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Statistics Bivariate Analysis
Minutes Exercised Per Day
vs. Weighted GPA
By: Student 1, 2, 3
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
student’s 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.
Collected
Data
N=30
Exercise per day (minutes)
X
30
30
0
0
60
120
120
30
120
30
90
180
0
150
180
120
15
60
240
180
0
0
23
60
240
40
60
60
160
35
Weighted GPA
Y
3.7
3.5
3.7
3.5
3.2
3.12
3.67
3.2
3.5
3.6
3.7
2.6
3.33
4.3
3.7
3.6
3.52
3.5
3.33
3.7
3.65
4.0
3.5
3.0
3.7
3.9
3.0
3.2
3.5
3.4
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
Outliers?
In order to find outlier, we used the two formulas:
 #<Q1-1.5(IQR)
 #>Q3+1.5(IQR)

0<30-1.5(90)
 240>120+1.5(90)
 0<-105
 240>255 NO OUTLIERS

2.6<3.33-1.5(.37)
 4.3>3.7=1.5(.37)
 2.6<-2.22
 4.3>4.255 4.3 is an OUTLIER
Histogram of X (exercise in min)
The shape of the data is slightly right skewed.
Histogram of Y (Weighted GPA)
The graph has a bell-shaped distribution. Outlier=4.5
Empirical Rule Test
Exercise (X)
Mean=81.1 Standard Deviation=72.887


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
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
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.

Scatterplot
GPA vs. Excercise
5
4.5
GPA (weighted)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
50
100
150
Exercise (m inutes)
200
250
300
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.
Regression Line on Scatterplot
Excersise Vs. GPA
y = -0.0002x + 3.508
R2 = 0.0015
5
4.5
GPA (weighted)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
50
100
150
Excersise (m inutes)
Equation: y= 3.508 + -.0002x
200
250
300
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.
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.

•

•

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
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 =
y
2
–
b0  y – b1  xy
n–2
Se= .3353
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.
Residual Plot
Residual Plot
0
0
50
100
150
-20
-40
-60
-80
-100
-120
-140
-160
GPA (weighted)
200
250
300
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.
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.
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.
The End.