Deck 17: Correlation and Regression

Question 1

is a statistical procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables.

A) Product moment correlation
B) Partial correlation coefficient
C) ANOVA
D) Regression analysis

Answer 1

D

Question 2

The denotes the change in the predicted value, Y^{^} , per unit change in X₁ when the other independent variables, X₂ to X_k, are held constant.

A) part regression coefficient
B) part correlation coefficient
C) partial correlation coefficient
D) partial regression coefficient

Answer 2

D

Question 3

Which of the following is a measure of nonmetric correlation?

A) Pearson product moment correlation
B) Kendall's tau
C) Spearman's rho
D) both B and C

Answer 3

D

Question 4

Which statement about the correlation coefficient, r, is true?

A) Data obtained by using rating scales with a small number of categories tends to deflate r.
B) The calculation of r assumes that X and Y are metric variables whose distributions have the same shape.
C) The correlation coefficient computed for a population is denoted by q(rho).
D) All of the statements are true.

Question 5

Which statement is not true about partial regression coefficients?

A) Partial regression coefficients have an order associated with them.
B) The combined effects of X₁ and X₂ on Y are additive. In other words, if X₁ and X₂ are each changed by one unit, the expected change in Y would be (b₁ + b₂).
C) The beta coefficients are the partial regression coefficients obtained when all the variables (Y, X_1, X_2...X_k) have been standardized to a mean of 0 and a variance of 1 before estimating the regression equation.
D) Both A and B are not true.

Question 6

A technique for fitting a straight line to a scattergram by minimizing the square of the vertical distances of all the points from the line is known as the _ .

A) scatter diagram plot
B) maximum residual procedure
C) sum of square errors procedure
D) least- square procedure

Question 7

In bivariate regression, which statement is true concerning the coefficient of determination, r²?

A) r² varies between 0 and 1.
B) r² is the square of the simple correlation coefficient obtained by correlating the two variables.
C) r² signifies the proportion of the total variation in Y accounted for by the variation in X.
D) All are correct.

Question 8

The equation for r is represented as _.

A) S_xS_y/COV
B) COV_xy/ S_xS_y
C) COV_xy/ S_x²S_y² D) S_x²S_y²/COV

Question 9

Which statistic is associated only with multiple regression and not with bivariate regression?

A) partial F test
B) adjusted R²
C) estimated or predicted value (Y^{^} )
D) both A and B

Question 10

Which statement is not true about regression analysis?

A) Regression analysis is a powerful and flexible procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables.
B) Regression can be used to predict the values of the dependent variable.
C) The terms dependent or criterion variables and independent or predictor variables in regression analysis do not imply that the criterion variable is dependent on the independent variables in a causal sense.
D) Regression analysis can be used to determine if color preference is related to product size and price.

Question 11

r² measures .

A) the proportion of error variation
B) the proportion of variation in Y related to the variation of the categories of X
C) the proportion of variation in one variable that is explained by the other
D) the proportion of variation in Y due to the variation within each of the categories of X

Question 12

What is the bivariate regression equation if sample observations are used to predict Y?

A) Y^{^} _i = a + bx_i B) Y^{^} = þ₀ + þ₁ X_i
C) Y^{^} = a + b₁X₁ + b₂X₂ D) Y^{^} _i = þ₀ + þ₁ X_{i +} e_i

Question 13

is best to use to determine how strongly sales are related to advertising expenditures.

A) Multiple regression analysis
B) Partial correlation coefficient
C) Product moment correlation (r)
D) ANOVA

Question 14

When considering nonmetric correlation, as a rule of thumb, is to be preferred when a large number of cases fall into a relatively small number of categories (thereby leading to a large number of ties).

A) Spearman's rho
B) Pearson product moment correlation
C) chi- square
D) Kendall's tau

Question 15

variables may be used as predictors or independent variables by coding them as dummy variables.

A) Categorical
B) Ratio
C) Interval
D) All of the above

Question 16

Which statement is not correct about the partial correlation coefficient?

