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2.
A colleague of yours has suggested a new way to measure the variability (or ¡°spread-outness¡±) of the data you are studying. They suggest the following formula for the data values you are studying. They also state that you add every other data value, and every other¡±error¡°in the numerator.
In case you have 8 data values, for example, they suggest you proceed as follows:
x
1
+ (
x
2
− x
) +
x
3
+ (
x
4
− x
) +
x
5
+ (
x
6
− x
) +
x
7
+ (
x
8
− x
)
d
=
8
a
What might cause issues with this approach?
b
How does this compare with the M.A.D.?
Regression and Estimation
3.
A colleague decides that they would like to use a regression model to predict a variable,
Y
, as a
response
to a variable,
X
a.
For a value of
x
= 7, what would you predict as the corresponding
y
value?
b.
For a value of
x
= 9, what would you predict as the corresponding
y
value?
c.
For the
y
value you found in
a.
above, give an estimate of the likely range or variability in the possible values of
y
that we might observe.
d.
Does this model give a good prediction of
y
in response to
x
? Why or why not?
4.
A regression model is built to predict the pH pf well water from Bicarbonate content in p.p.m. After performing the work in Excel, the following results are obtained:
Coefficients
Intercept 432.15 Slope -37.78
a.
At a pH of 7.3, what is the estimated Bicarb in p.p.m.?
b.
Is this scatterplot reflective of a strong relationship between pH and Bicarb? Why or why not?
c.
Is it fair to say the Intercept of 432.15 is reflective of the Bicarb at a pH of 0? If so why? If not, why not?
d.
Consider the putput given below:
Regression Statistics
R Square 0.115
Observations 34
Is
y
=
−
37
.
78 + 432
.
15 a good prediction model for Bicarb in p.p.m. as a response to pH? Why or Why not?