Deck 12: Multiple Regression

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سؤال
The mean square in an Analysis of Variance (ANOVA) for multiple regression is the explained sum of squares (MSR) divided by the unexplained sum of squares (MSE).
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سؤال
The standard error of the estimate (sy.x) in multiple linear regression is the square of the Mean Square Error (MSE).
سؤال
In regression analysis, a set of binary (0-1) variables can be used to introduce qualitative (categorical) variables into the model.
سؤال
The square root of the Mean Square Error (MSE) gives the standard error of estimate in regression analysis.
سؤال
Introducing a series of highly correlated independent variables into a regression analysis will make it difficult to interpret the estimated regression coefficients because they may tend to fluctuate widely in response to small changes in the model or data set.
سؤال
In multiple regression, one's goal should be to effectively explain the variation in the dependent variable by using as many independent variables as possible.
سؤال
Residual analysis may make use of a plot showing the residuals or errors to evaluate the assumptions about the error term.
سؤال
In simple linear regression analysis, when testing for significance, the F test and the t test will always yield consistent results.
سؤال
In simple linear regression analysis, when testing for significance, the F test and the t test will always result in the same conclusion.
سؤال
The Mean Square Regression (MSR) in an Analysis of Variance (ANOVA) for multiple regression is the sum of squares divided by (sample size -1) degrees of freedom.
سؤال
In regression analysis, a data point that does not fall along the least squares line (or plane) is called a residual.
سؤال
The mean square (MS) values in an Analysis of Variance (ANOVA) for multiple regression are the sum of squares (SS) values divided by their corresponding degrees of freedom.
سؤال
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a dummy variable.
سؤال
In multiple regression, adding more independent variables to the model will never decrease the value of r2.
سؤال
In regression analysis, a residual plot that shows a clear pattern rather than random behavior can be generally considered an indication that at least one assumption regarding the error terms is being violated.
سؤال
In multiple regression analysis, multicollinearity (or simply collinearity) refers to the correlation among the independent variables.
سؤال
In multiple regression, an adjusted r2 value can be used to help avoid adding more and more potentially collinear independent variables to the model.
سؤال
In multiple linear regression, the correlation coefficient is reported as a non-negative value.
سؤال
The coefficient of determination r2, a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y (SSR) to the total variation in y (SST), and takes on values between 0 and 1.
سؤال
In multiple linear regression analysis, rejecting the "all β\beta s are 0" null hypothesis means that you have found no useful relationship between the variables.
سؤال
Which of the following relationships in linear regression is correct?

A)SSE = SSR + SST
B)SSR = SSE + SST
C)SST = (SSR)2
D)SST = SSR + SSE
E)none of the above
سؤال
In residual analysis for multiple regression, if the assumptions about the error term are valid and the model is an adequate representation of the relationships between the variables, then the plot of the residuals versus the predicted y values

A)shows a horizontal band of points
B)has a funnel shape
C)has a curved shape
D)is upward sloping
E)none of the above
سؤال
A regression analysis linking demand (y in 1000 units) to price (x1 in dollars) and advertising (x2 in $1000s) resulted in the following equation: estimated Y = 9 - 5x1 + 2x2.This equation implies that a $1 increase in price can be associated with a ____ in demand.

A)9000 - 5000 = 4000 unit increase
B)9000 unit decrease
C)9000 + 5000 = 14,000 unit decrease
D)5,000 unit decrease
E)none of the above
سؤال
Adding independent variables to a regression model will typically_______ the value of r2.

A)decrease
B)increase
C)not affect
D)nullify
E)reduce by half or more
سؤال
In regression analysis, which of the following is NOT a required assumption about the error term, ε\varepsilon ?

A)the expected value of the error term is zero
B)the error term has a normal distribution
C)the standard deviation of the error term is constant
D)the values of the error term are independent
E)none of the above, all are required assumptions
سؤال
A term used to describe the case when the independent variables in a multiple regression model are correlated is

A)auto-regression
B)multi-collinearity
C)correlation
D)coefficient of determination
E)none of the above
سؤال
Which of the following is true regarding the F distribution?

