mkt research ch 12

If the coefficient of correlation between two variables is -0.6, their coefficient of determination will be: a) -0.6 b) 0.4 c) 0.36 d) -0.36 e) 0.6

0.36

beta coefficient

an estimated regression coefficient that has been recalculated to have a mean of 0 and a standard deviation of 1. Such a change enables independent variables with different units of measurement to be directly compared on their association with the dependent variable

regression coefficient

an indicator of the importance of an independent variable in predicting a dependent variable. Large coefficients are good predictors and small coefficients are weak predictors

A researcher plots a scatter diagram of two variables. The dots on the plot are scattered roughly as a narrow strip that goes up from left to right. This indicates that the relationship (covariation) between the two variables: a) Is linear, positive b) Is linear, negative c) Is circular, positive d) Is circular, negative e) Is very close to zero

is very close to zero

If a researcher is interested in measuring the effect of two independent variables on a dependent variable, he/she should use: a) the Pearson correlation coefficient. b) the Spearman correlation coefficient. c) bivariate regression analysis. d) multiple regression analysis. e) simple regression.

multiple regression analysis.

When knowledge about the behavior of one variable allows you to predict the behavior of another variable, this is another way of studying the ________ of the relationship. a) Presence b) Direction c) Strength of association d) Type e) None of the above

presence

unexplained variance

the amount of variation in the dependent variable that cannot be accounted for by the combination of independent variables

Heteroskedasticity

the pattern of covariation around the regression line is not constant around the regression line, and varies in some way when the values change from small to medium and large

Homoskedasticity

the pattern of the covariation is constant around the regression line, whether the values are small, medium, or large

covariation

The amount of change in one variable that is consistently related to the change in another variable of interest.

When a researcher evaluates the absolute size (value) of the correlation coefficient, the researcher wants to test the ______ of the relationship. a) Strength of association b) Presence c) Type d) Direction e) None of the above

strength of association

While studying the relationship between advertising and sales growth, a researcher determines that the relationship is sometimes weak and at other times moderate. This variation from one situation to another is the variation in the ___________ of the relationship between advertisement and sales growth. a) Strength of association b) Presence c) Type d) Direction e) None of the above

strength of association

scatter diagram

A graphic plot of the relative position of two variables using a horizontal and a vertical axis to represent the values of the respective variables.

A scatter diagram is: a) A condition under which there is a consistent and systematic linkage between two or more variables b) The assumption that the nature of the relationship is linear c) A relationship between two variables whereby the strength and/or direction of their relationship changes over the range of both variables d) The amount of change in one variable that is consistently related to the change in another variable of interest e) A graphic plot of the relative position of two variables using a horizontal and vertical axis to represent the values of the respective variables

A graphic plot of the relative position of two variables using a horizontal and vertical axis to represent the values of the respective variables

Coefficient of determination (r2)

A number measuring the proportion of variation in one variable accounted for by another. The r2 measure can be thought of as a percentage and varies from 0.0 to 1.00.

In bivariate regression analysis, the procedure used to determine the best fitting line is called the: a) Least squares procedure b) Squared error procedure c) Sum of errors procedure d) Least error procedure e) Minimum error procedure

Least squares procedure

For a given sample, which of the following correlation coefficients is most likely to be found statistically significant? a) 0.01 b) 0.05 c) 0.10 d) 0.50 e) 0.90

0.90

For a retail store, there exists a strong relationship between the amount spent on local television advertising and store sales. As it increases advertising expenditure, sales go up. Which of the following seems to be the most appropriate Pearson correlation coefficient for this relationship? a) 0.01 b) 0.05 c) 0.90 d) -0.50 e) 99.

0.90

In a bivariate regression analysis, there is/are ____ predictor variable(s). a) 0 b) 1 c) 2 d) 3 e) 4

1

A linear relationship is: a) A condition under which there is a consistent and systematic linkage between two or more variables b) A relationship between two variables whereby the strength and nature of the relationship remains the same over the range of both variables c) A relationship between two variables whereby the strength and/or direction of their relationship changes over the range of both variables d) The amount of change in one variable that is consistently related to the change in another variable of interest e) A graphic plot of the relative position of two variables using a horizontal and vertical axis to represent the values of the respective variables

A relationship between two variables whereby the strength and nature of the relationship remains the same over the range of both variables

Curvilinear relationship

A relationship between two variables whereby the strength and/or direction of their relationship changes over the range of both variables.

