Serial correlation, also known as autocorrelation, describes the extent towhich the result in one period of a time series is related to the result in thenext period. A time series with high serial correlation is said to be verypredictable from one period to the next. If the serial correlation is low (ornear zero), the time series is considered to be much less predictable. Formore information about serial correlation, see the book Ibbotson SBBIpublished by Morningstar.A research veterinarian at a major university has developed a new vaccine toprotect horses from West Nile virus. An important question is: Howpredictable is the buildup of antibodies in the horse's blood after thevaccination is given? A large random sample of horses were given thevaccination. The average antibody buildup factor (as determined from bloodsamples) was measured each week after the vaccination for 8 weeks. Resultsare shown in the following time series.Original Time SeriesWeek123478Buildup Factor2.3 4.66.27.58.09.410.612.1To construct a serial correlation, we simply use data pairs (x, y) wherex = original buildup factor data and y = original data shifted ahead by1 week. This gives us the following data set. Since we are shifting 1 weekahead, we now have 7 data pairs (not 8).Data for Serial Correlationx 2.3 4.6 6.2 7.5 | 8.09.410.6y 4.6 6.2| 7.5 8.0 9.4 | 10.612.1A USE SALTFor convenience, we are given the following sums.Ex = 48.6, Ey = 58.4, Ex² = 385.86, Ey² = 526.98, Exy = 448.7(a) Use the sums provided (or a calculator with least-squares regression) tocompute the equation of the sample least-squares line, ŷ = a + bx. (Roundyour answers to four decimal places.)a =b =If the buildup factor was x = 5.4 one week, what would you predict thebuildup factor to be the next week? (Round your answer to two decimalplaces.) (b) Compute the sample correlation coefficient r and the coefficient ofdetermination 2. (Round your answers to four decimal places.)!!%3Dp>o at the 1% level of significance. (Round your answers to threedecimal places.)Testcritical tConclusionReject the null hypothesis, there is sufficient evidence that p > 0.O Reject the null hypothesis, there is insufficient evidence that p > 0.O Fail to reject the null hypothesis, there is insufficient evidence that p> 0.Fail to reject the null hypothesis, there is sufficient evidence thatp >0.Would you say the time series of antibody buildup factor is relativelypredictable from one week to the next? Explain.No, the data do not support a high serial correlation and do notindicate a predictable original time series from one week to the next.Yes, the data support a high positive serial correlation and indicate apredictable original time series from one week to the next.O Yes, the data support a high negative serial correlation and indicate apredictable original time series from one week to the next.

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Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week 4 7 8 Buildup Factor 2.3 4.6 6.2 7.5 8.0 9.4 10.6 12.1 To construct a serial correlation, we simply use data pairs (x, y) where x = original buildup factor data and y = original data shifted ahead by 1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8). Data for Serial Correlation x 2.3 4.6 6.2 7.5 8.0 9.4 10.6 y 4.6 6.2 7.5 8.0 9.4 10.6 12.1 A USE SALT For convenience, we are given the following sums. Ex = 48.6, Ey = 58.4, Ex² = 385.86, Ey? = 526.98, Exy = 448.7 (a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, 9 = a + bx. (Round your answers to four decimal places.) If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.)

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P