Deck 6: Regression Analysis

Question 1

In a simple regression model Y = ß₀ + ß₁X + ε,ε represents the ________.

A)slope of the regression line
B)intercept
C)error term
D)mean value of X

Answer 1

error term

Question 2

A confidence interval for the independent variable X would specify ________.

A)the uncertainty about the mean value of the dependent variable
B)the possible values of X that are uncorrelated with the dependent variable
C)all the possible values of X
D)the probability distribution for the various values of X

Answer 2

the uncertainty about the mean value of the dependent variable

Question 3

________ is a regression model that involves one dependent variable and one independent variable.

A)Multiple regression
B)Simple regression
C)Single regression
D)Step-wise regression

Answer 3

Simple regression

Question 4

How is the significance of regression tested?

A)by checking the sum of the squares of the residuals for statistical significance
B)by testing whether the slope of the independent variable is zero
C)by testing whether the intercept term is greater than or equal to 1
D)by checking the absolute value of the coefficient of the dependent variable

Question 5

For the least-squares equation = 3,698 + 2,538X,Y represents house prices and X represents number of rooms.Which of the following statements is true?

A)Only 36.98% of the variation in house prices can be explained by the number of rooms in the house.
B)For every additional room that is added in a house,house prices increase by $2,538.
C)As the number of rooms in the house increase,prices fall by $3,698.
D)25.38% of the house price is attributed to the number of rooms.

Question 6

The regression equation = 3,698 + 2,538X gives an R² value of 0.2645.This means that ________.

A)X and Y have a very high level of correlation
B)the percentage of variation in Y that is attributed to random factors is 26.45%
C)26.45% of the variation in Y can be explained by X
D)a one-percent change in Y will lead to a 26.45% change in X

Question 7

If the stock return is the same as the market return,the slope of the regression line is ________.

A)greater than one
B)equal to one
C)lesser than one
D)equal to zero

Question 8

Regression analysis can be described as ________.

A)a statistical hypothesis test in which the test statistic follows a Student's t-distribution if the null hypothesis is supported
B)a collection of statistical models in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation
C)a statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true
D)a tool for building statistical models that characterize relationships among a dependent variable and one or more independent variables,all of which are numerical

Question 9

The specific risk associated with a stock is measured by ________.

A)the slope of the regression line
B)the intercept of the regression equation
C)the standard error of the estimate
D)the sum of the squares of errors

Question 10

In a simple regression model Y = ß₀ + ß₁X + ε,ß₀ represents the ________.

A)slope of the regression line
B)intercept
C)error term
D)mean value of X

Question 11

To determine whether a linear relationship exists between variables,a ________ can be used.

A)bar chart
B)pie chart
C)scatter chart
D)stacked column chart

Question 12

R Square (R²)is also known as the ________.

A)sample correlation coefficient
B)coefficient of regression
C)test statistic
D)coefficient of determination

Question 13

A prediction interval for the independent variable X would specify ________.

A)all the possible values of the dependent variable Y
B)the probability distribution for the various values of X
C)the uncertainty in the dependent variable for a single value of X
D)all the possible values of X

Question 14

Specific risk associated with a single stock is ________.

A)variation in stock price explained by the market
B)variation in stock price due to factors such as earnings potential
C)characterized by a measure called beta
D)measured by the slope of the regression line

Question 15

If the stock return increases at a slower rate than the market return,the slope of the regression line is ________.

A)greater than one
B)equal to one
C)lesser than one
D)equal to zero

Question 16

In a simple regression model Y = ß₀ + ß₁X + ε,Y represents the ________.

A)slope of the regression line
B)independent variable
C)intercept
D)dependent variable

Question 17

In least-squares regression,the best-fitting line minimizes ________.

A)the sum of the squares of the dependent variables
B)the squares of the slope and intercept term
C)the squares of the mean values of X and Y
D)the sum of squares of the observed errors

Question 18

Systematic risk associated with a single stock is defined as the variation in the stock price explained by ________.

A)market movements
B)the firm's earnings potential
C)acquisition strategies
D)net losses

Question 19

When analyzing systematic risk of a stock,if the slope of the regression line is greater than 1,________.

A)the stock return exceeds market return
B)the market return and stock return move equally
C)the stock return increases at a slower rate than market
D)the stock return and market return are uncorrelated

Question 20

In a simple regression model Y = ß₀ + ß₁X + ε,ß₁ represents the ________.

A)slope of the regression line
B)intercept
C)error term
D)mean value of X

Question 21

A regression model displays multicollinearity when ________.

A)the correlation coefficient for dependent variables is 0.7
B)the variance inflation factor is equal to -1.
C)the correlation coefficient for independent variables is 1
D)the variance inflation factor is less than 3

Question 22

If the residuals for a regression model exhibit a parabolic shape,this would violate the assumption of ________.

A)homoscedasticity
B)linearity
C)autocorrelation
D)normality of errors

Question 23

For simple linear regression,the p-value associated with the test for the slope coefficient ________.

A)is usually a value greater than 1
B)will be equal to the Significance F value
C)measures the fit of the regression line to the data
D)explains the variation of the dependent variable around the mean

Question 24

The assumption of homoscedasticity means that ________.

