Concept explainers
IBM stock prices. Refer to Example 14.1 (p. 14-5) and the 2015 monthly IBM stock prices.
a. Use the exponentially smoothed series (with w = .5 from January to September 2015 to forecast the monthly values of the IBM stock price from October to December 2015. Calculate the forecast errors.
b. Use a simple linear regression model fit to the IBM stock prices from January to September 2015. Let time t
c. With what approximate precision do you expect to be able to predict the IBM stock price using the regression model?
d. Give the simple linear regression forecasts and the 95% forecast intervals for the October-December 2015 prices. How does the precision of these forecasts agree with the approximation obtained in part c?
e. Compare the exponential smoothing forecasts, part a, to the regression forecasts, part d, using MAD, MAPE, and RMSE.
f. What assumptions does the random error component of the regression model have to satisfy in order to make the model inferences (such as the forecast intervals in part c) valid?
g. Test to determine whether there is evidence of first-order positive autocorrelation in the random error component of the regression model. Use α = .05. What can you infer about the validity of the model inferences?
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Chapter 14 Solutions
STATISTICS F/BUS.+ECON.-18WK. MYSTATLAB
- 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_forwardConsider the following time series.t 1 2 3 4 5 6 7 Yt 120 110 100 96 94 92 88a. What type of pattern exists in the data?HorizontalSeasonal with upward trendDownward trendUpward trendSeasonal with downward trendb. Regression analysis yields the following forecast equation: 119.71 - 4.929t; what is the forecast for period 8? Round to the nearest hundredth.c. Regression analysis yields the following forecast equation: 119.71 - 4.929t; what is the MSE for this forecast method? Round to the nearest hundredth.arrow_forward
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- consider the following time series data.t 1 2 3 4 5 6 7yt10 9 7 8 6 4 4a. construct a time series plot. What type of pattern exists in the data?b. develop the linear trend equation for this time series.c. What is the forecast for t = 8?arrow_forwardWhich of the following are appropriate research questions for binary logistic regression?a.Predicting the likelihood of getting arrestedb.Predicting the likelihood of a tumor being cancerousc.Predicting the likelihood of having one vs. two carsd.Predicting the likelihood of drawing a 7 from a deck of cardsarrow_forwardAll of the following models would be appropriate for data comprised of randomness and trend except: a. Holt’s exponential smoothing b. Holt-winter’s exponential smoothing c. Average change model d. Linear trend regression (time series decomposition) e. All of the above would be appropriatearrow_forward
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