Question Details

Chapter 41 MULTIPLE CHOICE part 3

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.


48) Which of the following statements is true regarding a scatter diagram? 48)
A) It gives the percent of variation in the dependent variable that is explained by the
independent variable.
B) It provides very little information about the relationship between the regression variables.
C) It has a value between -1 and +1.
D) It is a line chart of the independent and dependent variables.
E) It is a plot of the independent and dependent variables.


49) The random error in a regression equation 49)
A) is the predicted error.
B) includes both positive and negative terms.
C) is maximized in a least squares regression model.
D) will sum to a large positive number.
E) is used the estimate the accuracy of the slope.


50) Which of the following equalities is correct? 50)
A) SSR = SST + SSE
B) SST = SSC + SSR
C) SST = SSR + SSE
D) SSE = SSR + SST
E) SSE = Actual Value - Predicted Value


51) The sum of squared error (SSE) is 51)
A) a measure of the total variation in Y about the mean.
B) a measure in the variation of Y about the regression line.
C) a measure in the variation of X about the regression line.
D) a measure of the total variation in X about the mean.
E) None of the above
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52) 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
52)
A) a multiple linear regression model is a good forecasting method for the data.
B) Y = a + bX is not a good forecasting method.
C) Y = a + bX is a good forecasting method.
D) a multiple linear regression model is not a good forecasting method for the data.
E) None of the above


53) Which of the following statements is true about r2? 53)
A) It represents the percent of variation in X that is explained by Y.
B) It ranges in value from -1 to + 1.
C) It is also called the coefficient of determination.
D) It is also called the coefficient of correlation.
E) It represents the percent of variation in the error that is explained by Y.


54) The coefficient of determination resulting from a particular regression analysis was 0.85. What
was the slope of the regression line?
54)
A) 0.922
B) -0.85
C) 0.85
D) There is insufficient information to answer the question.
E) None of the above


55) The diagram below illustrates data with a 55)
A) negative correlation coefficient.
B) positive correlation coefficient.
C) zero correlation coefficient.
D) correlation coefficient equal to +1.
E) None of the above
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56) The correlation coefficient resulting from a particular regression analysis was 0.25. What was the
coefficient of determination?
56)
A) -0.5
B) 0.0625
C) 0.5
D) There is insufficient information to answer the question.
E) None of the above


57) The coefficient of determination resulting from a particular regression analysis was 0.85. What
was the correlation coefficient, assuming a positive linear relationship?
57)
A) 0.922
B) 0.5
C) -0.5
D) There is insufficient information to answer the question.
E) None of the above


58) In a good regression model the residual plot shows 58)
A) a cone pattern.
B) an arched pattern.
C) an increasing pattern.
D) a decreasing pattern.
E) a random pattern.



59) Which of the following represents the underlying linear model for hypothesis testing? 59)
A) Y = b0 + b1 X +􀈱􀎉
B) Y = b0 + b1 X
C) Y =􀈱􀎆0 +􀈱􀎆1 X
D) Y = 􀎆0 + 􀎆1 X +􀈱􀎉
E) None of the above


60) Which of the following statements is false concerning the hypothesis testing procedure for a
regression model?
60)
A) The null hypothesis is rejected if the adjusted r2 is above the critical value.
B) The alternative hypothesis is that the true slope coefficient is not equal to zero.
C) The null hypothesis is that the true slope coefficient is equal to zero.
D) An 􀎅 level must be selected.
E) The F-test statistic is used.


61) 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?
61)
A) Y = b0 + 3b1 X, where X = time
B) Y = b0 + b1 X, where X = time1/3
C) Y = b0 + b1 X3, where X = time
D) Y = b0 + 3b1 X, where X = time3
E) Y = b0 + b1 X, where X = time3
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62) 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?
62)
A) The significance level for SAT indicates the slope is equal to zero.
B) SAT is not a good predictor for starting salary.
C) The significance level for SAT indicates the slope is not equal to zero.
D) The significance level for the intercept indicates the model is not valid.
E) None of the above


ESSAY. Write your answer in the space provided or on a separate sheet of paper.


63) An air conditioning and heating repair firm conducted a study to determine if the average outside temperature
could be used to predict the cost of an electric bill for homes during the winter months in Houston, Texas. The
resulting regression equation was:
Y = 227.19 - 1.45X, where Y = monthly cost, X = average outside air temperature
(a) If the temperature averaged 48 degrees during December, what is the forecasted cost of December's electric
bill?
(b) If the temperature averaged 38 degrees during January, what is the forecasted cost of January's electric bill?
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64) Bob White is conducting research on monthly expenses for medical care, including over-the-counter medicine.
His dependent variable is monthly expenses for medical care while his independent variable is number of
family members. Below is his Excel output.
(a) What is the prediction equation?
(b) Based on his model, each additional family member increases the predicted costs by how much?
(c) Based on the significance F-test, is this model a good prediction equation?
(d) What percent of the variation in medical expenses is explained by the size of the family?
(e) Can the null hypothesis that the slope is zero be rejected? Why or why not?
(f) What is the value of the correlation coefficient?


65) Consider the regression model Y = 389.10 - 14.6X. If the r2 value is 0.657, what is the correlation coefficient?
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66) Bob White is conducting research on monthly expenses for medical care, including over the counter medicine.
His dependent variable is monthly expenses for medical care while his independent variables are number of
family members and insurance type (government funded, private insurance and other). He has coded insurance
type as the following:
X2 = 1 if government funded, X3 = 1 if private insurance
Below is his Excel output.
(a) What is the prediction equation?
(b) Based on the significance F-test, is this model a good prediction equation?
(c) What percent of the variation in medical expenses is explained by the independent variables?
(d) Based on his model, what are the predicted monthly expenses for a family of four with private insurance?
(e) Based on his model, what are the predicted monthly expenses for a family of two with government funded
insurance?
(f) Based on his model, what are the predicted monthly expenses for a family of five with no insurance?
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