Statistical Analysis Intermediate Quiz

 



1) Measurements of nine earthquakes using a seismograph gave the following readings: 4.5, L, 5.5, H, 8.7, 8.9, 6.0, H, 5.2,Where L indicates that the earthquake had intensity below 4.0 and H indicates that the earthquake had intensity above 9.0. The median earthquake intensity of the sample is

1. Cannot be computed because all of the values are not known
2. 75
3. 6
4. 47

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2) X and Y are independent N(0,1) random variables. Which of the following is true

1. P(X<0)<P(X+Y<0)
2. P(X<0)=P(X-Y<0)
3. P(X>0)>P(X>Y)
4. P(X>Y)>P(X<Y)

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3) Y=Xβ + ε where Y is n×1 vector, X is n×n matrix  , β is n×1 vector of parameters  and ε is  N(0 n×1,I n×n) . Then the Best Linear Unbiased Estimator  (BLUE) of  β is

1. (XXT)-1XTY
2. (XTX)-1XTY
3. (XTX)T X-1Y
4. (XXT)XTY

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4) X and Y are N(0,1) random variables with positive correlation, then correlation between X+Y and X-Y is

1. 1
2. 0
3. Positive
4. Negative

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5) Which of the following does not fall into basic assumption of simple linear regression theory is

1. The parameters can be nonlinear
2. Error term follows normal distribution
3. The regressors can be nonlinear
4. Error components are uncorrelated

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6) If X follows LogNormal distribution then

1. Ln(X) is Normal
2. Density of X is Ln(density of normal)
3. Both of a and b
4. None of the above

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7) What parks method does?

1. Autoregressive model of order 1
2. Autoregressive model of order 2
3. Autoregressive model of order 5
4. Autoregressive model of order 10

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8) Poolability test?

1. F-test
2. Hausman Test
3. LM Test
4. None of the above

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9) Test for stationarity?

1. Dickey Fuller Test
2. Hausman Test
3. LM Test
4. Durbin Watson Test

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10) ARIMA means?

1. Autoregressive Independent Moving Average
2. Autoregressive Interlinked Moving Average
3. Autoregressive Initial Moving Average
4. Autoregressive Integrated Moving Average

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11) Hosmer –Lemeshow statistics follows which distribution?

1. Chi-square distribution
2. F distribution
3. t distribution
4. None of the above

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12) What is unbalanced panel data?

1. Unequal number of cross section for all time series
2. Unequal number of time series for all cross section
3. Both
4. None

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13) What is P-value?

1. The probability of obtaining a result at least as extreme as the one that was actually observed
2. Number of independent pieces of information that go into the estimate of a parameter
3. The probability that the test will reject a false null hypothesis
4. probability of making a decision to reject the null hypothesis when the null hypothesis is actually true

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14) What is Degrees Of Freedom?

1. Number of independent pieces of information that go into the estimate of a parameter
2. The probability that the test will reject a false null hypothesis
3. probability of making a decision to reject the null hypothesis when the null hypothesis is actually true
4. None of the above

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15) What is Power of a test?

1. The probability of obtaining a result at least as extreme as the one that was actually observed
2. Number of independent pieces of information that go into the estimate of a parameter
3. The probability that the test will reject a false null hypothesis
4. probability of making a decision to reject the null hypothesis when the null hypothesis is actually true

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16) What is Statistical significance?

1. The probability of obtaining a result at least as robust as the one that was actually observed
2. Number of independent pieces of information that go into the estimate of a parameter
3. The probability that the test will reject a false null hypothesis
4. Probability of making a decision to reject the null hypothesis when the null hypothesis is actually true

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17) The order of a AR process is determined by

1. Acf
2. Pacf
3. None of the above
4. Both ‘a’ and ’b’

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18) A plot of sample autocorrelations is termed as

1. Lag plot
2. Correlogram
3. Scatter plot
4. Spectral plot

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19) Correlogram is used in model identification stage for autoregressive moving average time series models

1. TRUE
2. FALSE
3. Can’t say
4. Maybe

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20) A finite order MA process cannot be expressed as an AR process of infinite order

