Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
To answer this question, we need to evaluate both the Assertion (A) and the Reason (R) individually, then determine if R explains A.
Assertion (A): Additive model considers the total of various components resulting in the given values of the overall time series and it is stated as: \(Y=T+C+S+I\).
The assertion describes the additive model of time series decomposition, where \(Y\) is the observed time series value, \(T\) is the trend, \(C\) is the cycle, \(S\) is the seasonal component, and \(I\) is the irregular component. In the additive model, these components are combined additively. This assertion is correct.
Reason (R): Multiplicative model assumes that the various components interact in a multiplicative manner to produce the given values of the overall time series and can be stated as \(Y=T \times C \times S \times I\).
The reason describes the multiplicative model of time series decomposition. In this model, the components interact with each other multiplicatively. The formulation given (\(Y=T \times C \times S \times I\)) is correct for the multiplicative model.
Evaluation:
- Both Assertion (A) and Reason (R) are individually correct statements. However, the reason (R) does not explain the assertion (A) because they describe different models of time series decomposition (additive vs. multiplicative).
Conclusion: Therefore, the correct answer is: Both (A) and (R) are correct but (R) is not the correct explanation of (A).
Important Questions from Statistics
- Match the LIST-I with LIST-II
LIST-I LIST-II A. Sampling error I. Values that describe the characteristics of a population B. Parameters II. The standard deviation of the sampling distribution C. Sampling fraction III. Variation among sample statistics due to change D. Standard error IV. Proportion of the population contained in a sample
Choose the correct answer from the options given below: Match List - I with List - II.
List - I List - II A. Sample proportion P = x/n I. $\frac{\sigma}{\sqrt{n}}$ B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ II. $\sigma^2 \sqrt{\frac{2}{n}}$ C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$
Choose the correct answer from the options given below :- The measurement or determinations of length, height, weight, volume, area, pressure etc. comes under:
- Which of the following options explain what a 'mean' assumes ?
(i) an interval level of measurement
(ii) a nominal level of measurement
(iii) an ordinal level of measurement
(iv) a ratio level of measurement - Match List I with List II:
List I List II (a) Alpha Level (I) The index of magnitude or strength of relationship (b) Level of Significance (II) The point at which one would reject the null hypothesis and accept the alternate hypothesis (c) Critical Region (III) Another name for alpha level (d) Effect size indicatior (IV) A marked area which would be called a rare event
