MKT Research and Analysis- Ch. 12
True or false: A large regression coefficient is a good predictor of a dependent variable.
True
Y
The dependent variable
Identify an assumption behind regression analysis.
A linear relationship is a good description of the relationship between the variables of interest.
Homoskedasticity
The pattern of covariation is constant around the regression line, whether the values are small, medium, or large.
Which of the following is a possibility that must be considered when the correlation coefficient between the two variables being measured is weak?
The variables do not share a consistent and systematic relationship.
An indicator of the importance of an independent variable in predicting a dependent variable is called a(n) ________ ________.
regression coefficient
In the bivariate regression analysis, the values of the independent variables being studied are selected, and _____.
the formula for a straight line is used to observe the behavior of the dependent variable
No relationships
It means that a consistent and systematic relationship between variables is absent.
Arrange the steps in the procedure that needs to be followed for evaluating the results of a regression analysis in the order of their occurrence. (Place the first step at the top.)
1. The F statistic and its associated probability are used to assess the statistical significance of the overall regression model. 2. The obtained r2 is evaluated to see how large it is. 3. The individual regression coefficients and their t statistics are examined to see which are statistically significant. 4. The relative influence of the independent variables is assessed by looking at the beta coefficients.
Graph Image. Given that variable X and variable Y have been plotted on the graph shown, identify the type of relationship between the two variables.
A negative relationship
Identify a possibility that must be considered when the correlation coefficient between the two variables being measured is weak.
A nonlinear association exists between the variables.
Partial least squares (PLS)
A statistical method that is an extension of multiple regression and helps researchers determine whether there are meaningful relationships between the variables
Composite variable
A variable that is measured with several separate questions
Structural model
A visual representation of the relationships between the variables
________ ________ _______ is a statistical technique that uses information about the relationship between an independent or predictor variable and a dependent variable to make predictions.
Bivariate regression analysis
_________ is defined as the amount of change in one variable that is consistently related to the change in another variable of interest.
Covariation
Identify a function of the least squares procedure in regression analysis.
It computes the values of the intercept and the slope that is used in the formula for a straight line.
Identify a function of a beta coefficient.
It enables researchers to see the change in a dependent variable for each unit change in the independent variable.
Identify a function of ordinary least squares that is used in regression analysis.
It guarantees the estimation of the best fitting line.
Normal curve
It indicates that the shape of the distribution of a variable is equal both above and below the mean.
In the context of regression analysis, identify a feature of unexplained variance.
It is depicted by the vertical distance between the estimated straight regression line and the actual data points.
Which of the following is true of a scatter diagram?
It is used to visually describe a covariation between two variables.
A weak association
It means that the variables may have some variance in common, but not much.
A moderate or strong association
It occurs when there is a consistent and systematic relationship between variables.
The outer model
It refers to the relationships between constructs and the variables (questions) that measure the constructs.
The inner model
It refers to the structural relationships between the constructs in the model.
MARA, an automobile company, conducts a survey on all its customers in order to improve the quality of its products and service. The customers are given ten factors, such as mileage of the vehicle, engine power, time taken for service, etc., and are required to arrange these factors in the order they consider important. Which method of correlation analysis should be used by MARA in this scenario?
The Spearman rank order correlation coefficient
X
The independent variable used to predict the dependent variable
a
The intercept or the point where the straight line intersects the Y-axis when X = 0
Heteroskedasticity
The pattern of covariation around the regression line is not constant, and varies in some way when the values change from small to medium and large.
Identify a true statement about the coefficient of determination.
There is a direct relationship between its size and the strength of the linear relationship between the two variables being examined.
True or false: The concept of covariation refers to the extent to which two variables are associated with each other.
True
True or false: Two or more variables are said to be related when a systematic relationship exists between them.
True
Which of the following is an example of a negative relationship between variable X and variable Y that have been plotted on a scatter diagram?
Variable X decreases when variable Y increases and increases when variable Y decreases.
In the context of the fundamentals of regression analysis, which of the following is the general formula for a straight line?
Y = a + bX + ei
A(n) _____ refers to an estimated regression coefficient that has been recalculated to have a mean of 0 and a standard deviation of 1.
beta coefficient
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 is called ________ ________ ________.
ordinary least squares
The size of a correlation coefficient can be used to _____.
quantitatively describe the strength of the association between two variables
A linear relationship between variable X and variable Y means that the strength and nature of the relationship between them _____.
remains constant over the range of both variables
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 is called a(n) ________ ________.
scatter diagram
To measure if a relationship between two variables exists, a researcher relies on the concept of _____.
statistical significance
The amount of variation in the dependent variable that cannot be accounted for by the combination of independent variables in regression analysis is called _______ _______.
unexplained variance
A statistical measure of the strength of a linear relationship between two metric variables is called the ________ _________ ________.
