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General Mathematics
| Date post: | 13-May-2015 |
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General Mathematics
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Number of Sickies
Age in Years
In order to answer this we need to collect some data
Is there a mathematical relationship between a person’s age and the number of sickies they take?
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
AGENUMBER OF
SICKIES27 1561 637 1023 1846 958 729 1436 1164 540 8
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Number of Sickies
Age in Years
To draw a line of best fit we have (as a rule of thumb), roughly as many points on one side of the straight line as we have on the other side
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Number of Sickies
Age in Years
To draw a line of best fit we have (as a rule of thumb), roughly as many points on one side of the straight line as we have on the other side
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Number of Sickies
Age in Years
60
19.5-6.1= 13.4
Gradient = 2233.060
4.13
run
rise
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Number of Sickies
Age in Years
The “y-intercept”
19.5
y = mx + b
“y” = Number of sickies (N)
“x” = Age in years (A)
N = -0.2233A + 19.5
A statistically more accurate way is to
find a median regression lineThis is a more fancy way of
finding the line of best fit, eliminating the possibility of getting variations from one person to another, ie. there is only one true line of best fit.
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Number of Sickies
Age in Years
Step 1: Divide all the points into three equal groups from left to right
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Number of Sickies
Age in Years
Step 2: In each block find the median from left to right
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Number of Sickies
Age in Years
Step 3: Find the median from top to bottom
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Number of Sickies
Age in Years
Step 4: Draw a line joining first and third median pts
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Number of Sickies
Age in Years
Step 5: Draw a line parallel to this through the middle median point
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
Step 6: Move the solid line ⅓ of the way towards the dotted line
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Number of Sickies
Age in Years
By removing all our construction lines we can see our median regression line clearly and can work out the equation.
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Number of Sickies
Age in Years
By removing all our construction lines we can see our median regression line clearly and can work out the equation.
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Number of Sickies
Age in Years
These points show some strong relationship between the person’s age and the number of sickies they take (Correlation)
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Number of Sickies
Age in Years
These points show a correlation that is not so strong:
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Number of Sickies
Age in Years
These points show a correlation that is relatively weak:
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Number of Sickies
Age in Years
These points show no correlation at all:
The degree of correlation
can be assigned a
number from –1 to 1
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Number of Sickies
Age in Years
These points are perfectly correlated, so they possess a correlation coefficient of +1 (positive because of positive slope)
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = +1
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = +0.98
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = +0.90
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = +0.36
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = 0
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = -0.41
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = -0.90
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Number of Sickies
Age in Years
Let us see what happens as the correlation gradually fades away:
Correlation = -0.97
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Number of Sickies
Age in Years
Let us see what happens has the correlation gradually fades away:
Correlation = -1
Correlation is negative because of negative slope
We can also assign words to describe
the degree of correlation
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Number of Sickies
Age in Years
Strong positive correlation
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Number of Sickies
Age in Years
Moderate positive correlation
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Number of Sickies
Age in Years
Weak positive correlation
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Number of Sickies
Age in Years
No correlation
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Number of Sickies
Age in Years
Weak negative correlation
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Number of Sickies
Age in Years
Moderate negative correlation
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Number of Sickies
Age in Years
Strong negative correlation
