest residual and therefore is the best choice for straightening the data.

Simple linear regression results: Dependent Variable: log of length Independent Variable: Width log of length = 1.2091506 + 0.023538532 Width Sample size: 29 R (correlation coefficient) = 0.85890519 R-sq = 0.73771813 Estimate of error standard deviation: 0.018991951

Parameter estimates:

Parameter

Estimate

Std. Err.

Alternative

DF

T-Stat

P-value

Intercept

1.2091506

0.027489381

≠ 0

27

43.986098

<0.0001

Slope

0.023538532

0.0027010735

≠ 0

27

8.7145099

<0.0001

Analysis of variance table for regression model:

Source

DF

SS

MS

F-stat

P-value

Model

1

0.027392086

0.027392086

75.942684

<0.0001

Error

27

0.0097387435

0.0003606942

Total

28

0.037130829

Bringing this back to my mini proposal, I’m not sure the data is strong enough to prove a very strong correlation between the width of a shoe and it’s length. There are other factors that could impact the width of the shoe. Like style, brand, ect. I also think where on the shoe you measure would make a difference. I measured like widest part of the shoe, where the ball of your foot goes, but maybe measuring the middle of the shoe would have brought more diversity.

Link to data:https://docs.google.com/spreadsheets/d/1-4FVia132mdr2GQmLz5RcaQRLgmY0N1k_Q5GYGHHRxMSimple linear regression results:Dependent Variable: LengthIndependent Variable: Width Length = 12.325859 + 1.5597885 WidthSample size: 29R (correlation coefficient) = 0.85807111R-sq = 0.73628603Estimate of error standard deviation: 1.2631656Parameter estimates:Parameter Estimate Std. Err. Alternative DF T-Stat P-valueIntercept 12.325859 1.8283346 ≠ 0 27 6.741577 <0.0001Slope 1.5597885 0.17964996 ≠ 0 27 8.6823761 <0.0001Analysis of variance table for regression model:Source DF SS MS F-stat P-valueModel 1 120.28121 120.28121 75.383655 <0.0001Error 27 43.08086 1.5955874 Total 28 163.36207R and R^2 are moderately strong, showing that the data is linearThere is a strong positive association in both the fitted line and the scatter plot, however the residual scatter plot has no patterns that are glaringly obvious.I am going to try to straighten the data and see if I can strengthen the residualSquaring the data resulted in this:It’s identical to the original.Finding the log of the lengths gave me these results:The log of the lengths gave the smallest residual and therefore is the best choice for straightening the data.Simple linear regression results:Dependent Variable: log of lengthIndependent Variable: Widthlog of length = 1.2091506 + 0.023538532 WidthSample size: 29R (correlation coefficient) = 0.85890519R-sq = 0.73771813Estimate of error standard deviation: 0.018991951Parameter estimates:Analysis of variance table for regression model:Bringing this back to my mini proposal, I’m not sure the data is strong enough to prove a very strong correlation between the width of a shoe and it’s length. There are other factors that could impact the width of the shoe. Like style, brand, ect. I also think where on the shoe you measure would make a difference. I measured like widest part of the shoe, where the ball of your foot goes, but maybe measuring the middle of the shoe would have brought more diversity.Here is my picture of all the shoes measured,