Statistics Bivariate Analysis

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Statistics Bivariate Analysis
Minutes Exercised Per Day vs. Weighted GPA

• By Student 1, 2, 3

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Why did we choose this study?

• Exercise is a vital part of staying healthy and
  living an active and accomplished lifestyle.
• We believe that physical activity improves a
  students will to learn and may increase study
  habits.
• Previous studies have concluded that children who
  live a more active lifestyle are more compelled
  to succeed in school. We want to see if this is
  true at our school.
• We like to exercise, and we were curious to see
  if there is a correlation between these two
  variables.

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Collected Data
N30
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Vital Stats

• For X
• -X bar 81.1
• -Sx 72.886
• -5 Summary
• MinX 0
• Q1 30
• Med 60
• Q3 120
• MaxX 240

• For Y
• -Y bar 3.494
• -Sy .3297
• -5 Summary
• MinY 2.6
• Q1 3.33
• Med 3.5
• Q3 3.7
• MaxY 4.3

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Outliers?

• In order to find outlier, we used the two
  formulas
• ltQ1-1.5(IQR)
• gtQ31.5(IQR)
• 0lt30-1.5(90)
• 240gt1201.5(90)
• 0lt-105
• 240gt255 NO OUTLIERS
• 2.6lt3.33-1.5(.37)
• 4.3gt3.71.5(.37)
• 2.6lt-2.22
• 4.3gt4.255 4.3 is an OUTLIER

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Histogram of X (exercise in min)
The shape of the data is slightly right skewed.
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Histogram of Y (Weighted GPA)
The graph has a bell-shaped distribution.
Outlier4.5
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Empirical Rule Test

• Exercise (X)
• Mean81.1 Standard Deviation72.887
• 81.1 /- 72.887 153.986 8.213
• 81.1/- 72.887(2) 226.873 -64.674
• 81.1 /- 72.887(3) 299.76 -137.561
• 68 of the data falls between 153.986 8.213
• 95 of the data falls between 226.873 -64.674
• 99.7 of the data falls between 299.76 -137.561

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Empirical Rule Test

• GPA (Y)
• Mean 3.494, Standard Deviation .3297
• 3.494 /- .3297 3.8237 3.1634
• 3.494 /- .3297(2) 4.1534 2.8346
• 3.494 /- .3297(3) 4.4831 2.5049
• 68 of the data falls between 3.8237 3.1634
• 95 of the data falls between 4.1534 2.8346
• 99.7 of the data falls between 4.4831 2.5049

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Explanatory Response Variable

• The explanatory variable (X) in our data is the
  number of minuets exercised per day, it is used
  to predict changes in the response variable (Y)
  or GPA.
• GPA is the response variable, and is dependent on
  the other data. This allows us to find a
  relationship between the two values.

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Scatterplot
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Analysis

• The Scatterplot shows that there is no linear
  correlation between exercise and weighted GPA due
  to the graph. In order to receive that
  conclusion, we know that when a correlation graph
  has a pattern it is linear. When the correlation
  graph does not have a pattern it is not linear.
• The coefficient of correlation is r -0.038168.
  This also gives another reason why the scatter
  plot is not linear. If the r value is closer to 1
  then it is linear. If the r value rounds close to
  zero it is not linear. If the r value was close
  to one, it would be very strong but in this case
  the r value is not strong at all because it is
  closer to zero. The outlier in this scatter plot
  is 4.3 which slightly altered our data.

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Regression Line on Scatterplot
Equation y 3.508 -.0002x
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• The y-intercept of the regression line gives the
  predicted value of y for any given value of x.
• The slope shows the relationship between x and y
  as the steepness of the regression line is
  analyzed.
• Our data does not prove a correlation between
  weighted GPA and average minutes exercise
  performed in a day, so this equation should not
  be used to predict the response variable.

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R R Squared

• The r-squared value is explained variation over
  total variation and will give the accuracy (in a
  percentage) for a given value.
• R2 .00145681è .14 of the variation in Y is
  explained by the variation in x.
• R measures the strenght and direction of a
  linear relationshop between two variables
• R -.038168 negative, with no correlation.

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• Total Variation is the sum of the y values minus
  the mean of y values, squared
• 362595.172
• Explained Variation is the sum of the y-hat
  values minus the mean of y values, squared
• 181283.8495
• Unexplained Variation is the sum of the y values
  minus the y-hat values
• 181311.3225
• 362595.172 181283.8495 181311.3225

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Standard Error of Estimate

• The standard error of estimate is a measure of
  how sample points deviate from the regression
  line. Se measures the difference between the
  observed y-values and the predicted y-values. One
  would take the unexplained variable, divide that
  by the degree of freedom and square the result.

Se .3353
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95 Prediction Interval

• For X we choose 70
• With wanting to find the possible GPA of a person
  with an average 70 minute workout, there will be
  a .3353 standard of error. The GPA would fall
  between 2.6889 and 4.0855.

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Residual Plot
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Interpretation

• The Residual plot shows that it is not a good
  model for the LSRL. This is because the plot
  contains a pattern and is in the negative range.
  In other words, this graph is not linear. On the
  residual plot, the X-values equals GPA weighted
  and the Y-values is exercise in minutes.

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Conclusion

• In conclusion, we have found that there is no
  correlation between how many minuets a high
  school student exercises, and their GPA.
• Our graphs and data values are not strong enough
  to draw conclusions based on our sample.
• Despite the amount of time that a student does or
  does not spend working out, their grades will
  neither increase or decrease.

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Possible Problems

• If the sample had been larger, the results may
  have been more accurate.
• It is possible that subjects may have lied either
  about the amount they exercise or their true GPA,
  thus hindering our results.
• It is sometimes difficult to estimate how much
  you exercise each day because it varies depending
  on your changing daily activities.

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The End.