Concept explainers
Quarterly GOP values (cont’d). Refer to Exercise 14.66.
a. Use the simple linear regression model fit to the data to forecast the 2016 quarterly GDP. Place 95% prediction limits on the forecasts.
b. The GDP values given are seasonally adjusted, which means that an attempt to remove seasonality has been made prior to reporting the figures. Add quarterly dummy variables to the model. Use the partial F-test (discussed in Section 12.9) to determine whether the data indicate the significance of the seasonal component. Does the test support the assertion that the GDP figures are seasonally adjusted?
c. Use the seasonal model to forecast the 2016 quarterly GDP values.
d. Calculate the lime series residuals for the seasonal model and use the Durbin-Watson test to determine whether the residuals are autocorrelaled. Use α = .10.
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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?arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
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