Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the resultin 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 islow (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the bookIbbotson 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 thevaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8weeks. Results are shown in the following time series.Original Time SeriesWeekBuildup Factor2346.82.14.76.27.58.09.310.712.4To construct a serial correlation, we simply use data pairs (x, y) where x =1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8).original buildup factor data and y = original data shifted ahead byData for Serial Correlation2.14.76.26.27.510.77.58.09.39.3y4.78.010.712.4For convenience, we are given the following sums.Σx 48.5, Σy- 58.8 , Σx2386.17, Σy2535.52, Σxy= 452.1(a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line,ŷ = a + bx. (Use 4 decimal places.)ab.If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Use 2 decimal places.)(b) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.)Test p 0 at the 1% level of significance. (Use 2 decimal places.)critical tConclusionO Reject the null hypothesis, there is sufficient evidence that p 0.O Reject the null hypothesis, there is insufficient evidence that p 0.Fail to reject the null hypothesis, there is insufficient evidence that p 0.O Fail to reject the null hypothesis, there is sufficient evidence that p 0.Would you say the time series of antibody buildup factor is relatively predictable from one week to the next? Explain.O Yes, the data support a high negative serial correlation and indicate a predictable original time series from one week to the next.O Yes, the data support a high positive serial correlation and indicate a predictable original time series from one week to thenext.O No, the data do not support a high serial correlation and do not indicate a predictable original time series from one week to thenext.

Name: Serial correlation, also known as autocorrelation, describes the exte
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the resultin the next period. A time series with high serial correlation is said to be very predictable from one

Question

Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the resultin 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 islow (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the bookIbbotson 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 thevaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8weeks. Results are shown in the following time series.Original Time SeriesWeekBuildup Factor2346.82.14.76.27.58.09.310.712.4To construct a serial correlation, we simply use data pairs (x, y) where x =1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8).original buildup factor data and y = original data shifted ahead byData for Serial Correlation2.14.76.26.27.510.77.58.09.39.3y4.78.010.712.4For convenience, we are given the following sums.Σx 48.5, Σy- 58.8 , Σx2386.17, Σy2535.52, Σxy= 452.1(a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line,ŷ = a + bx. (Use 4 decimal places.)ab.If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Use 2 decimal places.)(b) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.)Test p > 0 at the 1% level of significance. (Use 2 decimal places.)critical tConclusionO Reject the null hypothesis, there is sufficient evidence that p > 0.O Reject the null hypothesis, there is insufficient evidence that p > 0.Fail to reject the null hypothesis, there is insufficient evidence that p > 0.O Fail to reject the null hypothesis, there is sufficient evidence that p > 0.Would you say the time series of antibody buildup factor is relatively predictable from one week to the next? Explain.O Yes, the data support a high negative serial correlation and indicate a predictable original time series from one week to the next.O Yes, the data support a high positive serial correlation and indicate a predictable original time series from one week to thenext.O No, the data do not support a high serial correlation and do not indicate a predictable original time series from one week to thenext.

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The intercept and the slope of an estimated simple linear regression model y^=a+bx is given by…