Pearson correlation coefficient
A statistical measure of the linear association between two variables where both have been measured using ordinal scales is called the _______ _________ ________ correlation coefficient.
Spearman rank order
_________ _________ (SM) is the process of identifying the relationships between variables and drawing a structural model.
Structural modeling
ei
The error for the prediction
Identify the assumption that forms a fundamental basis of regression analysis.
The independent and dependent variables have a straight-line relationship.
b
The slope or the change in Y for every 1 unit change in the independent variable
Identify an assumption made by researchers when they calculate the Pearson correlation coefficient.
The two variables under study have been measured using interval- or ratio-scaled measures.
Identify a feature of beta coefficients.
They range from 0.00 to 1.00.
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 is called a(n) ________ ________ ________.
model F statistic
A situation in which several independent variables are highly correlated with each other is defined as _____.
multicollinearity
A statistical technique which analyzes the linear relationship between a dependent variable and several independent variables by estimating coefficients for the equation for a straight line is called ________ ________ ________.
multiple regression analysis
Which of the following are assumptions made by researchers when they calculate the Pearson correlation coefficient? (Check all that apply.)
-The variables of interest have a normally distributed population. -The relationship being measured is linear.
Calculate the coefficient of determination when the correlation coefficient for two variables is 0.80.
0.64
Which of the following are features of the Pearson correlation coefficient? (Check all that apply.)
-Depending on the direction of the relationship between two variables, a positive or negative correlation coefficient is possible. -It varies between -1.00 and 1.00.
Which of the following are assumptions behind multiple regression analysis? (Check all that apply.)
-Homoskedasticity -The normal distribution of the variables of interest -A linear relationship between the variables of interest
Identify the reasons for the increasing popularity of structural modeling using partial least squares (PLS) path models in business and marketing research. (Check all that apply.)
-It works well with all types of data, and the measurement requirements are very flexible. -Solutions can be obtained with both large and small samples. -Many types of analysis are possible, such as mediation, group comparisons, moderation, and importance-performance analysis.
Identify the elements that need to be examined to determine the significance of a multiple regression model. (Check all that apply.)
-The model F statistic -The coefficient of determination or r2 -The individual beta coefficients -The individual regression coefficients for each independent variable
Which of the following are assumptions made when a simple regression model is used? (Check all that apply.)
-The variables of interest come from a normal population. -The variables of interest are measured on interval or ratio scales.
Arrange the steps involved in multiple regression analysis in the order of their occurrence.
1. Several independent variables are entered into the regression equation. 2. A separate regression coefficient is calculated for each variable that describes its relationship with the dependent variable. 3. A researcher studies the relative influence of each independent variable on the dependent variable.
Graph Image. Variable X and variable Y have been plotted on the graph shown. Identify the type of relationship between the two variables.
Curvilinear
True or false: Multicollinearity makes it easy for researchers to estimate separate or independent regression coefficients for the correlated variables.
False
True or false: Partial least squares (PLS-SEM) results are studied in one step, where the outer and the inner model are measured simultaneously.
False
A strong association between variables is indicated by a _____.
large correlation coefficient
In the context of a beta coefficient, the standardization of the independent variables in multiple regression analysis _____.
leads to the removal of the effects of using different scales of measurement
A regression approach that determines the best-fitting line by minimizing the vertical distances of all the points from the line is known as the _______ ________ _______.
least squares procedure
An association between two variables whereby the strength and nature of the relationship remains the same over the range of both variables is called a _____.
linear relationship
Correlation coefficients between .81 and 1.00 indicate that _____.
covariance is strongly shared between the two variables under study
A relationship between two variables whereby the strength and/or direction of their relationship changes over the range of both variables is called a(n) __________ __________.
curvilinear relationship
In a curvilinear relationship between variable X and variable Y that have been plotted on a scatter diagram, _____.
the relationship between the values of Y and the values of X varies for different values of the variables
If an F statistic is statistically significant, it means that _____.
there is an acceptably small chance of a regression model for a sample population to produce a large r2 when the population r2 is actually zero