A)it is the ratio of two variances from two normal populations
B)it is not symmetric
C)values can never be negative
D)it has numerator degrees of freedom from sample 1 and denominator degrees of freedom from sample 2
E)all of the above
سؤال
In regression analysis, if r2 = 1, then

A)SSE = SST
B)SSR = SST
C)SSR = SSE
D)SSE = 1
E)none of the above
سؤال
In simple linear regression analysis, which of the following is NOT true?

A)the F test and the t test yield the same results
B)the F test and the t test have different p-values
C)the relationship between x and y is represented by means of a straight line
D)the value of F = t2
E)none of the above
سؤال
Larger values of r2 imply that the observations are more closely grouped about the

A)average value of the independent variables
B)average value of the dependent variable
C)least squares line or plane
D)origin
E)none of the above
سؤال
Which of the following is NOT true regarding the coefficient of determination, r2?

A)it is the sum of squares error (SSE) divided by the sum of squares total (SST)
B)it is a measure of the goodness of fit of the estimated regression equation
C)it takes on values between 0 and 1
D)it explains the amount of variation in y associated with variation in x
E)none of the above: all are true
سؤال
The adjusted r2 value is adjusted for

A)the number of dependent variables
B)the number of independent variables
C)the number of equations
D)the number of numbers
E)none of the above
سؤال
In simple linear regression, if the correlation coefficient is a positive value, then the slope of the estimated regression line

A)must also be positive
B)can be either negative or positive
C)can be zero
D)must be negative
E)none of the above
سؤال
In simple linear regression, a least squares regression line

A)assumes a relationship between the slope of x and the intercept of y
B)may be used to predict a value of y if the corresponding x value is given
C)must be linear, upward-sloping and have a positive y-intercept
D)minimizes the sum of the deviations between the observed value of y and the estimated value of y
E)all of the above
سؤال
In a simple linear regression model, the variance of the error term ε\varepsilon is assumed to be

A)the same for all values of x
B)zero
C)increasing as x values increase
D)-1
E)none of the above
سؤال
In multiple linear regression, which of the following is NOT true about the hypothesis tests:

A)the F test measures the overall significance of the regression equation
B)the t test measures the significance of an individual regression coefficient
C)F = t2 just as in simple linear regression
D)the null hypothesis for the F test is that all the slopes are equal to 0
E)the null hypothesis for the t test is that the particular slope is equal to 0
سؤال
In the ANOVA table for simple linear regression, the mean square regression (MSR) is the

A)sum of squares regression (SSR) divided by degrees of freedom = 1
B)sum of squares regression (SSR) divided by degrees of freedom = n-2
C)mean square total minus mean square error
D)mean square error divided by mean square total
E)none of the above
سؤال
In multiple regression, the adjusted r2 value is generally

A)greater than r2
B)used to discourage adding more independent variables.
C)used to encourage adding more independent variables.
D)test for the significance of y
E)a and d
سؤال
Adding independent variables to a regression model will ______ decrease the value of r2.

A)sometimes
B)never
C)always
D)rarely
E)often
سؤال
In regression analysis, which of the following is not a required assumption about the error term ε\varepsilon :

A)the expected value of the error term is zero
B)the variance of the error term is constant
C)the values of the error term must be positive.
D)the error term is normally distributed
E)all of the above
سؤال
A simple regression analysis linking a dependent variable y to an independent variable x is conducted with 20 observations.The p-value value for tstat in the  = 0 hypothesis test turns out to be .0162.The p-value value for Fstat in the same test must be

A)1 - .0162 = .9838.
B)2 times .0162 = .0324
C).0162.
D)statistically significant at the 1% significance level.
E)none of the above
سؤال
1% of the values in an F distribution with numerator degrees of freedom= 5 and denominator degrees of freedom = 22 are greater than ___.

