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Statistics 1: Contingency Tables

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Questions and Answers

What do the sums of frequencies or relative frequencies in rows define?

The joint distribution of X and Y
The marginal distribution of the variable X (correct)
The variance of X
The conditional distribution of Y given X

What is the meaning of fi. in the context of contingency tables?

The joint frequency of X and Y
The variance of X
The relative frequency of the group of individuals presenting modality xi of X (correct)
The relative frequency of the group of individuals presenting modality yi of Y

What is the formula for the relative frequency fij?

fij = nij / (ni. * nj.)
fij = nij / n (correct)
fij = nij / (ni. * n.j)
fij = nij / nij

What is the meaning of n.j in the context of contingency tables?

The subtotal of the frequencies of the groups of individuals in the j-th column (A) Signup and view all the answers

What is the sum of the relative frequencies fij over all i and j?

1 (D) Signup and view all the answers

What is the name of the distribution defined by the sums of frequencies or relative frequencies in columns?

The second marginal distribution (A) Signup and view all the answers

What is the purpose of correlation coefficients, scatterplots, and regression equations?

To summarize and interpret the strength and direction of the relationship between the quantitative variables. (B) Signup and view all the answers

What is X in the context of contingency tables?

The response of an individual to the variable X. (A) Signup and view all the answers

What is represented by nij in a contingency table?

The frequency of the group of individuals presenting both modality xi of X and modality yj of Y. (B) Signup and view all the answers

What is the purpose of a contingency table?

To summarize the frequency of different groups of individuals presenting different modalities of two variables. (A) Signup and view all the answers

What is the graphical representation of the relationship between two quantitative variables?

Scatter plot (A) Signup and view all the answers

What are the elements of a contingency table?

Rows representing the modalities of X and columns representing the modalities of Y. (A) Signup and view all the answers

What does the conditional distribution given the number of rooms is 4 represent?

The probability of the surface area given the number of rooms (C) Signup and view all the answers

What is the formula to calculate the conditional variance?

V (X|Y = yi ) = k X fX=xi |Y =yj x2i − m2X|Y =yi (B) Signup and view all the answers

What is independence in the context of statistical variables?

The absence of a relationship between two statistical variables (B) Signup and view all the answers

What is the condition for two variables to be independent?

fij = fi..f.j , ∀i = 1,.., k and j = 1,.., l (D) Signup and view all the answers

What is represented in a contingency table?

The joint probability distribution of two variables (A) Signup and view all the answers

What is an example of a statistical problem that can be represented by a contingency table?

The relationship between the number of rooms and surface area of dwellings (B) Signup and view all the answers

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