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Match the LIST-I with LIST-II

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Observe the following table:

If the three-year moving averages of the above observations are A, B, C, D respectively, then the largest value of the three-year moving averages is :

For a straight line trend $y_t = a+bx$ for $n$ data by the method of least squares if, $n=8, \sum y=47.8, \sum xy=4.3$ and $\sum x^2=42$, then $y_t$ at $x=-3.5$ is _____.

[where $y_t$ represents trend value of y]

If the following table represents the three yearly moving averages of a data, then the value of $\frac{a+b+c+d}{3}$ is-

In reference to the Time Series Analysis, which of the following statements are correct?

A. Variations which generally occur due to the general tendency of the data to increase or decrease, are known as secular variations.

B. Variations which occur due to change in climate, wheather conditions, festivals etc. are known as seasonal variations.

C. Variations which occur due to some unpredictable forces are known as cyclic variations.

D. Variations which occur due to booms and depressions are known as irregular variations.

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Let $y_t=a+b(x_i-2021)$ be the straight line trend for the following data by least squares method:

the trend value for the year 2025 approximately is:

If 35, 70, 36, 59, 62 is the given annual time series, then 3-yearly moving averages are

If for the following data:

Using straight line trend by the method of least squares, the trend value for the year 2009 is :

Consider the following data:

Using method of least squares, the trend value for year 2004 will be

Which of the following statement(s) mentioned below do/does not specify the concept of time series analysis:-

A. Time series analysis comprises methods for analysing time series data in order to extract meaningful statistics and other characteristics of the data.

B. Time series analysis provides good forecasts or predictions of further values of the time series.

C. The time series analysis does not derive conclusions after arranging the time series in a systematic manner.

D. The measurement analysis and study of components of time series is called time series analysis.

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Which of the following graph plotted for the months against the three month moving average(3Yr MA) represents the given data correctly ?

[Four line graphs labelled 1-4, each plotting 3-Yr MA against month, showing different curve shapes and values]

A fire in a factory delaying production for some time is:

For the given five values 15, 24, 18, 33, 45, which of the following is not the three years moving average?

Consider the following data:

By using the method of least squares, the trend value for 1997 is :

For the given 9 values, 4,5,5,6,7,8,9,8,10, the three years moving averages are

Time series helps to

(A) derive conclusions after arranging the time series in a systematic manner.

(B) predict the future behavior of a variable.

(C) study the past behavior of data.

(D) plan future operations.

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If 18, Q, 19.2, T, 19.8 are the 5-year moving averages of the following series of observations:

16, P, 20, 18, R, 17, 19, S, 20, then

Match List-I with List-II

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The rise in prices of vegetables due to flood is an example of

For the given five values 10, a, 13, b, 25, the 3-years moving averages are 15, 18, 19. The value of a+b is

Irregular variations in a time series is :

For a certain data $(x_i, y_i)$, $i = 1,2,...,7$: $\sum_{i=1}^{7} y_i = 246$ and $\sum_{i=1}^{7} u_iy_i = 29$, $\sum_{i=1}^{7} u_i^2 = 28$ where $u_i = x_i - 2004$, then straight line trend by the method of least square is :

The pattern of data in the time series is influenced by a large variety of factors. Which of the following are not the components of the time series?

A. Regional component

B. Irregular component

C. Cyclone component

D. Seasonal component

Choose the correct answer from the options given below:

For the five values 12, $a$, 17, 21, 22, the three years moving averages are 13, 16, 20. The value of $a$ is

If for the following data:

If the equation of the straight line trend is $y=a+b(x_i-2013)$, then the trend value for the year 2018 is

For the given six values 17, 22, 21, 35, 40, 51, the three years moving averages are

For the following data:

The equation of the straight line trend is $y = a + b(x_i - 2007)$, then the trend value for the year 2011 is

Which of the following statements are correct?

A. If $x_1,x_2,x_3,\dots,x_n$ is the given annual time series, then 3-yearly moving averages are $\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots$

B. In the method of the least squares, if $(t_1,y_1),(t_2,y_2),\dots(t_n,y_n)$ denote the time series and $y_t$ are trend values of $y$, then $\sum(y-y_t)=0$

C. In the method of the least squares, the sum of squares of the deviations of the values of $y$ from their corresponding trend values is least.

D. The rise in prices before Diwali is an example of a cyclical trend.

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Match the components of time series with the examples associated to them.

Match List-I with List-II

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For the values 22, 25, 28, 31, 40, 43, the three yearly moving averages are

The break-even point is the level of production where