Homework answers / question archive / 1) Which of the following statements is true regarding a scatter diagram? A) It provides very little information about the relationship between the regression variables

1) Which of the following statements is true regarding a scatter diagram? A) It provides very little information about the relationship between the regression variables

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1) 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.

 

 

2) 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.

 

3) 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.

 

 

4) 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.

, D

 

5) 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

 

 

6) 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

 

 

7) 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

 

8) 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.

 

 

9) 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

 

10) 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.

 

 

11) 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.

 

12) 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.

 

 

13) 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

 

 

14) 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

 

 

15) 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

 

 

16) 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

 

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

A) 0

B) 1

C) 2

D) 3

E) 4

 

 

18) 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

 

 

19) 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

 

 

20) 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.

 

21) 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 = time1/3

 

 

22) 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

 

 

23) 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.

 

 

24) 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.

 

 

 

 

25) 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.

 

 

 

 

 

26) 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.

 

 

 

 

27) 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.

 

 

 

 

28) 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.

 

 

 

 

29) 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.

 

 

 

30) 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.

 

 

 

 

31) 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.

E) None of the above

 

 

 

 

32) 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.

 

 

 

 

33) 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.

E) sensitivity analysis.

 

 

 

 

34) 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.

E) None of the above