Deck 4: Regression Models

Question 1

The null hypothesis in the F-test is that there is a linear relationship between the X and Y variables.

Answer 1

False

Question 2

There is no relationship between variables unless the data points lie in a straight line.

Answer 2

False

Question 3

In regression, a dependent variable is sometimes called a predictor variable.

Answer 3

False

Question 4

The coefficient of determination gives the proportion of the variability in the dependent variable that is explained by the regression equation.

Question 5

The correlation coefficient has values between −1 and +1.

Question 6

Both the p-value for the F-test and r² can be interpreted the same with multiple regression models as they are with simple linear models.

Question 7

Errors are also called residuals.

Question 8

The regression line minimizes the sum of the squared errors.

Question 9

When the significance level is small enough in the F-test, we can reject the null hypothesis that there is no linear relationship.

Question 10

An F-test is used to determine if there is a relationship between the dependent and independent variables.

Question 11

The coefficients of each independent variable in a multiple regression model represent slopes.

Question 12

If the significance level for the F-test is high enough, there is a relationship between the dependent and independent variables.

Question 13

For statistical tests of significance about the coefficients, the null hypothesis is that the slope is 1.

Question 14

The multiple regression model includes several dependent variables.

Question 15

Estimates of the slope, intercept, and error of a regression model are found from sample data.

Question 16

Summing the error values in a regression model is misleading because negative errors cancel out positive errors.

Question 17

In regression, there is random error that can be predicted.

Question 18

In regression, an independent variable is sometimes called a response variable.

Question 19

Often, a plot of the residuals will highlight any glaring violations of the assumptions.

Question 20

If the assumptions of regression have been met, errors plotted against the independent variable will typically show patterns.

Question 21

A dummy variable can be assigned up to three values.

Question 22

If multicollinearity exists, then individual interpretation of the variables is questionable, but the overall model is still good for prediction purposes.

Question 23

The random error in a regression equation

A)is the predicted error.
B)includes both positive and negative terms.
C)will sum to a large positive number.
D)is used to estimate the accuracy of the slope.

Question 24

A high correlation always implies that one variable is causing a change in the other variable.

Question 25

Multicollinearity exists when a variable is correlated to other variables.

Question 26

The adjusted r² will always increase as additional variables are added to the model.

Question 27

The best model is a statistically significant model with a high r-square and few variables.

Question 28

Which of these statements is best?

A)In regression, an independent variable is sometimes called a response variable.
B)A scatter diagram is a graphical depiction of the relationship between the dependent and independent variables.
C)In a scatter diagram, the dependent variable is typically plotted on the horizontal axis.
D)There is no relationship between variables unless the data points lie in a straight line.

Question 29

Dummy variables for regression analysis can take on a value of either -1 or +1.

Question 30

Which of the following statements is true regarding a scatter diagram?

A)It provides very little information about the relationship between the regression variables.
B)It is a plot of the independent and dependent variables.
C)It is a line chart of the independent and dependent variables.
D)It has a value between -1 and +1.

Question 31

The value of r² can never decrease when more variables are added to the model.

Question 32

The multiple regression model includes several intercept terms.

Question 33

In regression, a binary variable is also called an indicator variable.

Question 34

Transformations may be used when nonlinear relationships exist between variables.

Question 35

The number of dummy variables must equal 1 less than the number of categories of the qualitative variable.

Question 36

A variable should be added to the model regardless of the impact (increase or decrease)on the adjusted r² value.

Question 37

Another name for a dummy variable is a binary variable.

Question 38

Which of these statements is best?

A)In regression, an independent variable is sometimes called a response variable.
B)One purpose of regression is to understand the relationship between variables.
C)One purpose of regression is to predict the value of one variable based on the standard deviation of that variable.
D)The variable to be predicted is the independent variable.

Question 39

A reference to the criterion used to select the regression line, to minimize the squared distances between the estimated straight line and the observed values is called

A)Mean square error.
B)Sum of Squares.
C)Maximum likelihood.
D)Least Squares.

Question 40

The multiple regression model includes multiple slope coefficients.

Question 41

Which of the following conditions can be detected from residual analysis?

A)nonconstant variance
B)multicollinearity
C)dummy variables
D)presence of transformations

Question 42

The problem of nonconstant error variance is detected in residual analysis by which of the following?

A)a cone pattern
B)an arched pattern
C)a random pattern
D)an increasing pattern

Question 43

Which of these statements is best?

A)The regression model assumes the error terms are dependent.
B)The regression model assumes the errors are normally distributed.
C)The errors in a regression model are assumed to have an increasing mean.
D)The errors in a regression model are assumed to have zero variance.

Question 44

The correlation coefficient resulting from a particular regression analysis was 0.25.What was the coefficient of determination?

A)0.5
B)-0.5
C)0.0625
D)There is insufficient information to answer the question.

Question 45

The coefficient of determination resulting from a particular regression analysis was 0.85.What was the slope of the regression line?

