Test Bank Statistics For Business Decision Making and Analysis 2nd Edition Robert Stine, Dean Foster

 

Test Bank Statistics for Business Decision Making and Analysis 2nd Edition Robert Stine, Dean Foster

Download full at:  at: https://testbankdata.com/download/test-bank-statistics-business-decisionmaking-analysis-2nd-edition-robert-stine-dean-foster/   making-analysis-2nd-edition-robert-stine-dean-foster/ Chapter 19: Linear Patterns

Quiz A

Objectii ves: Object ves:      

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Interpret the intercept and slope that define defi ne a linear regression equation. Define extrapolation. Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals. Interpret residuals. Use residuals from the regression equation to check that the equation is an appropriate summary of the data. Identify and graph the response and explanatory variable associated with a linear regression equation.

An insurance agent has selected a sample of drivers that she insures whose ages are in tthe he range from 16-42 years old. For each driver, she records the age of the t he driver and the dollar amount of claims clai ms that the driver filed in the  previous 12 months. A scatterplot showing the dollar amount of claims as the response variable and the age as the  predictor shows a linear trend. The least squares regression line is determined to be:  y   37 3715 15  75 75.4 .4x.  A plot of the ˆ

residuals versus age of the drivers showed no pattern, and the following were reported: 2

r 

 .822  

Standard deviation of the residuals  se



312 312 .1  

Section 19.2  –  Interpreting  Interpreting the Fitted Line [Objective: Interpret the intercept and slope that define a linear regression equation.] 1.  If the age of a driver increases by one year, by how much and in what direction would the dollar amount of claims be predicted to change for the driver? (a)  Increase by 75.4 dollars (b)  Decrease by 75.4 dollars (c)  Increase by 3715 dollars (d)  Increase by 312.1 dollars

[Objective: Define extrapolation.] 2.  Using the fitted line given above to estimate the dollar amount of claims for a driver whose age is 55 years would provide a prediction that is unreliable because it is an __________________. (a)  (b)  (c)  (d) 

unsolvable problem extended result extrapolation extorted point

Section 19.4  –  Explaining  Explaining Variation [Objective: Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals.] 3.  What percentage of the variation in the dollar amount of claims is due to factors other than age? (a)  82.2% (b)  0.822% (c)  75.4% (d)  31.21%

Section 19.1  –  Fitting  Fitting a line to data  

 

[Objective: Interpret the intercept and slope that define a linear regression equation.] 4.  For the response variable and the predictor described above, is the t he correlation r   between the variables positive or negative? Explain how you reached your conclusion. (a)  Positive –  because  because the slope is positive. (b)  Positive –  because  because the y-intercept is positive. (c)   Negative –  because  because the slope is negative. (d)   Negative –  because  because the y-intercept is negative.

Section 19.3  –  Properties  Properties of Residuals [Objective: Interpret residuals.] 150 0  using the fitted line given above. Did the 5.  A driver in the data set whose age is 25 years had a residual of $15 regression line overestimate or underestimate the driver’s dollar amount of claims? Explain how you reached your conclusion. (a)  Overestimate, because the residual is negative and therefore the data value fell below the regression line. (b)  Overestimate, because the residual is negative and therefore the data value fell above the regression line. (c)  Underestimate, because the residual is negative and therefore the data value fell below the regression line. (d)  Underestimate, because the residual is negative and therefor the data value fell above the regression line.

[Objective: Use residuals from the regression equation to check that the equation is an appropriate summary of the data.] 6.  The histogram summarizing the residuals is reasonably symmetric around zero and bell-shaped. Using the

Empirical Rule, complete the sentence: Approximately 68% of the dollar amounts of claims are within  _____________________ dollars of the regression regression line. (a)  1(312.1)   (b)   2  312.1        12 

 312.1      12 

(c)   1  (d) 

 2(312.1)

 

Section 19.4  –  Explaining  Explaining Variation [Objective: Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals.] 7.  A kindergarten teacher developed a least squares regression equation predicting the height of her kindergarteners (in inches) from their age (in months). The resulting equation is  y   26.6 26.68 8  .293 .293x  with an ˆ

r 2 = .263. What will happen to the value of r 2 if she changes age in months to age in days? 2 (a)  r   will increase. 2 (b)  r   will decrease . 2 (c)  r   will remain the same.