Multicollinearity is: a) A statistical procedure that estimates regression equation coefficients which produce the lowest sum of squared differences between the actual and predicted values of the dependent variable b) A statistical technique which analyzes the linear relationship between a dependent variable and multiple independent variables by estimating coefficients for the equation for a straight line c) An estimated regression coefficient which has been recalculated to have a mean of zero and a standard deviation of 1 d) A statistic which compares the amount of variation in the dependent measure "explained" or associated with the independent variables to the "unexplained" or error variance e) A situation in which several independent variables are highly correlated with each other

A situation in which several independent variables are highly correlated with each other

Multicollinearity

A situation in which several independent variables are highly correlated with each other. This characteristic can result in difficulty in estimating separate or independent regression coefficients for the correlated variables.

Model F statistic

A statistic that compares the amount of variation in the dependent measure "explained" or associated with the independent variables to the "unexplained" or error variance. A larger F statistic indicates that the regression model has more explained variance than error variance.

Spearman rank order correlation coefficient

A statistical measure of the linear association between two variables where both have been measured using ordinal (rank order) scales

The Spearman rank order correlation coefficient is: a) Not used when two variables have been measured using ordinal scales b) A number measuring the proportion of variation in one variable accounted for by another c) A statistical measure of the linear association between two variables where both have been measured using ordinal scales d) A measure that tends to produce the highest coefficient and is not considered a conservative measure e) When the nature and extent of a relationship between two variables is known with certainty.

A statistical measure of the linear association between two variables where both have been measured using ordinal scales

Pearson correlation coefficient

A statistical measure of the strength of a linear relationship between two metric variables.

The effect of high levels of multicollinearity is to: a) Make it difficult or impossible for the regression equation to separate out the independent contributions of the independent or predictor variables b) Have a significant F-statistic and still have no regression coefficients that are statistically different from zero c) Have a reasonably large r-squared and still have no regression coefficients that are statistically significant from zero d) Inflate the standard error of the coefficient and lower the t-statistic associated with it e) All of the above

All of the above

The regression equation in multiple regression indicates that: a) There may be a relationship between several independent variables and a dependent variable b) We have to think about multiple dimensions instead of just a single straight line c) The easiest way to examine relationships is to examine regression coefficients for each independent variable d) Each particular regression coefficient describes the relationship between that independent variable and the dependent variable e) All of the above

All of the above

linear relationship

An association between two variables whereby the strength and nature of the relationship remains the same over the range of both variables.

Relationships between variables can be described in all of the following ways EXCEPT: a) Presence b) Dispersion c) Direction d) Strength of associations e) Type

Dispersion

The difference between the observed value of the dependent variable and the predicted value of the dependent variable in a regression equation is called the: a) Error b) Beta weight c) Slope d) Y-intercept e) None of the above

Error

As a rule of thumb, the relationship between two variables is considered very strong if the absolute value of the Pearson correlation coefficient is: a) Greater than 0.1 b) Greater than 0.5 c) Greater than 0.8 d) Greater than 1.0 e) Greater than 0.0

Greater than 0.8

A relationship between X and Y is negative when ________ in X are associated with ________ in Y. a) Increases; decreases b) Increases; increases c) Decreases; decreases d) All of the above e) None of the above

Increases; decreases

Which of the following statements is true of statistical significance? a) Many times not all the independent variables in a regression equation will be statistically significant. b) If a regression coefficient is not statistically significant, the value of the dependent variable changes with the value of the statistically insignificant independent variable changes. c) The statistical significance of each coefficient must be examined before the regression coefficients have been estimated. d) If the F statistic is statistically significant, it means the chances of the regression model for a sample producing a large coefficient of determination are acceptably high. e) If a regression coefficient is statistically significant, that means the independent variable does not have a relationship with the dependent variable.