A)0.85
B)-0.85
C)0.922
D)There is insufficient information to answer the question.

Question 46

Which of the following statements is true about r²?

A)It is also called the coefficient of correlation.
B)It is also called the coefficient of determination.
C)It represents the percent of variation in X that is explained by Y.
D)It represents the percent of variation in the error that is explained by Y.

Question 47

Which of the following is not an assumption of the regression model?

A)The errors are independent.
B)The errors should have a standard deviation equal to one.
C)The errors are normally distributed.
D)The errors have constant variance.

Question 48

Which of these statements is best?

A)The SST measures the total variability in the dependent variable about the regression line.
B)The SSE measures the total variability in the independent variable about the regression line.
C)The SSR indicates how much of the total variability in the dependent variable is explained by the regression model.
D)The coefficient of determination takes on values between -1 and + 1.

Question 49

A dummy variable is also called a(n)

A)indicator variable.
B)dependent variable.
C)continuous variable.
D)response variable.

Question 50

In a good regression model the residual plot shows

A)a cone pattern.
B)an arched pattern.
C)a random pattern.
D)an increasing pattern.

Question 51

The diagram below illustrates data with a

A)negative correlation coefficient.
B)zero correlation coefficient.
C)positive correlation coefficient.
D)correlation coefficient equal to +1.

Question 52

The coefficient of determination resulting from a particular regression analysis was 0.85.What was the correlation coefficient, assuming a positive linear relationship?

A)0.5
B)-0.5
C)0.922
D)There is insufficient information to answer the question.

Question 53

The sum of squared error (SSE)is

A)a measure of the total variation in Y about the mean.
B)a measure of the total variation in X about the mean.
C)a measure in the variation of Y about the regression line.
D)a measure in the variation of X about the regression line.

Question 54

Which of the following is an assumption of the regression model?

A)The errors are independent.
B)The errors are not normally distributed.
C)The errors have a standard deviation of zero.
D)The errors have an irregular variance.

Question 55

Which of the following statements is not true about regression models?

A)Estimates of the slope are found from sample data.
B)The regression line minimizes the sum of the squared errors.
C)The error is found by subtracting the actual data value from the predicted data value.
D)The dependent variable is the explanatory variable.

Question 56

Which of the following equalities is correct?

A)SST = SSR + SSE
B)SSR = SST + SSE
C)SSE = SSR + SST
D)SST = SSC + SSR

Question 57

Which of these statements is best?

A)If the assumptions of regression have been met, errors plotted against the independent variable will typically show patterns.
B)The error standard deviation is estimated by MSE.
C)Often, a plot of the residuals will highlight any glaring violations of the assumptions.
D)The standard error of the estimate is also called the variance of the regression.

Question 58

Which of these statements is best?

A)In any regression model, there is an implicit assumption that there is no preexisting relationship between the variables.
B)In regression, there is random error that can be predicted.
C)Estimates of the slope, intercept, and error of a regression model are found from sample data.
D)Error is the difference in the actual value and the predicted value.

Question 59

If computing a causal linear regression model of Y = a + bX and the resultant r² is very near zero, then one would be able to conclude that

A)Y = a + bX is a good forecasting method.
B)Y = a + bX is not a good forecasting method.
C)a multiple linear regression model is a good forecasting method for the data.
D)a multiple linear regression model is not a good forecasting method for the data.

Question 60

The problem of a nonlinear relationship is detected in residual analysis by which of the following?

A)a cone pattern
B)an arched pattern
C)a random pattern
D)an increasing pattern

Question 61

When an independent variable is correlated with one other independent variable, the variables are said to be

A)collinear.
B)pairwise.
C)independent.
D)mutually exclusive.

Question 62

Which of the following is true regarding a regression model with multicollinearity, a high r² value, and a low F-test significance level?

A)The model is not a good prediction model.
B)The high value of r² is due to the multicollinearity.
C)The interpretation of the coefficients is valuable.
D)The significance level tests for the coefficients are not valid.

Question 63

If a qualitative variable has three categories, how many dummy variables are needed?

A)0
B)1
C)2
D)3
E)4

Question 64

A prediction equation for starting salaries (in $1,000s)and SAT scores was performed using simple linear regression.In the regression printout shown below, what can be said about the level of significance for the overall model? SUMMARY OUTPUT
ANOVA

A)SAT is not a good predictor for starting salary.
B)The significance level for the intercept indicates the model is not valid.
C)The significance level for SAT indicates the slope is equal to zero.
D)The significance level for SAT indicates the slope is not equal to zero.

Question 65

The sum of the squares total (SST)

A)measures the total variability in Y about the mean.
B)measures the total variability in X about the mean.
C)measures the variability in Y about the regression line.
D)measures the variability in X about the regression line.