A) The partial correlation coefficient can be calculated by a knowledge of the simple correlations alone.
B) Partial correlations can be helpful for detecting spurious relationships.
C) The partial correlation coefficient represents the correlation between Y and X when the linear effects of the other independent variables have been removed from X but not from Y.
D) The partial correlation coefficient is generally viewed as more important than the part correlation coefficient.

Question 17

Partial correlations have an order associated with them. The order indicates how many variables are being adjusted or controlled. The simple correlation coefficient, r, has a , as it does not control for any additional variables when measuring the association between two variables. The coefficient r_sy.z is a partial correlation coefficient, as it controls for the effect of one additional variable, Z.

A) first- order; second- order
B) zero- order; second- order
C) first- order; third- order
D) zero- order; first- order

Question 18

Which statement is not true about the constant b in the bivariate regression equation Y^{^} _i = a + bX_i?

A) It is the slope of the regression line and it indicates the expected change in Y when X is changed by one unit.
B) It may be computed as b = COV_xy/S_x².
C) It is the intercept of the regression line and it indicates the value of Y when X is zero.
D) It is usually referred to as the non- standardized regression coefficient.

Question 19

is the appropriate test statistic to use to determine the significance of the coefficient of determination in bivariate regression.

A) F statistic
B) m² C) Z statistic
D) T statistic

Question 20

The relationship between X and Y is spurious if .

A) the correlation between X and Y disappears when the effect of Z is controlled
B) Y decreases exponentially with decreases in X
C) Y increases exponentially with increases in X
D) both A and C are correct

Question 21

r_y(x.z) represents the .

A) partition correlation
B) Pearson correlation
C) part correlation
D) partial correlation

Question 22

The is a statistic summarizing the strength of association between two metric variables.

A) ANOVA
B) partial correlation coefficient
C) product moment correlation
D) multiple regression analysis

Question 23

Which equation depicts the relationship between the standardized and non- standardized regression coefficients?

A) B²_yx = b_yx(S_x/S_y)
B) B²_yx = b_yx(S²_x/S²_y)
C) B_yx = b_yx(S_x/S_y)
D) B_yx = b_yx(S²_x/S²_y)

Question 24

is a statistical technique that simultaneously develops a mathematical relationship between two or more independent variables and an interval- scaled dependent variable.

A) Multiple regression
B) Bivariate regression
C) The least- squares procedure
D) Chi- square

Question 25

Which statement is not true about correlation matrices?

A) A correlation matrix indicates the coefficient of correlation between each pair of variables.
B) The upper triangular portion of the matrix is a mirror image of the lower triangular portion.
C) Usually only the lower portion of the matrix is considered.
D) The diagonal elements all equal 0.

Question 26

The regression equation for a categorical variable with four categories would be modeled as .

A) Y^{^} = b₁ D_{1 +} b₂ D_{2 +} b₃D_{3 +} b₄D₄ B) Y^{^} = b₁ D_{1 +} b₂ D_{2 +} b₃D₃
C) Y^{^} _i = a + b₁ D_{1 +} b₂ D_{2 +} b₃D_{3 +} b₄D₄ D) Y^{^} _i = a + b₁ D_{1 +} b₂ D_{2 +} b₃D₃

Question 27

is a procedure for deriving a mathematical relationship, in the form of an equation, between a single metric dependent variable and a single metric independent variable.

A) Multiple regression
B) Chi- square
C) Part correlation
D) Bivariate regression

Question 28

Which statement is true about cross- validation.

A) It examines whether the regression model continues to hold on comparable data not used in the estimation.
B) A special form of validation is called double cross- validation where the sample is split into halves.
C) It can be used for evaluating the model for chance variations in the data and other problems associated with regression.
D) All of the above statements are true.

Question 29

The standard deviation of b, or the standard error, is denoted as .

A) SSY_b B) SE_b
C) SD_b D) none of the above

Question 30

is a regression procedure in which the predictor variables enter or leave the regression equation one at a time.

A) Dummy variable regression
B) Multiple regression
C) Stepwise regression
D) Bivariate regression

Question 31

The equation for r involves dividing the by .