Many times not all the independent variables in a regression equation will be statistically significant.

Which of the following is true of relationships between variables? a) A curvilinear relationship is much simpler to work with than a linear relationship. b) Marketers are often interested in describing the relationship between variables they think influence purchases of their products. c) A negative relationship exists between two variables if low levels of one variable are associated with low levels of another. d) The strength of association is determined by the size of the correlation coefficient, with smaller coefficients indicating a stronger association. e) The null hypothesis for the Pearson correlation coefficient states that there is a strong association between two variables.

Marketers are often interested in describing the relationship between variables they think influence purchases of their products.

The coefficient of determination: a) Describes the variation in the dependent variable described by the control variable b) Tells you the percent of the total variation in the independent variable explained by the dependent variable c) Ranges from -1.0 to +1.0 d) Ranges from zero to +1.0 e) None of the above

Ranges from zero to +1.0

A researcher runs a multiple regression analysis with independent variables that are measured with very different scales. In order to make relative comparisons between regression coefficients to see which independent variables had the most influence on the dependent variable, she should calculate: a) Normalized mean residuals b) Non-standardized coefficients c) Standardized regression coefficients d) Adjusted R-square e) Modified R-square

Standardized regression coefficients

The formula for a straight line is Y = a + bX, where Y stands for: a) The dependent variable b) The independent variable c) The Y intercept d) The slope e) None of the above

The dependent variable

The use of a simple regression assumes: a) The variables are measured on an ordinal scale b) The variables come from a univariate population c) The error terms are normally distributed d) The error terms are dependent upon one another e) None of the above

The error terms are normally distributed

The formula for a straight line is Y = a + bX, where X stands for: a) The dependent variable b) The independent variable c) The Y intercept d) The slope e) None of the above

The independent variable

Which of the following statements is true of the correlation analysis? a) The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables. b) The Pearson correlation coefficient measures the degree of linear association which ranges from 0 to 1.0. c) The larger the correlation coefficient, the weaker the association between two variables. d) The null hypothesis for the Pearson correlation coefficient states that the correlation coefficienti s zero. e) The Pearson correlation coefficient measures the degree of linear association between three variables.

The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.

In a regression analysis, it is established that 10% of the variation in the dependent variable is explained by the independent variable. This implies that the value of: a) The regression coefficient is 0.10 b) The r2 is 0.10 c) The significance level is 0.10 d) The t statistic is 0.10 e) None of the above

The r2 is 0.10

In a bivariate regression analysis: a) The relationship between two variables is derived from a linear line b) The slope coefficient tells how much change in X to expect from a change in Y c) The best prediction is one in which the difference between the actual value of X and the predicted value of X is the largest. d) All of the above e) None of the above

The relationship between two variables is derived from a linear line

When the correlation coefficient is weak, the researcher must consider two possibilities: a) There simply is no consistent, systematic relationship between the two items in the population and the association exists, but is not linear and must be investigated further b) There is a consistent, systematic relationship between the two items in the population, but is not linear and must be investigated further c) There simply is no consistent, systematic relationship between the two items in the population and the association exists, but is linear and must be investigated further d) There simply is no consistent, systematic relationship between the two items in the population and the association exists, but is not linear and does not need be investigated further e) None of the above

There simply is no consistent, systematic relationship between the two items in the population and the association exists, but is not linear and must be investigated further

normal curve

a curve that indicates the shape of the distribution of a variable is equal both above and below the mean

least squares procedure

a regression approach that determines the best-fitting line by minimizing the vertical distances of all the points from the line

ordinary least squares

a statistical procedure that estimates regression equation coefficients that produce the lowest sum of squared differences between the actual and predicted values of the dependent variable

bivariate regression analysis

a statistical technique that analyzes the linear relationship between two variables by estimating coefficients for an equation for a straight line. One variable is designated as a dependent variable and the other is called an independent or predictor variable

multiple regression analysis

a statistical technique which analyzes the linear relationship between a dependent variable and multiple independent variables by estimating coefficients for the equation for a straight line