nerdasdasd
Dont.msg.me.about.english
how do you do 4.2c?
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STATS / actuarial Q (1 Viewer)
- Thread starter nerdasdasd
- Start date
nerdasdasd
Dont.msg.me.about.english
Yes.Are any of these correct?:
New equation is.
stays the same.
how did you get the answer?
nerdasdasd
Dont.msg.me.about.english
SER = 10.2 x 0.4536 = 4.6267kg
To get the new equation for the model, we just use the conversion factors of in to cm and lb to kg:
1 in = 2.54 cm = a cm (letting a = 2.54), and 1 lb = 0.453 kg (approx.) = b kg (letting b = 0.453).
Then this means: w lb = w' kg, where w' = bw
and h in = h' cm, where h' = ah.
Then our original equation was: w (in lb) = M×h (where h is in inches, and M has units of lb/in) + B (where B was in lb).
Replace w with w'/b, and h with h'/a (where w' is the corresponding weight in kg for a weight result of w lb), and similarly h' corresponds to the cm expression for h in:
w'/b = M×(h'/a) + B
multiply through by b: w' = (M×b/a)×h' + bB. This is our new equation for the model.
Then sub. in M = 3.94, B = -99.41, and the b and a values, to get the numerical values.
This gives the model for weight in kg vs. height in cm.
ah right, forgot the original SER (thought it was 200 >_<...that was the no. of measurements)
Yes, that's what I'd get if I'd used 10.2.
nerdasdasd
Dont.msg.me.about.english
Thanks for taking your time =)
I'll denote corresponding new values of quantities with a prime ('). E.g. R2' refers to the new R2 value, whilst R2 refers to the old R2 value.
Proof why R2 is unchanged
(quick reason: R2 is unitless so just depends on the actual data.)
proof of this:
,
where^2)
is the sum of squared deviations of the actual data values and predicted data values (i.e. sum of squared residuals). wi is a data value of weight (in lb, because I didn't put a prime) for a corresponding height measurement, and fi is what the old model predicted would be the weight value for that height value. Also, ^2)
is the sum of squared distances of your weight data from the weight mean 
. We show that 
and 
. In other words, we show that the NEW 
and new 
are both the same ratio compared to their old ones, so that when we plug them into the R2 formula to get the new R2, these common factors of b2 will cancel and we will be left with our original R2 value as our new one.
Now,
But this fi is just our old model, that is, fi = Mh + B, where M and B are given in your question.
So,)^2)
.
Now, for our new one,^2)
. But 
and h^\prime + bB)
(i.e. our new model, found earlier in the Q).
Therefore,
h^\prime + bB\right)\right)^2)
h^\prime + B\right)\right)^2)
, since we can factor out the b, and it becomes a b2 since it was inside a square
)^2)
, because h'/a = h (i.e. new h values are a times the old ones, by our definition of a)
, as required.
Now,^2)
.
And
^2)
^2)
(because the new average is b times the old one, since multiplying a set of scores by a constant also does this to their average)
^2)
, as required. 
.
So R2 doesn't change.
Proof why R2 is unchanged
(quick reason: R2 is unitless so just depends on the actual data.)
proof of this:
where
Now,
But this fi is just our old model, that is, fi = Mh + B, where M and B are given in your question.
So,
Now, for our new one,
Therefore,
Now,
And
So R2 doesn't change.
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We now show that SER changes by a factor of b, that is, that 
.
The general formula for
is:
(see page 3 of this document: http://users.wfu.edu/cottrell/ecn215/regress.pdf ), where n is the no. of measurements, and p is the number of parameters to be estimated (n – p is called the number of degrees of freedom). In our case, n = 200 and p = 2.
Since n and p do not change between our old units and new units, we only need to consider how changes.
But we already showed before that
.
Therefore,
(general formula)
(as n' = n and p' = p, as these don't change)
(
, as b > 0)
, as we wanted to show.
i.e. the new SER is b times the old one.
The general formula for
Since n and p do not change between our old units and new units, we only need to consider how
But we already showed before that
Therefore,
i.e. the new SER is b times the old one.
Welcome
However, I'm not sure they wanted you to actually derive these facts, I think they probably proved or gave these facts somewhere in a textbook and wanted you to apply them to this Q?
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