A) product of the variances of X and Y (S_x²S_y²); COV_xy
B) COV_xy; the product of the variance of X and Y (S_x²S_y²)
C) COV_xy; the product of the standard deviation of X and Y (S_xS_y)
D) product of the standard deviation of X and Y (S_xS_y); COV_xy

Question 32

In the equation COV_xy/ S_xS_y, S_x and S_y represent .

A) the means of X and Y
B) the strength of the effects of X and Y
C) the variances of X and Y
D) the standard deviation of X and Y

Question 33

The is a measure of the association between two variables after controlling or adjusting for the effects of one or more additional variables.

A) partial correlation coefficient
B) regression analysis
C) product moment correlation
D) ANOVA

Question 34

r = 0 indicates .

A) X and Y have a relationship
B) X and Y don't have a linear relationship
C) X and Y have a linear relationship
D) X and Y are unrelated

Question 35

The product moment correlation is also known as the Pearson correlation coefficient and as .

A) correlation coefficient
B) simple correlation
C) bivariate correlation
D) all of the above

Question 36

In multiple regression, if the overall null hypothesis is rejected, which statement is true?

A) We know which specific þs are nonzero.
B) We can use t = b/SE_b to determine which þs are nonzero.
C) We do not know which þs are nonzero.
D) Both B and C are correct.

Question 37

Which of the following is not a problem associated with multicollinearity?

A) Predictor variables may be incorrectly included or removed in stepwise regression.
B) It becomes difficult to assess the relative importance of the independent variables in explaining the variation in the dependent variables.
C) It becomes difficult to compute the correct test statistic.
D) The partial regression coefficients may not be estimated precisely. The standard errors are likely to be high.

Question 38

Which of the following situations is best addressed by regression?

A) Is there an association between market share and size of the sales force after adjusting for the effect of sales promotion?
B) Determine how much of the variation in the dependent variable (store sales) can be explained by the independent variables (price and level of advertisement).
C) Are consumers' perceptions of quality related to their perceptions of prices when the effect of brand image is controlled?
D) Is there an association between market share and the size of the sales force?

Question 39

The question of "How strongly are sales related to advertising expenditures when the effect of price is controlled?" is best answered via .

A) product moment correlation
B) bivariate regression analysis
C) partial correlation coefficient
D) ANOVA

Question 40

The general form of the multiple regression model is estimated by which equation?

A) Y^{^} _i = a + bX_i B) Y^{^} _i = þ₀ + þ₁ X_{i +} e_i
C) Y^{^} = a + b₁X₁ + b₂X₂ D) Y^{^} = a + b₁ X_{1 +} b₂ X_{2 +} b₃X_{3 + ... +} b_kX_k

Question 41

When determining the statistical significance of the relationship between two variables measured by using r, the hypotheses to be tested are H₀: q = 0 and H₁:q × 0

Question 42

The coefficient of multiple determination is adjusted for the number of dependent variables and the sample size to account for diminishing returns.

Question 43

In multiple regression, if the overall null hypothesis is rejected, .

A) the mean value of the dependent variable will be different for different categories of the independent variable
B) there is an association between the independent variables
C) the means of the independent variables are not equal
D) one or more population partial regression coefficients have a value different from 0

Question 44

The product moment correlation helps us determine the strength of the association between two metric variables. Regression analysis helps us determine which variables cause a change in other variables.

Question 45

In the absence of ties, Kendall's l yields a closer approximation to the Pearson product moment correlation coefficient, q, than Spearman's q_s.

Question 46

The estimated parameter b is usually referred to as the non- standardized regression coefficient.

Question 47

is a state of very high intercorrelations among independent variables.

A) Partial collinearity
B) Variable collinearity
C) Multicollinearity
D) Hypercollinearity

Question 48

To estimate the accuracy of predicted values, Y^{^} , found in bivariate regression, it is useful to calculate the , the standard deviation of the actual Y values for the predicted Y^{^} values.

