The Least Squares Assumptlons In the Multiple Regression Model Y; = Bo + BX1; + BzXy+ · …· + BXµi + U;, i = 1, ...,n, where 1. u; has conditional mean zero given X15, Xy, . .., Xg; that is, E(u;|X15, X3, … .. , Xy3) = 0 2. (X15 Xy .. , Xµ, Y), i = 1, …,n, are independently and identically distrib- uted (i.i.d.) draws from their joint distribution. 3. Large outliers are unlikely: X15 . . . , X; and Y; have nonzero finite fourth moments. 4. There is no perfect multicollinearity.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
(Yi, X1i, X2i) satisfy the assumptions of the attachment in addition,var(ui | X1i, X2i) = 4 and var(X1i) = 6. A random sample of size n = 400is drawn from the population.a. Assume that X1and X2 are uncorrelated. Compute the variance of β˄1.b. Assume that corr(X1, X2) = 0.5. Compute the variance of β˄1. c. Comment on the following statements: “When X1 and X2 are
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