Section 19.1  –  Fitting  Fitting a Line to Data [Objective: Identify and graph the response and explanatory variable associated with a linear regression equation.] 8.  In the situation described above, which variable is the explanatory variable? (a)  Height (b)  Age (c)  Months (d)  Inches  

 

Section 19.5  –  Conditions  Conditions for Simple Regression [Objective: Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals.] 9.  (True or False) Two variables that have a least l east square regression line fit of r 2 = 0 have no relationship.

[Objective: Use residuals from the regression equation to check that the equation is an appropriate summary of the data.] 10.  List the three conditions needed when summarizing the association between two variables with a line.

 

 

Answers: 1.  2.  3.  4. 

B C A C

5.  A 6.  D 7.  C 8.  B 9.  False 10.   No obvious lurking variables, linear, random residual variation

 

 

Chapter 19: Linear Patterns

Quiz B

Objectii ves: Object ves:      

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Interpret the intercept and slope that define defi ne a linear regression equation. Understand extrapolation. Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals. Use residuals from the regression equation to check that the equation is an appropriate summary of the data.

Section 19.2  –  Interpreting  Interpreting the Fitted Line [Objective: Interpret the intercept and slope that define a linear regression equation] 1.  A least squares regression line is determined from a sample of values for variables variables x  and y  x  and  y , where  x   the size

of a listed home (in square feet), and  y  the selling price of the home. Which of the following statements is true concerning the fitted line  y   b0 ˆ

 b1 x

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(a)  If there is a positive correlation r  between  between  x and and y  y , then the slope b1  must also be positive. (b)  The units on the intercept b0  and the slope b1  will be the same as the units on the variable  y . (c)  If the residuals associated with the fitted values are all equal to zero, then  x  and  and y  y  have a correlation r   0 . (d)  If r 

2



0.85 , then it is appropriate to conclude that a change in  x  will cause a change in  y .

(e)   None of (a) –  (d)  (d) is true.

Section 19.2  –  Interpreting  Interpreting the Fitted Line [Objective: Understand extrapolation.] 2.  When making predictions using a least squares sq uares regression line that has been determined from a set of data, extrapolation occurs if: 2 (a)  r   1  but the equation is still being used to predict a value for  y  y from a given value of  x  x . ,

(b)  the percentage of the variation in the response variable that is being described by the fitted line is very large. (c)  the scatterplot of the  x  and  y  values shows variation around the fitted line. (d)  the linear condition for simple regression is not met. (e)   None of (a) –  (d)  (d) represents extrapolation.

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Section 19.4Summarize  Explaining [Objective: theVariation precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals.] 3.  In order for a least squares regression line to provide the most accurate predictions of the average value of tthe he response variable y variable  y for a given value of  x , which of the following follo wing results is considered to be desirable based on

the data? (a)  An unexpectedly large value for the standard deviation of the t he residuals,  s e . (b)  A value of r  no larger than 0.50. (c)  A scatterplot of  x  and  y values that shows a high degree of correlation between the variables. 2

(d)  A plot of the residuals versus the  x -values that shows an unexpectedly large amount of variation in the residuals. (e)  Both (c) and (d) would be considered desirable results for accurate predictions.