A)3.988
B)2.661
C)4.102
D)3.939
E)2.699
سؤال
A regression analysis involved 4 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the numerator degrees of freedom should be

A)15
B)4
C)2
D)16
E)none of the above
سؤال
In multiple regression analysis

A)there can be any number of dependent variables but only one independent variable
B)there must be only one independent variable
C)the coefficient of determination must be larger than 1
D)there can be several independent variables, but only one dependent variable
E)none of the above
سؤال
A simple regression analysis linking dependent variable y to independent variable x is conducted with 25 observations.The value of Fstat used to test the β\beta = 0 null hypothesis turns out to be 12.7.The value of tstat for the x coefficient is

A)15
B)3.56
C)12.7
D)161.29
E)cannot be determined from the information given
سؤال
A simple regression analysis linking dependent variable y to independent variable x is conducted with 20 observations.The F ratio used to test the  = 0 null hypothesis indicates that the slope coefficient is statistically significant at the 5% significance level.The value of tstat for the x coefficient will also show that the slope coefficient is

A)statistically significant at the 2.5% significance level.
B)greater than F
C)statistically significant at the 5% significance level.
D)statistically significant at the 1% significance level.
E)none of the above
سؤال
A regression analysis involved 5 independent variables and 15 observations..In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)9
B)10
C)14
D)4
E)none of the above
سؤال
5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 12 are greater than ___.

A)3.634
B)4.451
C)6.112
D)6.226
E)3.490
سؤال
A regression analysis involved 6 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)26
B)13
C)14
D)25
E)none of the above
سؤال
A multiple regression analysis uses 5 independent variables and 15 observations.The F ratio for testing the 'all s are 0' null hypothesis turns out to be statistically significant at the 5% significance level.It must be true that ____ of the regression coefficients are (is) statistically significant at the 5% level.

A)all
B)at least one
C)most
D)none
E)none of the above
سؤال
A regression analysis involved 6 independent variables and 27 observations.The t distribution in which we will find the critical value of t for testing the significance of each of the independent variable coefficients will have

A)20 degrees of freedom
B)21 degrees of freedom
C)26 degrees of freedom
D)27 degrees of freedom
E)none of the above
سؤال
In an F distribution with numerator degrees of freedom of 4 and denominator degrees of freedom of 8, 99% of the values are less than ______ .

A)3.838
B)6.041
C)7.006
D)14.799
سؤال
5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 17 are greater than ___.

A)3.758
B)2.576
C)2.549
D)3.812
E)3.197
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ملء الشاشة (f)
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Deck 12: Multiple Regression
1
The mean square in an Analysis of Variance (ANOVA) for multiple regression is the explained sum of squares (MSR) divided by the unexplained sum of squares (MSE).
False
2
The standard error of the estimate (sy.x) in multiple linear regression is the square of the Mean Square Error (MSE).
False
3
In regression analysis, a set of binary (0-1) variables can be used to introduce qualitative (categorical) variables into the model.
True
4
The square root of the Mean Square Error (MSE) gives the standard error of estimate in regression analysis.
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5
Introducing a series of highly correlated independent variables into a regression analysis will make it difficult to interpret the estimated regression coefficients because they may tend to fluctuate widely in response to small changes in the model or data set.
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6
In multiple regression, one's goal should be to effectively explain the variation in the dependent variable by using as many independent variables as possible.
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7
Residual analysis may make use of a plot showing the residuals or errors to evaluate the assumptions about the error term.
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8
In simple linear regression analysis, when testing for significance, the F test and the t test will always yield consistent results.
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9
In simple linear regression analysis, when testing for significance, the F test and the t test will always result in the same conclusion.
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10
The Mean Square Regression (MSR) in an Analysis of Variance (ANOVA) for multiple regression is the sum of squares divided by (sample size -1) degrees of freedom.
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11
In regression analysis, a data point that does not fall along the least squares line (or plane) is called a residual.
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12
The mean square (MS) values in an Analysis of Variance (ANOVA) for multiple regression are the sum of squares (SS) values divided by their corresponding degrees of freedom.
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13
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a dummy variable.
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14
In multiple regression, adding more independent variables to the model will never decrease the value of r2.
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15
In regression analysis, a residual plot that shows a clear pattern rather than random behavior can be generally considered an indication that at least one assumption regarding the error terms is being violated.
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16
In multiple regression analysis, multicollinearity (or simply collinearity) refers to the correlation among the independent variables.
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17
In multiple regression, an adjusted r2 value can be used to help avoid adding more and more potentially collinear independent variables to the model.
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18
In multiple linear regression, the correlation coefficient is reported as a non-negative value.
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19
The coefficient of determination r2, a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y (SSR) to the total variation in y (SST), and takes on values between 0 and 1.
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20
In multiple linear regression analysis, rejecting the "all β\beta s are 0" null hypothesis means that you have found no useful relationship between the variables.
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21
Which of the following relationships in linear regression is correct?

