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Discuss multiple regression analysis.

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In most problems faced by managers, ther...

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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.

F) B) and E)
G) A) and C)

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To measure whether a relationship between two variables exists, we rely on the concept of statistical significance.

A) True
B) False

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When two variables have a curvilinear relationship, the formula that best describes the linkage is very simple.

A) True
B) False

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A fundamental basis of regression analysis is the assumption of:


A) a curvilinear relationship between two weakly associated dependent variables.
B) a straight line relationship between the independent and dependent variables.
C) the lack of a relationship between independent variables.
D) a uniform normal distribution between dependent variables.
E) the existence of two independent variables for every dependent variable.

F) A) and E)
G) A) and D)

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Scatter diagrams are a visual way to describe the relationship between two variables and the covariation they share.

A) True
B) False

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With regard to the least squares procedure, any data point that does not fall on the regression line is the result of:


A) specific variance.
B) nonresidual variance.
C) unexplained variance.
D) sum of the squared errors.
E) multicollinearity.

F) None of the above
G) B) and E)

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Which of the following statements is true of model F statistics?


A) A larger F statistic indicates that the regression model has more explained variance than error variance.
B) An F statistic shows the change in the dependent variable for each unit change in the independent variable.
C) Analysis of linear relationships between a dependent variable and multiple independent variables requires that F statistics be smaller than beta coefficients.
D) Bivariate regression becomes multiple regression analysis when F statistics are used.
E) Standardization using beta coefficient augments the effects of using different scales of measurement.

F) A) and B)
G) A) and C)

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A

The Spearman rank order correlation coefficient differs from the Pearson correlation coefficient in that the Spearman rank order correlation:


A) primarily establishes a weak association between variables, whereas the Pearson correlation coefficient establishes a strong association between variables.
B) is used when variables have been measured using ordinal scales, whereas the Pearson correlation coefficient is used when variables have been measured using ratio scales.
C) assumes that variables have a normally distributed population, whereas the Pearson correlation coefficient assumes that variables have a uniform distribution.
D) is used for linear relationships, whereas the Pearson correlation coefficient is used for curvilinear relationships.
E) is a qualitative measure of the degree of variation, whereas the Pearson correlation coefficient is a quantitative measure of the degree of variation.

F) A) and B)
G) A) and C)

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


A) linear
B) curvilinear
C) constant
D) proportional
E) collinear

F) A) and B)
G) All of the above

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When the correlations between independent variables in regression are high enough to cause problems, one approach is to create summated scales consisting of the independent variables that are highly correlated.

A) True
B) False

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The use of the Pearson correlation coefficient assumes the variables have a normally distributed population.

A) True
B) False

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True

The smaller the size of the coefficient of determination, the stronger the linear relationship between the two variables being examined.

A) True
B) False

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The least squares procedure determines the best-fitting line by maximizing the vertical distances of all the data points from the line.

A) True
B) False

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False

The coefficient of determination:


A) describes the variation in the dependent variable caused by the control variable.
B) tells you the percentage of the total variation in the independent variable caused by the dependent variable.
C) ranges from -1.0 to +1.0.
D) ranges from .00 to 1.0.
E) is a stronger measure than the Pearson correlation coefficient.

F) B) and D)
G) B) and C)

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A problem area for marketing researchers in multiple regression is when the independent variables are highly correlated among themselves.

A) True
B) False

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A scatter plot wherein the dots form an ellipse indicates a positive relationship between variables.

A) True
B) False

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Which of the following is true of the fundamentals of regression analysis?


A) A fundamental basis of regression analysis is the assumption of a circular relationship between the independent and dependent variables.
B) Regression uses an estimation procedure called ordinary least squares that guarantees the line it estimates will be the best fitting line.
C) The differences between actual and predicted values of the dependent variable are known as regression coefficients and are represented by b.
D) The regression coefficient is calculated by squaring errors of each dependent variable.
E) Any point that falls on the line of a regression analysis is the result of unexplained variance.

F) A) and E)
G) C) and D)

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It is possible for a correlation to be statistically significant and still lack substantive significance.

A) True
B) False

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If the coefficient of correlation between two variables is -0.6, the coefficient of determination will be:


A) -0.6.
B) 0.4.
C) 0.36.
D) -0.36.
E) 0.6.

F) B) and D)
G) A) and E)

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