Deck 4: Regression Models

Question 1

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

Answer 1

False

Question 2

The dependent variable is also called the response variable.

Answer 2

True

Question 3

In any regression model,there is an implicit assumption that a relationship exists between the variables.

Answer 3

True

Question 4

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

Question 5

One purpose of regression is to predict the value of one variable based on the other variable.

Question 6

Error is the difference in the actual value and the predicted value.

Question 7

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

Question 8

In a scatter diagram,the dependent variable is typically plotted on the horizontal axis.

Question 9

The coefficient of determination takes on values between -1 and + 1.

Question 10

One purpose of regression is to understand the relationship between variables.

Question 11

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

Question 12

The SST measures the total variability in the dependent variable about the regression line.

Question 13

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

Question 14

The SSE measures the total variability in the independent variable about the regression line.

Question 15

The variable to be predicted is the dependent variable.

Question 16

The regression line minimizes the sum of the squared errors.

Question 17

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

Question 18

The SSR indicates how much of the total variability in the dependent variable is explained by the regression model.

Question 19

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

Question 20

A scatter diagram is a graphical depiction of the relationship between the dependent and independent variables.

Question 21

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

Question 22

The errors in a regression model are assumed to have an increasing mean.

Question 23

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

Question 24

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

Question 25

The error standard deviation is estimated by MSE.

Question 26

The multiple regression model includes multiple slope coefficients.

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

The errors in a regression model are assumed to have zero variance.

Question 32

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

Question 33

The multiple regression model includes several intercept terms.

Question 34

The regression model assumes the error terms are dependent.

Question 35

The regression model assumes the errors are normally distributed.

Question 36

Errors are also called residuals.

Question 37

The multiple regression model includes several dependent variables.

Question 38

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 39

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

Question 40

The standard error of the estimate is also called the variance of the regression.

Question 41

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

Question 42

A dummy variable can be assigned up to three values.

Question 43

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

Question 44

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)R-square.
E)Least Squares.

Question 45

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

Question 46

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.
E)It gives the percent of variation in the dependent variable that is explained by the independent variable.

Question 47

Which of the following equalities is correct?

A)SST = SSR + SSE
B)SSR = SST + SSE
C)SSE = SSR + SST
D)SST = SSC + SSR
E)SSE = Actual Value - Predicted Value

Question 48

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.
E)None of the above

Question 49

Transformations may be used when nonlinear relationships exist between variables.

Question 50

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

Question 51

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

Question 52

Another name for a dummy variable is a binary variable.

Question 53

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

Question 54

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

Question 55

Multicollinearity exists when a variable is correlated to other variables.

Question 56

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.
E)None of the above

Question 57

Which of the following statements is/are 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.
E)The intercept coefficient is not typically interpreted.

Question 58

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.
E)is maximized in a least squares regression model.

Question 59

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

Question 60

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

Question 61

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/are not true?

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.
E)Payroll is the independent variable.

Question 62

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

A)Nonlinearity Nonconstant variance
B)Multicollinearity
C)A and B
D)A,B,and C

Question 63

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.
E)The alternative hypothesis is that the true slope coefficient is not equal to zero.

Question 64

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

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

Question 65

A dummy variable is also called a(n)

A)indicator variable.
B)dependent variable.
C)continuous variable.
D)response variable.
E)None of the above

Question 66

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?

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.
E)None of the above

Question 67

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

A)The errors are independent.
B)The errors are normally distributed.
C)The errors have constant variance.
D)The mean of the errors is zero.
E)The errors should have a standard deviation equal to one.

Question 68

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
E)a decreasing pattern

Question 69

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.
E)Neither binary nor dummy variables are necessary for the regression model.

Question 70

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
E)None of the above

Question 71

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
E)a decreasing pattern

Question 72

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.
E)None of the above

Question 73

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.
E)It ranges in value from -1 to + 1.

Question 74

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.
E)None of the above

Question 75

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.
E)The errors follow a cone pattern.

Question 76

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.
E)None of the above

Question 77

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.
E)None of the above

Question 78

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.
E)None of the above

Question 79

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.
E)a decreasing pattern.

Question 80

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
E)Y = b₀ + b₁ X,where X = time^1/3