A)SSE = SSR + SST
B)SSR = SSE + SST
C)SST = (SSR)2
D)SST = SSR + SSE
E)none of the above
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22
In residual analysis for multiple regression, if the assumptions about the error term are valid and the model is an adequate representation of the relationships between the variables, then the plot of the residuals versus the predicted y values

A)shows a horizontal band of points
B)has a funnel shape
C)has a curved shape
D)is upward sloping
E)none of the above
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23
A regression analysis linking demand (y in 1000 units) to price (x1 in dollars) and advertising (x2 in $1000s) resulted in the following equation: estimated Y = 9 - 5x1 + 2x2.This equation implies that a $1 increase in price can be associated with a ____ in demand.

A)9000 - 5000 = 4000 unit increase
B)9000 unit decrease
C)9000 + 5000 = 14,000 unit decrease
D)5,000 unit decrease
E)none of the above
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24
Adding independent variables to a regression model will typically_______ the value of r2.

A)decrease
B)increase
C)not affect
D)nullify
E)reduce by half or more
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25
In regression analysis, which of the following is NOT a required assumption about the error term, ε\varepsilon ?

A)the expected value of the error term is zero
B)the error term has a normal distribution
C)the standard deviation of the error term is constant
D)the values of the error term are independent
E)none of the above, all are required assumptions
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26
A term used to describe the case when the independent variables in a multiple regression model are correlated is

A)auto-regression
B)multi-collinearity
C)correlation
D)coefficient of determination
E)none of the above
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27
Which of the following is true regarding the F distribution?

A)it is the ratio of two variances from two normal populations
B)it is not symmetric
C)values can never be negative
D)it has numerator degrees of freedom from sample 1 and denominator degrees of freedom from sample 2
E)all of the above
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28
In regression analysis, if r2 = 1, then

A)SSE = SST
B)SSR = SST
C)SSR = SSE
D)SSE = 1
E)none of the above
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29
In simple linear regression analysis, which of the following is NOT true?

A)the F test and the t test yield the same results
B)the F test and the t test have different p-values
C)the relationship between x and y is represented by means of a straight line
D)the value of F = t2
E)none of the above
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30
Larger values of r2 imply that the observations are more closely grouped about the

A)average value of the independent variables
B)average value of the dependent variable
C)least squares line or plane
D)origin
E)none of the above
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31
Which of the following is NOT true regarding the coefficient of determination, r2?

A)it is the sum of squares error (SSE) divided by the sum of squares total (SST)
B)it is a measure of the goodness of fit of the estimated regression equation
C)it takes on values between 0 and 1
D)it explains the amount of variation in y associated with variation in x
E)none of the above: all are true
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32
The adjusted r2 value is adjusted for

A)the number of dependent variables
B)the number of independent variables
C)the number of equations
D)the number of numbers
E)none of the above
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33
In simple linear regression, if the correlation coefficient is a positive value, then the slope of the estimated regression line

A)must also be positive
B)can be either negative or positive
C)can be zero
D)must be negative
E)none of the above
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34
In simple linear regression, a least squares regression line

A)assumes a relationship between the slope of x and the intercept of y
B)may be used to predict a value of y if the corresponding x value is given
C)must be linear, upward-sloping and have a positive y-intercept
D)minimizes the sum of the deviations between the observed value of y and the estimated value of y
E)all of the above
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35
In a simple linear regression model, the variance of the error term ε\varepsilon is assumed to be

A)the same for all values of x
B)zero
C)increasing as x values increase
D)-1
E)none of the above
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36
In multiple linear regression, which of the following is NOT true about the hypothesis tests:

A)the F test measures the overall significance of the regression equation
B)the t test measures the significance of an individual regression coefficient
C)F = t2 just as in simple linear regression
D)the null hypothesis for the F test is that all the slopes are equal to 0
E)the null hypothesis for the t test is that the particular slope is equal to 0
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37
In the ANOVA table for simple linear regression, the mean square regression (MSR) is the

A)sum of squares regression (SSR) divided by degrees of freedom = 1
B)sum of squares regression (SSR) divided by degrees of freedom = n-2
C)mean square total minus mean square error
D)mean square error divided by mean square total
E)none of the above
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38
In multiple regression, the adjusted r2 value is generally

A)greater than r2
B)used to discourage adding more independent variables.
C)used to encourage adding more independent variables.
D)test for the significance of y
E)a and d
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39
Adding independent variables to a regression model will ______ decrease the value of r2.

A)sometimes
B)never
C)always
D)rarely
E)often
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40
In regression analysis, which of the following is not a required assumption about the error term ε\varepsilon :

A)the expected value of the error term is zero
B)the variance of the error term is constant
C)the values of the error term must be positive.
D)the error term is normally distributed
E)all of the above
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41
A simple regression analysis linking a dependent variable y to an independent variable x is conducted with 20 observations.The p-value value for tstat in the  = 0 hypothesis test turns out to be .0162.The p-value value for Fstat in the same test must be

A)1 - .0162 = .9838.
B)2 times .0162 = .0324
C).0162.
D)statistically significant at the 1% significance level.
E)none of the above
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42
1% of the values in an F distribution with numerator degrees of freedom= 5 and denominator degrees of freedom = 22 are greater than ___.

A)3.988
B)2.661
C)4.102
D)3.939
E)2.699
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43
A regression analysis involved 4 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the numerator degrees of freedom should be

A)15
B)4
C)2
D)16
E)none of the above
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44
In multiple regression analysis

A)there can be any number of dependent variables but only one independent variable
B)there must be only one independent variable
C)the coefficient of determination must be larger than 1
D)there can be several independent variables, but only one dependent variable
E)none of the above
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45
A simple regression analysis linking dependent variable y to independent variable x is conducted with 25 observations.The value of Fstat used to test the β\beta = 0 null hypothesis turns out to be 12.7.The value of tstat for the x coefficient is

A)15
B)3.56
C)12.7
D)161.29
E)cannot be determined from the information given
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46
A simple regression analysis linking dependent variable y to independent variable x is conducted with 20 observations.The F ratio used to test the  = 0 null hypothesis indicates that the slope coefficient is statistically significant at the 5% significance level.The value of tstat for the x coefficient will also show that the slope coefficient is

A)statistically significant at the 2.5% significance level.
B)greater than F
C)statistically significant at the 5% significance level.
D)statistically significant at the 1% significance level.
E)none of the above
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47
A regression analysis involved 5 independent variables and 15 observations..In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)9
B)10
C)14
D)4
E)none of the above
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48
5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 12 are greater than ___.

A)3.634
B)4.451
C)6.112
D)6.226
E)3.490
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49
A regression analysis involved 6 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)26
B)13
C)14
D)25
E)none of the above
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50
A multiple regression analysis uses 5 independent variables and 15 observations.The F ratio for testing the 'all s are 0' null hypothesis turns out to be statistically significant at the 5% significance level.It must be true that ____ of the regression coefficients are (is) statistically significant at the 5% level.

A)all
B)at least one
C)most
D)none
E)none of the above
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51
A regression analysis involved 6 independent variables and 27 observations.The t distribution in which we will find the critical value of t for testing the significance of each of the independent variable coefficients will have

A)20 degrees of freedom
B)21 degrees of freedom
C)26 degrees of freedom
D)27 degrees of freedom
E)none of the above
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52
In an F distribution with numerator degrees of freedom of 4 and denominator degrees of freedom of 8, 99% of the values are less than ______ .

A)3.838
B)6.041
C)7.006
D)14.799
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53
5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 17 are greater than ___.

A)3.758
B)2.576
C)2.549
D)3.812
E)3.197
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