Deck 17: Correlation and Regression

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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 5

Regression analysis is concerned with the nature and degree of association between variables and does not imply or assume any causality.

Question 6

The covariance may be either positive or negative.

Question 7

In the absence of ties,Kendall's τ yields a closer approximation to the Pearson product moment correlation coefficient,ρ,than Spearman's ρs.

Question 8

The product moment correlation,r,is the most widely used statistic summarizing the strength of association between two metric (interval or ordinal scaled)variable,say X and Y.

Question 9

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 10

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 11

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 12

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 13

In bivariate regression,the null hypothesis is that no linear relationship exists between X and Y,or H0: β1 = 0.

Question 14

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

Question 15

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.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

Regression analysis models helped Avon realize that employee benefits and the appointment fee that representatives pay for materials were significant variables affecting the decline in their sales staff.

Question 21

Stepwise procedures result in regression equations that are optimal,in the sense of producing the largest R2,for a given number of predictors.

Question 22

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

Question 23

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

Question 24

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 25

The hypotheses for the test for significance of the coefficient of determination are: H0: R2pop = 0 ;H1: R2pop > 0.

Question 26

A residual is the difference between the observed value of Yi and the value predicted by the regression equation,i.

Question 27

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

Question 28

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

Question 29

The formula for the coefficient of determination is r2 = SSreg/ SSy.

Question 30

The statistical significance of the linear relationship between X and Y may be tested by examining the hypotheses: H0: β1 ≠ 0;H1: β1 = 0.

Question 31

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 32

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

Question 33

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 34

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

Question 35

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

Question 36

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

Question 37

The general form of the multiple regression model is: Y = β0 + β1 X1 + β2 X2 + β3X3 + ....+ βkXk + e

Question 38

The vertical distance from a point to the regression line is the squared error,e2.

Question 39

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

Question 40

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 41

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

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

Question 42

Which statement is not true about correlation matrices?

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

Question 43

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

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

Question 44

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

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

Question 45

r = 0 indicates ________.

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

Question 46

In regression with dummy variables,the predicted for each category is the mean of Y for each category.

Question 47

r2 measures ________.

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

Question 48

Which of the following is a measure of nonmetric correlation?

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

Question 49

ry(x.z)represents the ________.

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

Question 50

The equation for r is represented as ________.

A) Sx2Sy2/COV
B) COVxy/ SxSy
C) SxSy/COV
D) COVxy/ Sx2Sy2

Question 51

Which statement is not correct about the partial correlation coefficient?

A) Partial correlations can be helpful for detecting spurious relationships.
B) 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.
C) The partial correlation coefficient is generally viewed as more important than the part correlation coefficient.
D) The partial correlation coefficient can be calculated by a knowledge of the simple correlations alone.

Question 52

Multicollinearity arises when intercorrelations among the predictors are very low.

Question 53

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 rsy.z is a ________ partial correlation coefficient,as it controls for the effect of one additional variable,Z.

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

Question 54

In the equation COVxy/ SxSy,Sx and Sy represent ________.

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

Question 55

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

Question 56

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

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

Question 57

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 increases exponentially with increases in X
C) Y decreases exponentially with decreases in X
D) both A and C are correct

Question 58

The equation for r involves dividing the ________ by ________.

A) product of the variances of X and Y (Sx2Sy2);COVxy
B) product of the standard deviation of X and Y (SxSy);COVxy
C) COVxy;the product of the variance of X and Y (Sx2Sy2)
D) COVxy;the product of the standard deviation of X and Y (SxSy)

Question 59

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

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

Question 60

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

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

Question 61

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

Question 62

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

Question 63

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

A) F statistic
B) Z statistic
C) ω2
D) T statistic

Question 64

To estimate the accuracy of predicted values,,found in bivariate regression,it is useful to calculate the ________,the standard deviation of the actual Y values for the predicted values. C:\Users\user\Dropbox\Quizplus Parsing Documents\To Be Parsed\More\TB4782,Marketing Research An Applied Orientation Global 6th Edition by Naresh K.Malhotra\TB4782,Marketing Research An Applied Orientation Global 6th Edition by Naresh K.Malhotra\Images\chapter_17_55.jpg

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

Question 65

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

A) Yi =β0 + β1 Xi + ei
B) Y = β0 + β1 Xi
C) = a + b1X1 + b2X2
D) i = a + bXi

Question 66

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

A) SEb
B) SSYb
C) SDb
D) none of the above

Question 67

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

A) i = a + bXi
B) =a + b1 X1 + b2 X2 + b3X3 + ...+ bkXk
C) = a + b1X1 + b2X2
D) i =β0 + β1 Xi + ei

Question 68

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

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

Question 69

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

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

Question 70

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

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

Question 71

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

A) B2yx = byx(Sx/Sy)
B) B2yx = byx(S2x/S2y)
C) Byx = byx(S2x/S2y)
D) Byx = byx(Sx/Sy)

Question 72

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

Question 73

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

A) = a + b1X1 + b2X2
B) i =β0 + β1 Xi + ei
C) = β0 + β1 Xi
D) i = a + bxi

Question 74

Which statement is not true about partial regression coefficients?

A) The beta coefficients are the partial regression coefficients obtained when all the variables (Y,X1,X2...Xk)have been standardized to a mean of 0 and a variance of 1 before estimating the regression equation.
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) Partial regression coefficients have an order associated with them.
D) Both A and B are not true.

Question 75

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

Question 76

________ 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) The least-squares procedure
C) Chi-square
D) Bivariate regression

Question 77

The ________ denotes the change in the predicted value,,per unit change in X1 when the other independent variables,X2 to Xk,are held constant.

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

Question 78

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

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

Question 79

Which statement is not true about the constant b in the bivariate regression equation i = a + bXi?

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 is the intercept of the regression line and it indicates the value of Y when X is zero.
C) It may be computed as b=COVxy/Sx2.
D) It is usually referred to as the non-standardized regression coefficient.

Question 80

Which statement is not true about regression analysis?

A) 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.
B) Regression can be used to predict the values of the dependent variable.
C) Regression analysis can be used to determine if color preference is related to product size and price.
D) Regression analysis is a powerful and flexible procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables.