Boston University Department of Biomedical Engineering
ENG BE200: Introduction to Probability
Fall 2010
Exam 1
Show ALL the steps in your calculations including the equations.
Problem 1
[40 pts]
a)
[ 5 ]
b)
M
x
= 15/4 = 3.75
[ 10 ]
M
y
= 25/4 = 6.25
S
x
2
=
(
x
i
−
M
x
)
2
i
=
1
4
∑
4
−
1
= 6.25
S
x
= 2.5
S
y
2
=
(
y
i
−
M
y
)
2
i
=
1
4
∑
4
−
1
= 10.917
S
y
= 3.304
c)
r
xy
= S
xy
/( S
x
* S
y
)
[ 10 ]
=
(
x
i
−
M
x
)(
y
i
−
M
y
)
i
=
1
4
∑
(4
−
1)*
S
x
*
S
y
= 23.25 / ( 3 * 2.5 * 3.304 )
0
2
4
6
8
10
12
0
2
4
6
8
Y
X
Scatterplot
Scatterplot
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View Full Document= 0.938
The data does indicate a strong correlation between the x values and y values however
this doe not tell us that there is a causal relationship between these two variables.
It is
impossible to say if x causes y or y causes x given the data.
The value of r
2
is a measure of the fit of the data to the line of best fit.
The closer the
value is to one the better the fit of the data to the line.
Alternatively 1 r
2
represents the
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 Fall '09
 ddd
 Regression Analysis, linear regression line, AC AC AC, Boston University Department, Engineering ENG BE200

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