1. Recall that in the normal linear regression analysis formalism the random variable Y given X- is assumed to follow N(a + ßr, σ2) so that a maximu in likelihood calculation leads to the point e...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
5. So far in our linear modeling, we have assumed that Ylz ~ NA,+Az,σ2); that is, there is a normal distribution of common variance around the regression line. Here, we change this up! Suppose that X~Unif(0, 1) and that for a given r, we know YlN(,22). (Here, the regression lne is 01z and the variance around the regression grows as r grows.) a. In R, figure out how to generate 1000 data points that follow this model and plot them....