# In an article in Statistics and Computing [""An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis"" (1991, pp. 119-128)], Carlin and Gelfand investigated the age (x) and length (y) of 27 captured dugongs (sea cows). x 1.0 1.5 1.5 1.5 2.5 4.0 5.0 5.0 7.0 8.0 8.5 9.0 9.5 9.5 10.0 12.0 12.0 13.0 13.0 14.5 15.5 15.5 16.5 17.0 22.5 29.0 31.5 y 1.80 1.85 1.87 1.77 2.02 2.27 2.15 2.26 2.47 2.19 2.26 2.40 2.39 2.41 2.50 2.32 2.32 2.43 2.47 2.56 2.65 2.47 2.64 2.56 2.70 2.72 2.57" (a) Fin

###### Question:

In an article in Statistics and Computing [""An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis"" (1991, pp. 119-128)], Carlin and Gelfand investigated the age (x) and length (y) of 27 captured dugongs (sea cows).
x 1.0 1.5 1.5 1.5 2.5 4.0 5.0 5.0 7.0 8.0 8.5 9.0 9.5 9.5 10.0 12.0 12.0 13.0 13.0 14.5 15.5 15.5 16.5 17.0 22.5 29.0 31.5
y 1.80 1.85 1.87 1.77 2.02 2.27 2.15 2.26 2.47 2.19 2.26 2.40 2.39 2.41 2.50 2.32 2.32 2.43 2.47 2.56 2.65 2.47 2.64 2.56 2.70 2.72 2.57"
(a) Find the least squares estimates of the slope and the intercept in the simple linear regression model. Find an estimate of σ2
(b) Estimate the mean length of dugongs at age 11.

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