ah.png - 4 Straight-line regression through the origin In this question we shall make the following assumptions(1 Y is related to x by the simple linear

ah.png - 4 Straight-line regression through the origin In...

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This preview shows page 1 out of 1 page. Unformatted text preview: 4. Straight-line regression through the origin: In this question we shall make the following assumptions: (1) Y is related to x by the simple linear regression model Y, = Ar, e, (i = 1,2.....&quot;), i.e., E(Y | X = x,) = Ax, 2.8 Exercises 41 (2) The errors e, em.., e, are independent of each other (3) The errors e, e,..., e, have a common variance &quot; (4) The errors are normally distributed with a mean of 0 and variance of (espe- cially when the sample size is small), i.e., e | X-N(0.o?) In addition, since the regression model is conditional on X we can assume that the values of the predictor variable, A,, do ..., x, are known fixed constants. (a) Show that the least squares estimate of P is given by (b) Under the above assumptions show that E(P X) =B (i) Var(B] X) =- (iii) BIX-N(B. IM- IM-...
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