Chapter 10 Business Analytics
The correlation value ranges from
-1 to be +1
In regression analysis, which of the following causal relationships are possible
All of these options
Which of the following is an example of a nonlinear regression model?
All of these options
is/are especially helpful in identifying outliers.
Scatterplots
The residual is defined as the difference between the actual and predicted, or fitted values of the response variable.
True
The two primary objectives of regression analysis are to study relationships between variables and to use those relationships to make predictions
True
We should include an interaction variable in a regression model if we believe that the effect of one explanatory variable on the response variable depends on the value of another explanatory variable
True
When the scatterplot appears as a shapeless swarm of points, this can indicate that there is no relationship between the response variable and the explanatory variable at least none worth pursuing
True
n reference to the equation,, the value 0.10 is the expected change in per unit change in
True
In multiple regression, the coefficients reflect the expected change in:
Y when the associated X value increases by one unit
In choosing the "best-fitting" line through a set of points in linear regression, we choose the onewith the
a smallest sum of squared residuals
An important condition when interpreting the coefficient for a particular independent variable in a multiple regression equation is that
all of the other independent variables remain constant
Data collected from approximately the same period of time from a cross-section of a population arecalled
cross-sectional data
In regression analysis, the variable we are trying to explain or predict is called the
dependent variable
The weakness of scatterplots is that they:
do not actually quantify the relationships between variables
A single variable can explain a large percentage of the variation in some other variable when the two variables are:
highly correlated
Regression analysis asks
how a single variable depends on other relevant variables
In regression analysis, the variables used to help explain or predict the response variable are called the
independent variables
The covariance is not used as much as the correlation because
it is difficult to interpret
Outliers are observations that
lie outside the typical pattern of points on a scatterplot
In regression analysis, if there are several explanatory variables, it is called
multiple regression
A correlation value of zero indicates.
no linear relationship
A scatterplot that appears as a shapeless mass of data points indicates
no relationship among the variables
In linear regression, the fitted value is the
predicted value of the dependent variable
In linear regression, we can have an interaction variable. Algebraically, the interaction variable is the other variables in the regression equation
product
In linear regression, we fit the least squares line to a set of values (or points on a scatterplot). The distance from the line to a point is called the
residual
The percentage of variation (R^2 ) can be interpreted as the fraction (or percent) of variation of the
response variable explained by the regression line
The standard error of the estimate (Se) is essentially the
standard deviation of the residuals
The adjusted R^2 adjusts R^2 for
the number of explanatory variables in a multiple regression model
Given the least squares regression line, ^Y=8-3X
the relationship between X and Y is negative
Correlation is a summary measure that indicates
the strength of the linear relationship between pairs of variables
The term auto correlation refers to
time series variables are usually related to their own past values
In linear regression, a dummy variable is used:
to include categorical variables in the regression equation
The percentage of variation (R^2) ranges from
0 to +1
The percentage of variation explained is the square of the correlation between the observed values and the fitted values
True
The primary purpose of a nonlinear transformation is to "straighten out" the data on a scatterplot
True
A logarithmic transformation of the response variable is often useful when the distribution of is symmetric.
False
A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 32 + 8. This implies that an increase of $1 in advertising is expected to result in 40 dollars of sale
False
Correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship.
False
If a categorical variable is to be included in a multiple regression, a dummy variable for each category of the variable should be used, but the original categorical variables should not be used.
False
In a nonlinear transformation of data, the variable or the variables may be transformed, but not both
False
In a simple linear regression problem, if the percentage of variation explained is 0.95, thismeans that 95% of the variation in the explanatory variable can be explained by regression
False
Scatterplots are used for identifying outliers and quantifying relationships between variables.
False
The coefficients for logarithmically transformed explanatory variables should be interpreted as the percent change in the dependent variable for a 1% percent change in the explanatory variable.
False
The least squares line is the line that minimizes the sum of the residuals.
False
To help explain or predict the response variable in every regression study, we use one or more explanatory variables. These variables are also called response variables or independent variables
False
The adjusted R^2 is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model
True
The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric
True
A negative relationship between an explanatory variable and a response variable means that as increases, Y decreases, and vice versa.
True
A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 84 +7. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is $140,000.
True
A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 84 +7. This implies that if there is no advertising, then the predicted amount of sales (in dollars) is $84,000.
True
A regression analysis between weight ( in pounds) and height ( in inches) resulted in the following least squares line: = 140 + 5. This implies that if the height is increased by 1 inch, the weight is expected to increase on average by 5 pounds.
True
A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis)versus fitted values (on the horizontal axis), where a "good" fit not only has small residuals, but it has residuals scattered randomly around zero with no apparent pattern.
True
A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis)versus fitted values (on the horizontal axis), where a "good" fit not only has small residuals, but ithas residuals scattered randomly around zero with no apparent pattern.
True
An outlier is an observation that falls outside of the general pattern of the rest of the observations on a scatterplot.
True
Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y
True
Cross-sectional data are usually data gathered from approximately the same period of time from across-sectional of a population.
True
For the multiple regression model , if were to increase by 5 units,holding and constant, the value of would be expected to decrease by 50 units.
True
In a multiple regression problem with two explanatory variables if, the fitted regression equation is
True
In every regression study there is a single variable that we are trying to explain or predict. This is called the response variable or dependent variable.
True
Regression analysis can be applied equally well to cross-sectional and time series data
True
The R^2 can only increase when extra explanatory variables are added to a multiple regression model
True
The adjusted R^2 is adjusted for the number of explanatory variables in a regression equation, and it has the same interpretation as the standard R^2.
True