Question 66

A healthcare executive is using regression to predict total revenues.She is deciding whether or not to include both patient length of stay and insurance type in her model.Her first regression model only included patient length of stay.The resulting r² was .83, with an adjusted r² of .82 and her level of significance was .003.In the second model, she included both patient length of stay and insurance type.The r² was .84 and the adjusted r² was .80 for the second model and the level of significance did not change.Which of the following statements is true?

A)The second model is a better model.
B)The first model is a better model.
C)The r² increased when additional variables were added because these variables significantly contribute to the prediction of total revenues.
D)The adjusted r² always increases when additional variables are added to the model.

Question 67

Suppose that you believe that a cubic relationship exists between the independent variable (of time)and the dependent variable Y.Which of the following would represent a valid linear regression model?

A)Y = b₀ + b₁ X, where X = time³
B)Y = b₀ + b₁ X³, where X = time
C)Y = b₀ + 3b₁ X, where X = time³
D)Y = b₀ + 3b₁ X, where X = time

Question 68

Which of these statements about multiple regression is best?

A)The p-value for the F-test may not be interpreted the same with multiple regression models as they are with simple linear models.
B)The multiple regression model includes several dependent variables.
C)The multiple regression model includes several intercept terms.
D)The multiple regression model includes multiple slope coefficients.

Question 69

In the model Y = β₀ + β₁X₁ + β₂X₂ + ε, which of these parameters represents an independent variable?

A)the X₁
B)the Y
C)the β₁
D)the ε

Question 70

An automated process to systematically add or delete independent variables from a regression model is called

A)nonlinear regression.
B)linear regression.
C)residual analysis.
D)stepwise regression.

Question 71

Which of the following statements provides the best guidance for model building?

A)If the value of r² increases as more variables are added to the model, the variables should remain in the model, regardless of the magnitude of increase.
B)If the value of the adjusted r² increases as more variables are added to the model, the variables should remain in the model.
C)If the value of r² increases as more variables are added to the model, the variables should not remain in the model, regardless of the magnitude of the increase.
D)If the value of the adjusted r² increases as more variables are added to the model, the variables should not remain in the model.

Question 72

The condition of an independent variable being correlated to one or more other independent variables is referred to as

A)multicollinearity.
B)statistical significance.
C)linearity.
D)nonlinearity.

Question 73

The mean square error (MSE)is

A)denoted by s.
B)denoted by k.
C)the SSE divided by the number of observations.
D)the SSE divided by the degrees of freedom.

Question 74

Which of the following statements is false concerning the hypothesis testing procedure for a regression model?

A)The F-test statistic is used.
B)The null hypothesis is that the true slope coefficient is equal to zero.
C)The null hypothesis is rejected if the adjusted r² is above the critical value.
D)An α level must be selected.

Question 75

A prediction equation for sales and payroll was performed using simple linear regression.In the regression printout shown below, which of the following statements is not true? SUMMARY OUTPUT
ANOVA

A)Payroll is a good predictor of Sales based on α = 0.05.
B)There is evidence of a positive linear relationship between Sales and Payroll based on α = 0.05.
C)Payroll is not a good predictor of Sales based on α = 0.01.
D)The coefficient of determination is equal to 0.833333.

Question 76

Which of the following represents the underlying linear model for hypothesis testing?

A)Y = b₀ + b₁ X + ε
B)Y = b₀ + b₁ X
C)Y = β₀ + β₁ X + ε
D)Y = β₀ + β₁ X

Question 77

The primary difference between r² and the adjusted r² is that

A)the adjusted r² accounts for the total number of variables in the regression model.
B)the adjusted r² accounts for the number of independent variables in the regression model.
C)the adjusted r² accounts for the number of dependent variables in the regression model.
D)the adjusted r² accounts for multicollinearity.

Question 78

Which of the following is not a common pitfall of regression?

A)If the assumptions are not met, the statistical tests may not be valid.
B)Nonlinear relationships cannot be incorporated.
C)Two variables may be highly correlated to one another but one is not causing the other to change.
D)Concluding that a statistically significant relationship implies practical value.

Question 79

A healthcare executive is using regression to predict total revenues.She has decided to include both patient length of stay and insurance type in her model.Insurance type can be grouped into the following categories: Medicare, Medicaid, Managed Care, Self-Pay, and Charity.Which of the following is true?

A)Insurance type will be represented in the regression model by five binary variables.
B)Insurance type will be represented in the regression model by six dummy variables.
C)Insurance type will be represented in the regression model by five dummy variables.
D)Insurance type will be represented in the regression model by four binary variables.

Question 80

A healthcare executive is using regression to predict total revenues.She has decided to include both patient length of stay and insurance type in her model.Insurance type can be grouped into three categories: Government-Funded, Private-Pay, and Other.Her model is

A)Y = b₀.
B)Y = b₀ + b₁ X₁.
C)Y = b₀ + b₁ X₁ + b₂ X₂.
D)Y = b₀ + b₁ X₁ + b₂ X₂ + b₃ X₃.