The data in Table 4.6 of (Dobson and Barnett 2018) are times to death, yi, in weeks

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The data in Table 4.6 of (Dobson and Barnett 2018) are times to death, yi, in weeks from diagnosisand log10 (initial white blood cell count), xi, for seventeen patients suffering from leukemia. (This isExample U from [@{cox2018applied])

a. Plot yi against xi. Do the data show any trend?

b. A possible specification for E(Y ) is

μi = E(Yi) = exp(β0 + β1xi),

which will ensure that E(Y ) is non-negative for all values of the parameters and all values of x. Whichlink function is appropriate in this case?

c. The Exponential distribution is often used to describe survival times.

The probability distribution is f(y; θ) = θe−θy. This is a special case of the Gamma distribution with shapeparameter α = 1. Show that E(Y ) = 1/θ and var(Y ) = 1/θ2 .

d. Fit a model with the equation for μi = E(Yi)given in (b) and the Exponential distribution using appropriate statistical software.

Find the Score function, the estimating equation and the information matrix.