A) coefficient of determination
B) covariance
C) standard error of the estimate
D) standard error

Question 49

The statistical significance of the linear relationship between X and Y may be tested by examining the hypotheses: H₀: fi₁ × 0; H₁: fi₁ = 0.

Question 50

If a variable explains a significant proportion of the residual variation, it should be considered for inclusion in the regression equation.

Question 51

Both r and r² are symmetric measures of association. In other words, the correlation of X and Y is the same as the correlation of Y and X.

Question 52

If the nonmetric variables are nominal and numeric, Spearman's rho and Kendall's tau are two measures of nonmetric correlation that can be used to examine the correlation between them.

Question 53

The general form of the multiple regression model is: Y = þ₀ + þ₁ X₁ + þ₂ X₂ + þ₃X₃ + + þ_kX_{k +} e

Question 54

Standardized variables have a mean of 1 and a variance of zero.

Question 55

A correlation matrix indicates the coefficient of correlation between each pair of variables.

Question 56

The bivariate regression model that accounts for the probabilistic or stochastic nature of the relationship between X and Y is _ .

A) Y^{^} = a + b₁X₁ + b₂X₂ B) Y^{^} _i = a + bX_i
C) Y = þ₀ + þ₁ X_i D) Y_i = þ₀ + þ₁ X_{i +} e_i

Question 57

The term beta coefficient, or beta weight, is used to denote the standardized regression coefficient.

Question 58

A partial correlation coefficient measures the association between two variables after controlling for or adjusting for the effects of one or more additional variables.

Question 59

Because r indicates the degrees to which variation in one variable is related to variation in another, it can also be expressed in terms of the decomposition of the total variation.

Question 60

The formula for the coefficient of determination is r² = SS_reg/ SS_y.

Question 61

In bivariate regression, the null hypothesis is that no linear relationship exists between X and Y, or H₀: fi₁ = 0.

Question 62

If an examination of the residuals indicates that the assumptions underlying linear regression are not met, the researcher can transform the variables in an attempt to satisfy the assumptions.

Question 63

In multiple regression, if the overall null hypothesis is rejected, we know which specific coefficients (þ_is) are nonzero.

Question 64

Regression in which a single independent variable has been recoded into dummy variables is equivalent to one- way analysis of variance.

Question 65

The purpose of stepwise regression is to select, from a large number of predictor variables, a small subset of variables that account for most of the variation in the dependent or criterion variable.

Question 66

When fitting a straight line to a scattergram, the best- fitting line is called the regression line.

Question 67

The multiple correlation coefficient, R, can also be viewed as the simple correlation coefficient, r, between Y and Y^{^} .

Question 68

The product moment correlation, r², is an index used to determine whether a linear, or
straight- line, relationship exists between X and Y. It indicates the degree to which the variation in one variable, X, is related to the variation in another variable, Y.

Question 69

The order associated with a partial correlation indicates how many variables are being adjusted or controlled.

Question 70

A residual is the difference between the observed value of Y_i and the value predicted by the regression equation, Y^{^} _i.

Question 71

When there are a large number of independent variables and the researcher suspects that not all of them are significant, stepwise regression should be used.

Question 72

The standard error of estimate, SEE, may be interpreted as a kind of average residual or average error in predicting Y from the regression equation.

Question 73

R² cannot decrease as more independent variables are added to the regression equation.

Question 74

The partial correlation coefficient is generally viewed as more important than the part correlation coefficient.

Question 75

The correlation coefficient between two variables varies depending on their underlying units of measurement.

Question 76

The covariance may be either positive or negative.

Question 77

When determining the correlation coefficient, r, it does matter which variable is considered to be the dependent variable and which is the independent.

Question 78

The hypotheses for the test for significance of the coefficient of determination are: H₀: R²_pop = 0 ; H₁: R²_pop > 0.

Question 79

The standard error of estimate, SEE, is the standard deviation of the actual Y values from the predicted Y^{^} values.

Question 80

The partial correlation coefficient is a measure of the correlation between Y and X when the linear effects of the other independent variables have been removed from X but not from Y.