Bivariate Statistical Analysis Flashcards

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Bivariate regression can be applied on two metric variables.

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The mathematical symbol Y is commonly used for the independent variable, and X typically denotes the dependent variable.

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The statistical significance of a correlation can be tested using the t-test.

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In correlation analysis, if associated values of the two variables differ from their means in the same direction, their covariance will be negative.

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'Test of association' is a general term that refers to a number of bivariate statistical techniques used to measure whether or not two variables are associated with each other.

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In situations in which the data are ordinal, the Pearson correlation technique may be used.

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Regression is a statistical technique for measuring the curvilinear association between a dependent and independent variable.

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In correlation analysis, the alternative hypothesis is typically stated as ρ ≠ 1.

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If r = 0, it indicates that the two variables under study are interdependent.

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The Pearson's correlation coefficient is a standardised measure of effect size.

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The coefficient of determination measures the part of the total variance of Y that is accounted for by knowing the value of X.

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Correlation and regression analysis can be used to test for simple associations between two nominal variables.

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The Chi-square test is typically used for nominal variables which are dichotomous in nature.

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In correlation analysis, the null hypothesis is typically stated as ρ = 0.

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The Pearson correlation analysis is a statistical procedure that tests for differences between two interval variables.

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If the value of r is +1.0, there is no relationship between the two variables under study.

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If the value of r = 0, there is a perfect positive relationship between the two variables under study.

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A correlation analysis can be used to ascertain whether or not gender is related to brand awareness.

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The Pearson's correlation coefficient is a statistical measure of causality between two variables.

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In a regression equation, the slope of the line

\beta

is the change in Y that occurs due to a corresponding change of one unit of X.

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A correlation matrix can quickly give the researcher an overview of the direction, strength and statistical significance of each paired relationship.

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To compute the Chi-square value for the contingency table, the researcher must first identify an expected distribution for that table.

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To calculate the expected frequencies for the cells in a cross tabulation, the actual observed numbers of respondents in each individual cell is required.

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The Chi-square test analyses the significance of the data in an R x C contingency table, in which R stands for row and C stands for column.

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All of the following statistical tests can be used to test for associations between variables, except:

A) Spearman's rank correlation.
B) regression analysis.
C) Chi-square test.
D) ANOVA.

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Which type of statistical test is appropriate for testing whether or not there is an association between two ordinal variables?

A) Chi-square test
B) Spearman's rank correlation
C) Regression analysis
D) Paired-samples t-test

Question

A researcher would like to test whether or not gender (that is, male or female) is related to brand awareness (that is, aware or unaware). Which of the following statistical tests would you suggest?

A) Spearman's rank correlation
B) Independent samples t-test
C) Chi-square test
D) Regression analysis

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One of the simplest techniques for describing sets of relationships between two interval variables is the cross-tabulation.

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All of the following statements about the Correlation Coefficient are true, except:

A) It provides direction of association.
B) It provides strength of association.
C) It provides statistical significance of association.
D) It provides the variance in associations.

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In regression analysis, the error of a predicted score is found by subtracting the predicted value of Y from the actual value of Y.

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An F-test can be applied to a regression to determine the residual error.

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A Spearman's rank-order correlation coefficient examines the relationship between two ordinal variables.

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If there is no relationship between two variables, then the Pearson's correlation coefficient between them will be:

A) +1.0.
B) -1.0.
C) +0.50.
D) 0.

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When testing for association between two variables, it is possible that they can be statistically significant but not appear to be meaningfully associated.

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Bivariate linear regression investigates the relationship between a dependent variable and two independent variables.

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The Chi-square test tests the goodness of fit of the observed distribution with the expected distribution.

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To use the Chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio or interval scale.

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The appropriate statistical test to use to calculate the association between two nominal variables is:

A) Spearman's rank correlation
B) regression analysis.
C) Chi-square test.
D) correlation analysis.

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The least-squares regression line minimises the sum of the squared deviations of the actual values from the predicted values in the regression line.

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A researcher would like to predict sales volume against advertising dollar expenditure. Which of the following statistical tests would you suggest?

A) Spearman's rank correlation
B) Correlation analysis
C) Chi-square analysis
D) Regression analysis

Question

The correlations table below indicates that: Correlations
** Correlation is significant at the 0.01 level (two-tailed).

A) about 75 per cent of variance in sales can be explained by the variance in advertising expenditure.
B) about 57 per cent of the variance in advertising expenditure can be explained by the variance in sales.
C) about 57 per cent of the variance in sales can be explained by the variance in advertising expenditure.
D) about 75 per cent of the variance in advertising expenditure can be explained by the variance in sales.

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To determine the proportion of variance in the dependent variable that is explained by the independent variable, which of the following needs to be derived?

A) The Pearson's correlation coefficient
B) The regression coefficient
C) The residual error
D) The coefficient of determination

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The coefficient of determination, r², ranges from:

A) zero to +1.0.
B) -1.0 to zero.
C) -1.0 to +1.0.
D) -2.0 to +2.0.

Question

In a regression equation, if the average value of X is 4.6, the average value of Y is 2.3, and the slope is -1.2, then the y-intercept is approximately:

A) 5.70.
B) 0.42.
C) 7.82.
D) 3.22.

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If the correlation between X and Y is -0.42, approximately what percentage of the variance in Y can be explained by X?

A) 18 per cent
B) 42 per cent
C) 21 per cent
D) 84 per cent

Question

The formula below is the formula for _______________________.