A)variation about the regression line is constant for all values of the independent variable
B)the residuals should appear to be randomly scattered about zero,with no apparent pattern
C)the errors for each individual value of X are normally distributed,with a mean of 0
D)the residuals should be scattered in a parabolic shape about zero

Question 25

________ indicates the strength of association between the dependent and independent variables in multiple regression.

A)Variance inflation factor
B)R square
C)Standard error
D)ANOVA

Question 26

Which of the following is not an assumption made in regression analysis?

A)The parameters of the regression equation are linear.
B)The values of successive observations are correlated.
C)The errors for each individual value of x are normally distributed.
D)Variation about the regression line is constant for all values of the independent variable.

Question 27

Autocorrelation in a data set can be identified by ________.

A)a high R Square value
B)residual plots with large differences in the variances at different values of the independent variable
C)residual plots having clusters of residuals with the same sign
D)nonlinear parameters in the regression equation

Question 28

If the variance inflation factor is equal to one,________.

A)the independent variables are not correlated
B)the value of Multiple R will also be one
C)the data exhibits autocorrelation
D)the p-values are most likely inflated

Question 29

When testing the significance of the regression,if the value of Significance F is ________,the null hypothesis is rejected.

A)less than the p-value
B)more than the level of significance
C)more than the p-value
D)less than the level of significance

Question 30

Which of the following correctly describes multicollinearity?

A)A condition occurring when two or more independent variables in the same regression model can predict each other better than the dependent variable.
B)A condition occurring when the standard residual in a regression model takes a zero value.
C)A condition occurring when the value of the regression coefficient is the same for two or more dependent variables.
D)A condition occurring when two or more dependent variables in the same regression model have a correlation coefficient equal to zero.

Question 31

A high R Square value means that there is ________.

A)a strong relationship between the independent and dependent variables
B)a weak relationship between the independent and dependent variables
C)no relationship between the independent and dependent variables
D)a curvilinear relationship between the independent and dependent variables

Question 32

Standard residuals are ________.

A)residuals minus the outlier values
B)the sum of squared residuals
C)residuals subtracted from their mean
D)residuals divided by their standard deviation

Question 33

For simple linear regression,________ is the regression statistic and it is also known as the sample correlation coefficient.

A)standard error
B)adjusted R²
C)R²
D)multiple R

Question 34

The Durbin-Watson statistic for a data set gives a value of 0.This means that ________.

A)the errors for each value of X are normally distributed
B)the data exhibits autocorrelation
C)a curvilinear regression model should be used for the data
D)the data is heteroscedastic

Question 35

The variability of the observed Y-values from the predicted values, is called the ________.

A)adjusted R²
B)standard error of the estimate
C)R²
D)multiple R

Question 36

Adding an independent variable to a multiple regression model will ________.

A)maximize the Adjusted R².
B)increase the value of the R²
C)lead to a negative t-statistic
D)decrease the p-value

Question 37

When the variance of the mean value is smaller than the variance of individual values,________.

A)the p-value is equal to the Significance F
B)the data set contains an outlier
C)the Adjusted R Square is equal to 1
D)the prediction interval is wider than the confidence interval

Question 38

If the data are clustered close to the regression line ________.

A)the correlation coefficient is likely to be 0
B)the standard error is likely to be small
C)the intercept term is likely to be large
D)the slope is likely to be negative

Question 39

Statistical hypothesis tests are based on all of the following assumptions about the data except ________.

A)linearity
B)normality of errors
C)dependence of errors
D)homoscedasticity

Question 40

The best way to measure multicollinearity is using the ________.

A)factor of sums
B)variance inflation factor
C)standard deviation
D)correlation matrix

Question 41

Insignificant variables in a multiple regression model can be removed using ________.

A)step-wise regression
B)dummy variables
C)the Durbin-Watson statistic
D)linear extrapolation

Question 42

Models having a Bonferroni Criterion (Cp)less than 1 ________.

A)have a substantial bias.
B)are good models to consider
C)need to be recalculated.
D)are underspecified models.

Question 43

What is meant by an underspecified model?

A)a model that has more independent variables than dependent variables
B)a model that does not have relevant predictors
C)a model that has only one dependent variable
D)a model that has a low R² value

Question 44

If a variable is removed from the regression model when the t-statistic is lesser than 1,________.

A)the standard error will decrease
B)the p-value will increase
C)the Adjusted R² will decrease
D)the Multiple R will increase

Question 45

Which of the following is an automated method that can be used to find the set of variables with the largest Adjusted R² in a multiple regression model?

A)best-subsets regression
B)ANOVA
C)the method of least squares
D)standardized residuals

Question 46

The t-test for the slope of the regression line is calculated by ________.

A)b₁-0/standard error
B)b₂/standard error
C)b₁-b₂/standard error
D)standard error/b₁+b₂

Question 47

Parsimony is where ________.

A)the model is kept as simple as possible
B)having as many variables as possible for accuracy
C)multiple models answer questions
D)none of the above

Question 48

An independent variable should be removed to improve the regression model if ________.

A)the correlation coefficient is -1
B)the R² value is 1
C)the t-statistic is lesser than 1
D)the p-value is greater than 0.05

Question 49

Stepwise regression carried out by deleting variables currently in the model and adding extra variables if none meet the criteria for removal is called ________.

A)forward selection
B)parsimony
C)general stepwise
D)backward elimination

Question 50

The best-subsets regression method ________.

A)evaluates best subsets of models for a fixed number of dependent variables
B)adds one variable at a time to the multiple regression model and tests for significance
C)evaluates all possible regression models for a set of independent variables
D)removes one variable at a time from the regression model

Question 51

Best-subsets regression evaluates models using a statistic called ________.

A)Durbin-Watson
B)degrees of freedom
C)Bonferroni criterion
D)sum of squares

Question 52

The Cp for a fully specified multiple regression model will always be equal to ________.

A)k - 1
B)k
C)k + 1
D)0

Question 53

ANOVA is applied to regression to ________.

A)check for correlation between the error terms
B)check if the differences between sample means is due to error
C)determine the value of the intercept term
D)test for the significance of regression

Question 54

Stepwise regression carried out by adding variables to a multiple regression model until no additional model makes a significant contribution is called ________.

A)forward selection
B)backward elimination
C)general stepwise
D)parsimony

Question 55

A stepwise regression technique where a model considers deleting variables currently in the model,and then considers adding an independent variable that is not in the model is called ________.

A)forward selection
B)backward selection
C)backward elimination
D)general stepwise

Question 56

If the Bonferroni Criterion (Cp)is much greater than 1,then ________.

A)they are good models to consider
B)there is a substantial bias
C)the models must be recalculated
D)none of the above

Question 57

If a variable is removed from the regression model when the t-statistic is greater than 1,________.

A)the standard error will decrease
B)the p-value will decrease
C)the Adjusted R² square will decrease
D)the Multiple R will decrease

Question 58

What does the principle of parsimony suggest?

A)A simple model with fewer independent variables may not produce an effective result.
B)The fewest number of explanatory variables that explain the independent variable need to be included in the model.
C)Good regression models are often based on sound technical analysis.
D)To avoid the problem of multicollinearity,the number of independent variables need to be sufficiently high.

Question 59

There is substantial bias in the estimates of the responses if the Bonferroni criterion is ________.

A)lower than k + 1
B)equal to k
C)greater than k + 1
D)equal to k + 1

Question 60

Categorical variables are included in regression analysis by ________.

A)removing the error term from the equation
B)applying the principle of parsimony
C)using dummy variables
D)using an intercept term

Question 61

The best-fitting regression line minimizes the sum of the squares of the observed errors.

Question 62

Regression analysis is used to build statistical models that characterize relationships among a dependent variable and one or more independent variables.

Question 63

Heteroscedasticity means that the variation about the regression line is constant for all values of the dependent variable.

Question 64

A regression model with a zero intercept term is not statistically significant.

Question 65

The risk associated with an individual stock can be measured in two ways: symmetric risk and asymmetric risk.

Question 66

Curvilinear regression models are often used in forecasting when ________.

A)dummy variables need to be used
B)the number of independent variables is high
C)the independent variable is time
D)the error term is approximately equal to zero

Question 67

A curvilinear regression model ________.

A)explains a linear relationship between variables
B)is used when the residual plot shows a linear relationship
C)is a model that is curvilinear in the parameters
D)shows a curvilinear relationship between the variables

Question 68

The specific risk associated with a stock is characterized by a measure called beta.

Question 69

Regression models that are extrapolated outside the ranges covered by the observations are still valid.

Question 70

Multiple R and R Square indicate the strength of association between the dependent and independent variables.

Question 71

When a categorical variable has 5 levels,________ dummy variables need to be added to the model.

A)5
B)0
C)4
D)2

Question 72

Confidence intervals provide information about the unknown values of the true regression coefficients,accounting for sampling error.

Question 73

The number of dummy variables to be added to the regression equation when a categorical variable has k levels is equal to ________.

A)1/ k - 1
B)k - 1
C)k²
D)k/1

Question 74

The value of R² lies between -1 and 1.

Question 75

What is meant by interaction in a multiple regression?

A)The coefficient of an independent variable depends on the value of the dummy variable.
B)the addition of independent variables in order to increase the value of the Adjusted R²
C)the process by which insignificant independent variables are removed sequentially in a model
D)the correlation between the dependent variables in a model

Question 76

Which of the following is an example of a curvilinear regression model?

A)Y = β₀ + β₁X² + ε
B)Y = β₀ + β₁X + β₂P + β₃C + ε
C)Y = β₀ + β₁X + ε
D)Y = β₀ + β₁X + (β₂)²P + ε

Question 77

R² is called the coefficient of determination.

Question 78

The standard error of the estimate is calculated by ________.

A) =
B) =
C) =
D) =

Question 79

When adjusted R square increase significantly from the original linear model and residual plots show more randomness,this is an indication of a ________.

A)multiple linear regression
B)stepwise regression
C)best subsets regression
D)curvilinear regression

Question 80

In regression models based on time-series data,the dependent variable is time or some function of time and the focus is on predicting the future.