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51.

Which of the following analysis is a statistical process for estimating the relationships among variables?(a) Causal(b) Regression(c) Multivariate(d) All of the mentionedThe question was posed to me by my college professor while I was bunking the class.The above asked question is from Binary and Count Outcomes in section Statistical Inference and Regression Models of Data Science

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The correct option is (b) Regression

To explain I would say: Regression MODELS provide the SCIENTIST with a POWERFUL tool, ALLOWING predictions about PAST, present, or future events to be made with information about past or present events.

52.

How many outcomes are possible with bernoulli trial?(a) 2(b) 3(c) 4(d) None of the mentionedThe question was posed to me by my college director while I was bunking the class.I need to ask this question from Binary and Count Outcomes topic in portion Statistical Inference and Regression Models of Data Science

Answer» RIGHT choice is (a) 2

To explain I WOULD say: Bernoulli TRIAL is a random experiment with EXACTLY two possible outcomes.
53.

Point out the wrong statement.(a) Additive response models don’t make much sense if the response is discrete, or strictly positive(b) Transformations are often easy to interpret in linear model(c) Regression models are used to predict one variable from one or more other variables(d) All of the mentionedI had been asked this question during an online interview.The doubt is from Binary and Count Outcomes topic in portion Statistical Inference and Regression Models of Data Science

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Correct OPTION is (b) Transformations are OFTEN easy to INTERPRET in linear model

Explanation: Transformations are often hard to interpret in linear model.

54.

CLT is mostly useful as an approximation.(a) True(b) FalseThis question was posed to me in final exam.This intriguing question originated from Likelihood topic in division Statistical Inference and Regression Models of Data Science

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The correct answer is (a) True

Explanation: The CLT APPLIES in an ENDLESS variety of settings.

55.

The _________ basically states that the sample mean is consistent.(a) LAN(b) LLN(c) LWN(d) None of the mentionedThe question was asked in exam.Question is taken from Common Distributions in division Statistical Inference and Regression Models of Data Science

Answer» RIGHT choice is (b) LLN

To explain: LLN stands for LAW of large NUMBERS.
56.

Which of the following is also referred to as random variable?(a) stochast(b) aleatory(c) eliette(d) all of the mentionedThis question was posed to me in semester exam.This interesting question is from Introduction to Statistical Inference topic in portion Statistical Inference and Regression Models of Data Science

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The correct OPTION is (B) aleatory

The EXPLANATION: RANDOM variable is also KNOWN as stochastic variable.

57.

The _________ of the Chi-squared distribution is twice the degrees of freedom.(a) variance(b) standard deviation(c) mode(d) none of the mentionedThe question was asked in an international level competition.Origin of the question is Likelihood topic in portion Statistical Inference and Regression Models of Data Science

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The correct OPTION is (a) variance

To EXPLAIN: The mean of the Chi-squared is its degrees of FREEDOM.

58.

Which of the following theorem states that the distribution of averages of iid variables, properly normalized, becomes that of a standard normal as the sample size increases?(a) Central Limit Theorem(b) Central Mean Theorem(c) Centroid Limit Theorem(d) All of the mentionedThis question was addressed to me in a national level competition.Origin of the question is Common Distributions in chapter Statistical Inference and Regression Models of Data Science

Answer» RIGHT choice is (a) Central LIMIT Theorem

Easy explanation - The Central Limit Theorem (CLT) is one of the most IMPORTANT theorems in statistics.
59.

Point out the wrong statement.(a) A random variable is a numerical outcome of an experiment(b) There are three types of random variable(c) Continuous random variable can take any value on the real line(d) None of the mentionedThe question was asked by my college director while I was bunking the class.My question is based upon Introduction to Statistical Inference topic in division Statistical Inference and Regression Models of Data Science

Answer» RIGHT ANSWER is (b) There are THREE types of RANDOM variable

Easiest explanation - There are two types of random variable-continuous and discrete.
60.

Which of the following implies no relationship with respect to correlation?(a) Cor(X, Y) = 1(b) Cor(X, Y) = 0(c) Cor(X, Y) = 2(d) All of the mentionedThis question was addressed to me in quiz.I would like to ask this question from Introduction to Regression Models topic in chapter Statistical Inference and Regression Models of Data Science

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Right option is (B) Cor(X, Y) = 0

Easy explanation - Correlation is a statistical technique that can show whether and how strongly pairs of VARIABLES are related.

61.

Which of the following tool is used for constructing confidence intervals and calculating standard errors for difficult statistics?(a) baggyer(b) bootstrap(c) jacknife(d) none of the mentionedI had been asked this question in exam.This interesting question is from Statistical Inference Concepts in section Statistical Inference and Regression Models of Data Science

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Right option is (B) BOOTSTRAP

The BEST EXPLANATION: The bootstrap procedure follows from the so called bootstrap principle.

62.

