Deck 17: Correlation and Regression

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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 6

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 7

The covariance may be either positive or negative.

Question 8

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

Question 9

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 10

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

Question 11

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 12

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

Question 13

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 14

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 15

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 16

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

Question 17

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 18

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

Question 19

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 20

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

Question 21

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

Question 22

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 23

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

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

Question 26

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

Question 27

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

Question 28

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 29

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

Question 30

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

Question 31

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

Question 32

The vertical distance from a point to the regression line is the squared error,e^2.

Question 33

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

Question 34

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 35

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

Question 36

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

Question 37

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

Question 38

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 39

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

Question 40

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

Question 41

r = 0 indicates ________.

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

Question 42

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

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

Question 43

The relationship between X and Y is spurious if ________.

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

Question 44

The equation for r is represented as ________.

A)COV_xy/ S_x^2S_y²
B)S_xS_y/COV
C)COV_xy/ S_xS_y
D)S_x^2S_y²/COV

Question 45

Multicollinearity arises when intercorrelations among the predictors are very low.

Question 46

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)partial correlation coefficient
C)ANOVA
D)product moment correlation

Question 47

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

Question 48

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

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

Question 49

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 is generally viewed as more important than the part correlation coefficient.
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 can be calculated by a knowledge of the simple correlations alone.

Question 50

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

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

Question 51

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

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

Question 52

Which statement is not true about correlation matrices?

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

Question 53

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 54

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

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

Question 55

The equation for r involves dividing the ________ by ________.

A)COV_xy;the product of the variance of X and Y (S_x^2S_y²)
B)product of the standard deviation of X and Y (S_xS_y);COV_xy
C)COV_xy;the product of the standard deviation of X and Y (S_xS_y)
D)product of the variances of X and Y (S_x^2S_y²);COV_xy

Question 56

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

Question 57

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

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

Question 58

r² measures ________.

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

Question 59

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

Question 60

r_y(x.z) represents the ________.

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

Question 61

Which of the following situations is best addressed by regression?

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

Question 62

Which statement is not true about partial regression coefficients?

A)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).
B)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.
C)Partial regression coefficients have an order associated with them.
D)Both A and B are not true.

Question 63

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

Question 64

To estimate the accuracy of predicted values,Ŷ,found in bivariate regression,it is useful to calculate the ________,the standard deviation of the actual Y values from the predicted Ŷ values.

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

Question 65

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

Question 66

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

A)Ŷ _i = a + bX_i
B)Ŷ _i =β₀ + β₁ X_{i +} e_i
C)Ŷ =a + b₁ X_{1 +} b₂ X_{2 +} b₃X_{3 + ...+} b_kX_k
D)Ŷ = a + b₁X₁ + b₂X₂

Question 67

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

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

Question 68

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

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

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 (Ŷ)
D)both A and B

Question 70

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

Question 71

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

Question 72

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

A)Ŷ = a + b₁X₁ + b₂X₂
B)Ŷ = β₀ + β₁ X_i
C)Ŷ _i =β₀ + β₁ X_{i +} e_i
D)Ŷ _i = a + bx_i

Question 73

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)the means of the independent variables are not equal
C)there is an association between the independent variables
D)one or more population partial regression coefficients have a value different from 0

Question 74

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

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

Question 75

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

A)Ŷ = a + b₁X₁ + b₂X₂
B)Y = β₀ + β₁ X_i
C)Y_i =β₀ + β₁ X_{i +} e_i
D)Ŷ _i = a + bX_i

Question 76

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

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

Question 77

Which statement is not true about the constant b in the bivariate regression equation Ŷ _i = a + bX_i?

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

Question 78

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

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

Question 79

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

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

Question 80

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

A)B_yx = b_yx(S²_x/S²_y)
B)B²_yx = b_yx(S_x/S_y)
C)B_yx = b_yx(S_x/S_y)
D)B²_{yx =} b_yx(S²_x/S²_y)