1. TRUE
2. FALSE
3. Can’t say
4. Maybe

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21) Which of the model is a regression of the time series values against the white noise

1. Moving average model
2. Autoregressive model
3. Linear regression
4. None of the above

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22) Which of the model is a regression of the time series values against its own lag values

1. Moving average model
2. Autoregressive model
3. Linear regression
4. None of the above

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23) An example of a Random Walk model is

1. stock prices
2. exchange rates
3. both a and b
4. none of the above

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24) A non-stationary time series is one with

1. Time-varying mean
2. Time-varying variance
3. Both a and b
4. Time invariant mean and variance

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25) A time series data whose mean, variance and autocovariance is time invariant is

1. Stationary series
2. Non stationary series
3. Random walk
4. Purely random series

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26) In random walk without drift

1. The effect of shock persists throughout the time period
2. The effect of shock in the past die out over time
3. The effect of shock drift away quickly
4. There is no effect of past shocks

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27) A non stationary series that becomes stationary on  first differencing the series twice is a series that is

1. integrated of order zero
2. integrated of order one
3. integrated of order two
4. integrated of order three

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28) A series that is example for difference stationary process is

1. Random walk with drift
2. Random walk without drift
3. Both A and B
4. none of the above

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29) Though two time series are individually non stationary, their linear combination is stationary. This is an example of

1. Random walk
2. Spurious regression
3. Trend stationary
4. Cointegration

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30) Testing for Cointegration is given by

1. Dickey-Fuller test
2. Engel-Granger test
3. Error correction mechanism
4. F-test

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31) The model where Y depends only on its value in the previous time period and a random term is

1. Single equation model
2. AR(1) model
3. MA(1) model
4. ARIMA(1,1) model

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32) When Y depends on current and the previous time period error term, it is a

1. Single model equation
2. AR(1) model
3. MA(1) model
4. ARIMA(1,1) model

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33) ARIMA(1,2,3) means

1. The series has to be first differenced to make it stationary
2. The series has to be differenced twice to make it stationary
3. The series has to be differenced thrice to make it stationary
4. Can’t say about the stationary condition from the above information

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34) Multicollinearity can be detected if the regression function has

1. High R2 with all coefficients having high t ratios
2. Low R2 with almost all coefficients having low t ratios
3. High R2 with very few or no coefficient having high t ratios
4. Low R2 with almost all coefficients having low t ratios

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35) An example of a perfect collinear relationship is a quadratic or cubic function

1. TRUE
2. FALSE
3. Can be
4. Can’t say

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36) If a quantitative variable has ‘m’ categories we can introduce

1. Only ‘m-1’ dummy variables
2. Only ‘m+1’ dummy variables
3. Only ‘m’ dummy variables
4. Only ‘m*2’ dummy variables

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37) In multiple regression model the adjusted R2

1. Cannot be negative
2. Will never be greater than the regression R2
3. Equals the square of the correlation coefficient r
4. Cannot decrease when an additional explanatory variable is added

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38) Multicollinearity does not hurt if the objective of estimation is only for forecasting

1. TRUE
2. FALSE
3. Can’t say
4. No relation with forecasting

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39) Area under the normal curve with mean 0.5 and variance 1 is

1. 5
2. 0
3. 1
4. 25

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40) In a Logistic regression some of the variables used in the modeling are found to have p-values <0.05. This implies that the variables

1. have a significant effect on the outcome
2. do not have a significant effect on the outcome
3. depends on what the null hypothesis is
4. Can’t say anything

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41) Linear regression is applicable in a situation when the dependent variable and a suitable transformation of the independent Variables are

1. Highly positively correlated
2. Not correlated at all
3. Only negatively correlated
4. None of the above

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42) The estimated ‘beta’ coefficient (when we fit a linear regression of the form y = a + beta*x, on a given data set) follows a

1. Z-distribution
2. ‘t’-distribution
3. Any of the above
4. None of the above

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43) in a class of 50 students 10 have failed and their average of marks is 2.5. the total marks secured by the entire class were 281. find the avg marks of those who have passed.

6. 4
7. 2
8. 2
9. 2

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44) which of the following statement is incorrect?

1. median is more likely to be affected by the fluctuations of sampling than the arithmatic average.
2. median ignores the values of extreme items.
3. we can find out the total values of the items if we know their number and median.
4. if big or small items in a series receive greater importance median would be an unsuitable average.

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45) Which of the following is not a measure of central tendency?

1. percentile
2. quartile
3. standard deviation
4. mode

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46) Which of the following describe the middle part of a group of numbers?

1. measures of central tendency
2. measures of variability
3. measures of shape
4. measures of association

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47) the mean and standard deviation of a sample size of 10 were found to be 9.5 and 2.5 respectively. Later on on an additional observation was available with value 15 which was included in the sample. Find the mean and standard deviation of the 11 observation.

2. mean=10, sd=2.9
3. mean=11, sd=3
4. mean=10, sd=3.3
5. mean=11, sd=2.9

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48) a sample size of 15 has mean 3.5 and standard deviation 3. another sample of size 22 has mean 4.7 and standard deviation 4. if the two samples are pooled together, find the mean and the standard deviation of the combined sample.

5. mean=5.213, sd=14.4
6. mean=3.213, sd=12.4
7. mean=4.012, sd=11.4
8. mean=4.213, sd=13.4

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49) Mean, coefficient of variation is 50, 40% respectively. What would be SD?

1. sd=23
2. sd=25
3. sd=18
4. sd=20

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50) The Assumption of classical linear regression model is named as:

1. Box-Jenkins Assumptions
2. Box-Tiao Assumptions.
3. Komogorov-Smirnov Assumptions
4. None of them

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51) Suppose we have a regression equation y=a+b1x1+b2x2+b3x3+b4x4+b5x5, where x1,x2 and x4,x5 are correlated. Then what is the rank of Hessian matrix

1. 5
2. 6
3. 4
4. 3

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52) Given the data set  4 , 10 , 7 , 7 , 6 , 9 , 3 , 8 , 7 Find the mode

1. 7
2. 9
3. 7,3
4. 7,9

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53) Average salary is an example of

1. Continuous variable
2. Discrete Variable
3. All of the above
4. None of the above

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54) Which one of the following variables is not categorical?

1. Age of a person
2. Gender of a person: male or female
3. Choice on a test item: true or false
4. Marital status of a person (single, married, divorced, other)

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55) Which of the following statements is NOT true?

1. In a symmetric distribution, the mean and the median are equal.
2. The first quartile is equal to the twenty-fifth percentile.
3. In a symmetric distribution, the median is halfway between the first and the third quartiles.
4. The median is always greater than the mean.

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56) Which of the following is FALSE?

1. The numbers 3, 3, 3 have a standard deviation of 0.
2. The numbers 3, 4, 5 have the same standard deviation as 1003, 1004, 1005.
3. The numbers 1, 5, 6, 10 has a larger standard deviation than the numbers 1231, 1232, 1233, 1234.
4. The numbers 1, 5, 9 have a smaller standard deviation than 101, 105, 109.

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57) A random sample of 15 bank customers is selected to see how long (in minutes) they
waited in line during the lunch hour. There results are as follows:
4 15 3 8 4 9 3 2 11 1 5 6 6 13 3 Calculate Arithmetic Mean

6. 5
7. 3
8. 2
9. 7

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58) What is mode

1. most frequent occurance in the distribution
2. avergae across all values in the distribution
3. Middle value of the distribution when orderd in terms of magnitude
4. None of the above

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59) standard deviation is the only measure that we should use when making decision about any given data

1. yes
2. no
3. can’t say
4. None of the above

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60) The correlation coefficient provides:

1. a measure of the extent to which changes in one variable cause changes in another variable.
2. a measure of the strength of the linear association between two categorical variables.
3. a measure of the strength of the association (not necessarily linear) between two categorical variables.
4. a measure of the strength of the linear association between two quantitative variables

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