The beta distribution is the default prior for parameters between ____________(a) 0 and 10(b) 1 and 2(c) 0 and 1(d) None of the mentionedThe question was asked in exam.My doubt stems from Likelihood in section Statistical Inference and Regression Models of Data Science

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Correct option is (c) 0 and 1

To EXPLAIN I would SAY: BAYESIAN statistics posits a prior on the parameter of interest.

63.

Point out the wrong statement.(a) The normal distribution is asymmetric and peaked about its mode(b) A constant times a normally distributed random variable is also normally distributed(c) Sample means of normally distributed random variables are again normally distributed(d) None of the mentionedI have been asked this question during an interview.This interesting question is from Common Distributions in chapter Statistical Inference and Regression Models of Data Science

Answer» CORRECT CHOICE is (a) The normal distribution is ASYMMETRIC and PEAKED about its mode

For EXPLANATION: The normal distribution is symmetric and peaked about its mean.
64.

Which of the following mean is a mixture of the MLE and the prior mean?(a) interior(b) exterior(c) posterior(d) all of the mentionedI have been asked this question during an interview.The origin of the question is Likelihood topic in chapter Statistical Inference and Regression Models of Data Science

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Right CHOICE is (c) posterior

To EXPLAIN I WOULD SAY: MLE stands for maximum LIKELIHOOD.

65.

Which of the following is a property of likelihood?(a) Ratios of likelihood values measure the relative evidence of one value of the unknown parameter to another(b) Given a statistical model and observed data, all of the relevant information contained in the data regarding the unknown parameter is contained in the likelihood(c) The Resultant likelihood is multiplication of individual likelihood(d) All of the mentionedThe question was asked in unit test.Question is from Likelihood in chapter Statistical Inference and Regression Models of Data Science

Answer» RIGHT answer is (d) All of the mentioned

Easiest explanation - Likelihood is the HYPOTHETICAL probability that an EVENT that has ALREADY occurred would yield a specific OUTCOME.
66.

Point out the correct statement.(a) Asymptotics are incredibly useful for simple statistical inference and approximations(b) Asymptotics often lead to nice understanding of procedures(c) An estimator is consistent if it converges to what you want to estimate(d) All of the mentionedThe question was posed to me during an internship interview.The above asked question is from Likelihood in division Statistical Inference and Regression Models of Data Science

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Right answer is (d) All of the mentioned

To explain I would say: Consistency is NEITHER NECESSARY nor SUFFICIENT for ONE estimator to be better than another.

67.

Which of the following of a random variable is a measure of spread?(a) variance(b) standard deviation(c) empirical mean(d) all of the mentionedI got this question in my homework.This interesting question is from Probability and Statistics topic in section Statistical Inference and Regression Models of Data Science

Answer» RIGHT option is (a) VARIANCE

The explanation is: Densities with a HIGHER variance are more SPREAD out than densities with a lower variance.
68.

The expected value or _______ of a random variable is the center of its distribution.(a) mode(b) median(c) mean(d) bayesian inferenceI got this question during an interview.My question is based upon Probability and Statistics in section Statistical Inference and Regression Models of Data Science

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Right OPTION is (C) mean

Explanation: A probability model CONNECTS the data to the population USING ASSUMPTIONS.

69.

Which of the following random variable that take on only a countable number of possibilities?(a) Discrete(b) Non Discrete(c) Continuous(d) All of the mentionedI got this question in an international level competition.My doubt is from Introduction to Statistical Inference in chapter Statistical Inference and Regression Models of Data Science

Answer» RIGHT choice is (a) Discrete

For explanation: Continuous RANDOM VARIABLE can take any value on some subset of the REAL line.
70.

Which of the following is the probability calculus of beliefs, given that beliefs follow certain rules?(a) Bayesian probability(b) Frequency probability(c) Frequency inference(d) Bayesian inferenceThis question was addressed to me in class test.The origin of the question is Introduction to Statistical Inference topic in section Statistical Inference and Regression Models of Data Science

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Right OPTION is (a) BAYESIAN probability

The explanation is: Data scientists tend to fall within shades of gray of these and various other SCHOOLS of INFERENCE.

71.

Which of the following outcome is odd man out in the below figure?(a) R Squared(b) Kappa(c) RMSE(d) All of the mentionedThis question was addressed to me in exam.This interesting question is from Introduction to Regression Models topic in portion Statistical Inference and Regression Models of Data Science

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The CORRECT OPTION is (B) Kappa

The explanation is: Kappa is categorical OUTCOME.

72.

The square root of the variance is called the ________ deviation.(a) empirical(b) mean(c) continuous(d) standardI have been asked this question in final exam.My query is from Probability and Statistics topic in portion Statistical Inference and Regression Models of Data Science

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Right choice is (d) STANDARD

Explanation: Standard DEVIATION (SD) is the MEASURE of spread of the NUMBERS in a set of data from its MEAN value.