2. Answer the following questions. Prove your answers using derivations, following the properties of summation operator, expectations operator, and variance operator. Consider a population regression equation: Y = P, + P,X + u. where B, and B, are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Var) Hint: Use computational formulas of Cov(X,Y) and Var(X). You may begin your derivation by taking the expectation of the equation on both sides. Given the measurement change in X, how will the following parameters change? t. Slope parameter, ß. E Intercept parameter, ß,

2. Answer the following questions. Prove your answers using derivations, following the properties of summation operator, expectations operator, and variance operator. Consider a population regression equation: Y = P, + P,X + u. where B, and B, are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Var) Hint: Use computational formulas of Cov(X,Y) and Var(X). You may begin your derivation by taking the expectation of the equation on both sides. Given the measurement change in X, how will the following parameters change? t. Slope parameter, ß. E Intercept parameter, ß,

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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