Question

working under the assumption thata set of data points obeys the exponential (a) Suppose you are model Y, Ae, BX. Derive the linearized model to which we can find a line of best fit (in the least squares sense). 3 marks (b) The lines of best fit for two repetitions of an experiment are reproduced below: Each data set has an obvious outlier. In each case, explain the effect that removing the outlier from the data set will have on the line of best ft. 4 marks

Answer 1

1)

Y = Ae BX

Taking natural logs, we get

In(YIn(A) +In()Xt In(B)

So we can fit
Xt, In(Y))
using linear regression to get an answer of the form
In(Y mXt c
and equate
m In(B), c = In(A)

2) In the left case the outlier is to the bottom and to the right, very far away from the sample mean. We can think of this outlier pushing the linear of regression towards it. As soon as it is removed, the line of best fit will become slightly move slightly vertically upwards and rotate slightly counterclockwise

In the right case, the outlier is extremely close to the center of the data, just slightly lower. So removing this will only shift the line of best fit slightly upwards. No rotation will be observed

$\blacksquare$

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