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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?Find the least linear regression of (1, 0), (3, 3), and (5, 6)If the points (x1, y1), (x2, y2),..., (xn, yn) lie on a straight line, what can you say about the regression line associated with these points?
- For the regression model Yi = b0 + eI, derive the least squares estimator.Construct an example of a regression model that satisfies the assumptionE(ui | Xi) = 0 but for which E(U | X ) ≠0n.Use the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).
- A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:The regression linear model between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to" 1.364x+1.955 1.364x+3.125 1.955x+1.364 1.25x+2 2x+1.25 correct option?find the least squares regression line equation from the given data.
