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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Buildup Factor | 2.1 | 4.6 | 6.2 | 7.5 | 8.0 | 9.3 | 10.6 | 12.4 |
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 | 2.1 | 4.6 | 6.2 | 7.5 | 8.0 | 9.3 | 10.6 |
y | 4.6 | 6.2 | 7.5 | 8.0 | 9.3 | 10.6 | 12.4 |
For convenience, we are given the following sums.
Σx = 48.3,
Σy = 58.6,
Σx2 = 383.11,
Σy2 = 532.46,
Σxy = 449.1
(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.)
a | |
b |
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 determinationr2.
(Use 4 decimal places.)
r | |
r2 |
Test
ρ > 0 at the 1% level of significance. (Use 2 decimal places.)
t | |
critical t |
Serial correlation, also known as autocorrelation, describes the extent to which the result in one period...
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...
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...
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...
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...
QUESTION 7 The data set Beer Large, which can be found in StatCrunch Shared Data Sets, gives the Alcohol, Carbohydrates and Calories for different brands of beer. The explanatory variable is x + Carbohydrates and the response variable is Y - Calories. Use this information to answer: Calculate the correlation between carbohydrates and calories. (4 decimal places) Row vars varo var var 8 var9 var 10 2 الميا ABV 4.1 5.4 4.43 4.13 5.9 4.9 Carbs 2.6 13.7 5.8 5...