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 company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year $ per capita 2 34.09 4 6 32.21 37.81 43.32 44.67 49.62 51.88 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 43.32 44.67 49.62 49.62 51.88 32.21 34.09 37.81 37.81 43.32V 34.09 44.67 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a 4.6884 |x b0.9650 |× If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.)
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A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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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 company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video
games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here.
Original Time Series
Year
$ per capita
2
3
4
6.
32.21
34.09
37.81
43.32
44.67
49.62
51.88
(a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y =
original data shifted ahead by
one time period. Construct the data set (x, y) for serial correlation by filling in the following table.
34.09
37.81
43.32
32.21
43.32
44.67
49.62
y
34.09
37.81
44.67
49.62
51.88
(b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal
places.)
a 4.6884
b0.9650
If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.)
$ 41.36
]× per capita
(c) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.)
r0.9615
20.9245
Test p> 0 at the 1% level of significance. (Use 2 decimal places.)
t7.00
critical t|5.60](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95b47d80-06eb-409d-8990-55d0162d335e%2F59c2c301-cbe9-4f67-ba87-5f6d17933ee4%2Fgyma0a_processed.png&w=3840&q=75)
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