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'How do you interpret a coefficient of determination;, equal to 0.80? Answer: 72 = 0.80 can be interpreted that the given model explains % of the variation in the data'
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Alright, since the given question we have been asked, how do you interpret a coefficient of determination? That is R squared is equal to 0.80. Okay, now, when we say coefficient of determination, what do we determine from this to the coefficient of determination? It basically measures the proportion of radiation, say in invariable why that is explained employee I. D. Independent variable X. In the regression model. Right now Here, the coefficient of value, the value of the coefficient of determination is .80 that we can interpret by the show that the given model explains 80% of the variation in Y. Right? So that is how we can interpret the given coefficient of determination. Right? So that will be the answer for the given question. Hope this helps you. Thank you for watching.
A. the variation in the residuals is the same for all fitted values of
In multiple regression analysis, residual analysis is used to test the requirement that
A. the variation in the residuals is the same for all fitted values of
B. the independent
variables are the direct cause of the dependent variable
C. the number of independent variables included in the analysis is correct
D. prediction error is minimized
C. the independent variables and the dependent variable have a linear relationship
A valid multiple regression analysis assumes or requires that
A. the
dependent variable is measured using an ordinal, interval, or ratio scale
B. the residuals follow an F-distribution
C. the independent variables and the dependent variable have a linear relationship
D. the observations are autocorrelated
C. Coefficient of multiple determination
How is the degree of association between a
set of independent variables and a dependent variable measured?
A. Confidence intervals.
B. Autocorrelation
C. Coefficient of multiple determination
D. Standard error of estimate
A. the regression sum of squares
In a multiple regression ANOVA table, explained variation is represented by
A. the regression
sum of squares
B. the total sum of squares
C. the regression coefficients
D. the correlation matrix
If the coefficient of multiple determination is 0.81, what percent of variation is not explained?
A. 19%
B. 90%
C. 66%
D. 81%
In multiple regression analysis, testing the global null hypothesis that the multiple regression coefficients are all zero is
based on
A. a z statistic
B. a t statistic
C. a F statistic
D. binomial distribution
What is the range of values for multiple R?
A. -100% to -100% inclusive
B. -100% to 0% inclusive
C. 0% to +100% inclusive
D. Unlimited range
C. The independent variables are highly correlated
When does multicollinearity occur in a multiple regression analysis?
A. The dependent variables are highly correlated
B. The independent variables are minimally correlated
C. The independent variables are highly correlated
D. The independent variables have no correlation
In multiple regression analysis, when the independent variables are highly correlated, this situation is
called ____________________.
A. Autocorrelation
B. Multicollinearity
C. Homoscedasticity
D. curvilinearity
In the general multiple regression equation which of the following variables represents the Y intercept?
A. b1
B. x1
C. Y^
D. a
B. regression coefficients.
If there are four independent variables in a multiple regression equation, there are also four
A. Y-intercepts.
B. regression coefficients.
C. dependent variables.
D. constant terms.
B. The "error" or variability in predicting Y
What does the multiple standard error
of estimate measure?
A. Change in for a change in X 1
B. The "error" or variability in predicting Y
C. The regression mean square error in the ANOVA table
D. Amount of explained variation
If a multiple regression analysis is based on ten independent variables collected from a sample of 125 observations, what will be the value of the denominator in the calculation of the multiple standard error of estimate?
A. 125
B. 10
C. 114
D. 115
D. An effective regression equation
If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?
A. Multicollinearity between these two independent variables
B. A
negative relationship is not possible
C. Only one of the two independent variables will explain a high percent of the variation
D. An effective regression equation
D. Both independent variables should be used to predict the dependent variable.
If the correlation between the two independent variables of a regression
analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?
A. Only one of the independent variables should be used in the regression equation.
B. The independent variables are strongly related.
C. Two separate regression equations are required.
D. Both independent variables should be used to predict the dependent variable.
B.
Simple correlation coefficients
What does the correlation matrix for a multiple regression analysis contain?
A. Multiple correlation coefficients
B. Simple correlation coefficients
C. Multiple coefficients of determination
D. Multiple standard errors of estimate
B. No relationship exists between the dependent
variable and any of the independent variables
What can we conclude if the global test of regression does not reject the null hypothesis?
A. A strong relationship exists among the variables
B. No relationship exists between the dependent variable and any of the independent variables
C. The independent variables are good predictors
D. Good forecasts are possible
C. At least one of the net regression coefficients is not equal to zero.
What can we conclude if the global test of regression rejects the null hypothesis?
A. Strong correlations exist among the variables
B. No relationship exists between the dependent variable and any of the independent variables
C. At least one of the net regression coefficients is not equal
to zero.
D. Good predictions are not possible
A. Number of independent variables
What are the degrees of freedom associated with the regression sum of squares?
A. Number of independent variables
B. 1
C. F-ratio
D. (n - 2)
Which of the following
is a characteristic of the F-distribution?
A. Normally distributed
B. Positively skewed
C. Negatively skewed
D. Equal to the t-distribution
In a regression analysis, three independent variables are used in the equation based on a sample of forty observations. What are the degrees of freedom associated with the F-statistic?
A. 3 and 39
B. 4 and 40
C. 3 and 36
D. 2 and 39
Hypotheses concerning individual regression coefficients are tested using which statistic?
A. t-statistic
B. z-statistic
C. X2 (chi-square statistic)
D. F
A. explained variation relative to total variation.
The coefficient of determination measures the proportion of
A.
explained variation relative to total variation.
B. variation due to the relationship among variables.
C. error variation relative to total variation.
D. variation due to regression.
E. All of these are correct
What happens as the scatter of data values about the regression plane increases?
A. Standard error of
estimate increases
B. R 2 decreases
C. (1 - R 2) increases
D. Error sum of squares increases
E. All of these are correct
For a unit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y^=5.2+6.3X1-7.1X2?
A. -7.1
B. +6.3
C. +5.2
D. +4.4
The best example of a null hypothesis for a global test of a multiple regression model is:
A. Ho:B1=B2=B3=B4
B. Ho:u1=u2=u3=u4
C. Ho:B1=0
D. If F is greater than 20.00 then reject
C. H1: Not all the B's are 0
The best example of an alternate hypothesis for a global test of a
multiple regression model is:
A. H1:B1=B2=B3=B4
B. H1:B1=/=B2=/=B3=/=B4
C. H1: Not all the B's are 0
D. If F is less than 20.00 then fail to reject
The best example of a null hypothesis for testing an individual regression coefficient is:
A. Ho:B1=B2=B3=B4
B. Ho:u1=u2=u3=u4
C. Ho:B1=0
D. If F is greater than 20.00 then reject
C. Evaluate homoscedasticity
In multiple regression analysis, residuals (Y - Y^) are used to:
A. Provide a global test of a multiple regression model.
B. Evaluate multicollinearity
C. Evaluate homoscedasticity
D. Compare two regression coefficients
C.
A nominal variable with only two values
In multiple regression, a dummy variable can be included in a multiple regression model as
A. An additional quantitative variable
B. A nominal variable with three or more values
C. A nominal variable with only two values
D. A new regression coefficient
B. A dependent
variable and several independent variables
Multiple regression analysis is applied when analyzing the relationship between
A. An independent variable and several dependent variables
B. A dependent variable and several independent variables
C. Several dependent variables and several independent variables
D. Several regression equations and a single sample