A) the standard error of the estimate
B) the standard error of the mean
C) the coefficient of determination
D) the Pearson's correlation coefficient

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In correlation analysis, the strength of the association between the variables under investigation is determined by:

A) how close the coefficient is to zero.
B) how close the significance value is to 1.
C) how close the coefficient is to ±1.
D) whether the coefficient is positive or negative.

Question

Which of the following statements is true?

A) Causation always exists when there is a high correlation between the variables.
B) Variables can be statistically related even if they are not causally related.
C) Regression can be used to measure the linear association between two nominal variables.
D) When the correlation between two variables is 0, it implies a perfect positive association.

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If the relationship between two variables is such that both variables are caused by a third variable, then the original relationship between the first two variables is said to be:

A) strong.
B) weak.
C) neutral.
D) spurious.

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In regression analysis, the deviation not explained by the regression is known as the:

A) sampling error.
B) residual error.
C) total error.
D) standardised error.

Question

Suppose that two groups of consumers (for example, males and females) are asked to rank, in order of preference, the brands of a product class (for example, microwave meals). Which statistical test would be appropriate to determine the agreement between the two groups?

A) Correlation analysis
B) Chi-square analysis
C) Spearman's correlation
D) Independent samples t-test

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What is the most common cut-off significance value for accepting or rejecting hypothesis?

A) .05
B) .15
C) .20
D) .25

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When examining regression results, how well the model fits the data is determined by consulting the:

A) R-square.
B) F statistic.
C) standardised coefficient.
D) calculated t-value.

Question

In the regression equation, $\beta$ is the: $Y = \alpha + \beta X$

A) residual error.
B) independent variable.
C) regression coefficient.
D) standardised coefficient.

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When the correlation between two variables is -0.32 and its associated significance level (p-value) is 0.0352, it is implied that:

A) there is no relationship between the variables.
B) there is a weak inverse relationship between the variables.
C) there is a moderate inverse relationship between the variables.
D) there is a strong inverse relationship between the variables.

Question

When the correlation between two variables is +0.52 and its associated significance level (p-value) is 0.153, it is implied that:

A) there is no relationship between the variables.
B) there is a weak positive relationship between the variables.
C) there is a moderate positive relationship between the variables.
D) there is a strong positive relationship between the variables.

Question

In the regression equation, is the symbol for the:

A) residual error.
B) y-intercept.
C) regression coefficient.
D) standard error of the estimate.

Question

The correlations table below indicates that: Correlations
** Correlation is significant at the 0.01 level (two-tailed).

A) about 35 per cent of variance in productivity can be explained by the variance in months employed.
B) about 71 per cent of the variance in productivity can be explained by the variance in months employed.
C) about 13 per cent of the variance in productivity can be explained by the variance in months employed.
D) there is no association between productivity and months employed.

Question

Which of the following is not true for regression?

A) It determines the direction of association.
B) It determines the strength of association.
C) It predicts value of one variable based on the value of another variable.
D) It determines the variance in the direction of the relationship between three or more variables.

Question

Under which of the following condition should the researcher examine the data for problem?

A) When a regression returns a standardized β coefficient less than 1 or greater than 1
B) When a regression returns a standardized β coefficient less than 2 or greater than 2
C) When a regression returns a standardized β coefficient less than 5 or greater than 5
D) When a regression returns a standardized β coefficient less than 10 or greater than 10

Question

Two groups of students - those looking to study science degrees and those looking to study business degrees - are asked to rank, in order of preference, the universities they are applying for. The researcher then wants to determine the correlation between the two groups. Which statistical test is most appropriate?

A) Pearson's correlation coefficient
B) Chi-square test
C) Spearman's rank-order correlation coefficient
D) Independent samples t-test

Question

The regression output for sales and advertising spend is shown below. Model summary
000) Coefficients(a) a Dependent variable: Sales (A a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) The above shows that: A) approximately 45 per cent of the variance in sales can be explained by advertising spend. B) approximately 43 per cent of the variance in Sales can be explained by advertising spend. C) approximately 14 per cent of the variance in sales can be explained by advertising spend. D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

" class="answers-bank-image d-block" loading="lazy" > a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) Coefficients(a) a Dependent variable: Sales (A a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) Coefficients(a) a Dependent variable: Sales (A a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) The above shows that: A) approximately 45 per cent of the variance in sales can be explained by advertising spend. B) approximately 43 per cent of the variance in Sales can be explained by advertising spend. C) approximately 14 per cent of the variance in sales can be explained by advertising spend. D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

" class="answers-bank-image d-block" loading="lazy" > a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) The above shows that: A) approximately 45 per cent of the variance in sales can be explained by advertising spend. B) approximately 43 per cent of the variance in Sales can be explained by advertising spend. C) approximately 14 per cent of the variance in sales can be explained by advertising spend. D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

" class="answers-bank-image d-block" loading="lazy" > a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) Coefficients(a) a Dependent variable: Sales (A a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) The above shows that: A) approximately 45 per cent of the variance in sales can be explained by advertising spend. B) approximately 43 per cent of the variance in Sales can be explained by advertising spend. C) approximately 14 per cent of the variance in sales can be explained by advertising spend. D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

" class="answers-bank-image d-block" loading="lazy" > a Predictors: (Constant), advertising spend
ANOVA(b)
11eb99e4_52c7_7aad_ab5d_a97cebb53082_TB8823_00 a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
11eb99e4_52c7_7aae_ab5d_e1db6a89764e_TB8823_00 a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

000) Coefficients(a) a Dependent variable: Sales (A a Dependent variable: Sales (A$'000)
The above shows that: