Deck 4: Regression Models

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

The dependent variable is also called the response variable.

Question 6

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

Question 7

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

Question 8

The variable to be predicted is the dependent variable.

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

The regression line minimizes the sum of the squared errors.

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

The error standard deviation is estimated by MSE.

Question 25

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

Question 26

Another name for a dummy variable is a binary variable.

Question 27

Errors are also called residuals.

Question 28

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

Question 29

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 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

The multiple regression model includes several dependent variables.

Question 36

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

Question 37

The regression model assumes the error terms are dependent.

Question 38

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

Question 39

The regression model assumes the errors are normally distributed.

Question 40

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

Question 41

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 42

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 43

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

Question 44

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

Question 45

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 46

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 47

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 48

Multicollinearity exists when a variable is correlated to other variables.

Question 49

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

Question 50

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 the estimate the accuracy of the slope.
E) is maximized in a least squares regression model.

Question 51

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 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.
E) None of the above

Question 53

A dummy variable can be assigned up to three values.

Question 54

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 55

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 56

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

Question 57

Transformations may be used when nonlinear relationships exist between variables.

Question 58

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

Question 59

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

Question 60

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

Question 61

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.
E) None of the statements provide accurate guidance.

Question 62

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 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

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.
E) Using a regression equation beyond the range of X is very questionable.

Question 65

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 66

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 67

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.
E) The significance level for the F-test is not valid.

Question 68

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.
E) The significance level for the F-test is not valid.

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

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

A) nonlinear transformations.
B) multicollinearity.
C) multiple regression.
D) least squares method.
E) None of the above

Question 71

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.
E) None of the above statements are true.

Question 72

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 73

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 74

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 75

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 76

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 77

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

Question 78

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.
E) indicates how much of the total variability in Y is explained by the regression model.

Question 79

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 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.
E) Y = b₀ + b₁ X₁ + b₂ X₂ + b₃ X₃ + b₄ X₄.