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Observations on Yare to be taken when X = 10, 20, 30, 40, and 50, respectively. The true regression function is E{Y) = 20 + l0X. The error terms are independent and normally distributed with
a. Generate a random Y observation for each X level and calculate both the ordinary and weighted least squares estimates of the regression coefficient ß1 in the simple linear regression function.
b. Repeal pan (a) 200 times. generating new random numbers each time.
c. Calculate the mean and variance of the 200 ordinary least squares estimates of ß1 and do the same for the 200 weighted least squares estimates.
d. Do both the ordinary least squares and weighted least squares estimators appear to be unbiased? Explain. Which estimator appears to be more precise here? Comment.
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Compare two models. Model #1 has an r-squared of .55 and an adjusted r-squared of .50. Model #2 has an r-squared of .52 and an adjusted r-squared of .51. Given this information, what model should you use?
Sketch the distribution involved.
Determine the expected value and standard error of the sum of 400 draws?
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At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.
To utilize the weighted least squares approach we need to know, up to a multiplicative constant, the variance of Y as a function of x. We will now present an argument that Var(Y) should be proportional to x.
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