 

 

A distribution center for a chain of electronics supply stores fills and ships orders to retail outlets. A random sample of orders is selected as they are received and the t he dollar amount of the order (in thousands of dollars) is recorded, and then the time (in hours) required to fill the order and have it ready for shipping is determined. A scatterplot showing the times as the response variable and the dollar amounts (in thousands of dollars) as the predictor shows a llinear inear 0 . 76   1 . 8  y      x trend. The least squares regression line is determined to t o be: . A plot of the residuals versus the dollar amounts showed no pattern, and the following values were reported: Correlation r    Standard deviation of the residuals  se   0.48   r 2   0.846    0.92;   ˆ

4.  What percentage of the variation in the t he times required to prepare an order for shipping is accounted for by the fitted line? (a)  92% (b) 48% (c)  84.6% (d) 1.8% (e) 68%

Section 19.3  –  Properties  Properties of Residuals [Objective: Use residuals from the regression equation to check that the equation is an appropriate summary of the data.] 5.  The histogram summarizing the residuals is reasonably symmetric around zero and bell-shaped. Which of the following conclusions can be drawn based on the Empirical Rule? (a)  Approximately 68% of the times to prepare an order are within .48 hours of the regression line. (b)  Approximately 95% of the times to prepare an order are within 1.692 hours of the regression line. (c)  84.6% of the times to prepare an order vary from the regression line by less than 1 hour. (d)  92% of the times to prepare an order can be predicted accurately based on the doll dollar ar amount of the order. (e)  84.6% of the variation in the t he times to prepare an order iiss due to factors other than the dollar amount of the order.

Section 19.2  –  Interpreting  Interpreting the Fitted Line [Objective: Interpret the intercept and slope that define a linear regression equation.] 6.  Which of the following statements is an appropriate interpretation and use of the regression line provided? (a)  If the dollar amount of an order from one store is $1000 more than the dol dollar lar amount of an order from another store, the larger order would be predicted to require 1.8 more hours to prepare than smaller order. (b)  The units on the slope b1    1.8 are: hours per per thousands of dollars. (c)  The predicted time to prepare an order for shipping that has an absolute dollar dol lar amount of $2500 would 5.26 hours. (d)  Not all of the residuals computed for the fitted values would be equal to zero. (e)  All of (a) –  (d)  (d) are appropriate.

A Statistics instructor gave the previous semester’s  test 2 as a practice exam for this semester’s test 2 . She wants to know how good the practice test grades (in %) are at predicting the actual test grades (in %). A least square regression equation was created the results are: 2 Standard deviation of residuals se    3.278   r     .958   r     0.98   Section 19.1  –  Fitting  Fitting a line to data [Objective: Interpret the intercept and slope that define a linear regression equation] 7.  Based on the information given, do the students do better or worse on the actual exam or the practice exam? Explain. 8.  If the slope is 0.997, does the practice test or the actual test have more variation? (a)  Practice test (b)  Actual test

 

 

Section 19.3  –  Properties  Properties of Residuals [Objective: Summarize the precision of a fitted regression equation using the r 2 statistics and the standard deviation of the residuals.] 9.  What are the units of  se ? (a)  Residuals (b)  % (c)  There are no units

 

(d) Standard deviations

Section 19.1  –  Fitting  Fitting a line to data 10.  Using the fitted line  y    1.27 1.27  0.99 0.997 7 x , what is the residual value of a student that makes a 93 on the practice   ˆ

test and a 95 on the actual test?

 

 

Answers: 1.  2.  3.  4.  5.  6.  7. 

A E C C A E The students perform better on the actual exam, because r is positive therefore the slope would be positive,

meaning the student did better on the actual exam. 8.  B 9.  B 10.  Residual = 1.009

 

 

Chapter 20: Curved Patterns

Quiz A

Objectii ves: Object ves:        

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Recognize the presence of curved patterns in models and data and pick an appropriate transformation. Explain the impact of nonlinear patterns on how the explanatory variable and response are related to each other. Interpret the slope and intercept in an equation that uses logs or reciprocals to capture the pattern in data. Predictions using logs or reciprocal transformation equations.

Each worker at an assembly plant that produces clock radios is responsible for the entire assembly of each unit they work on. The plant manager has collected data from a sample of workers: the number of years of experience working at the plant (YRS), and the number of hours per unit (TIME) required for assembly. The scatterplot of TIME versus YRS is shown below.

Estimated hours/unit = 13.676  3.776  Years 2

r   



0.769

 

 se   1.824

 

 

Section 20.1  –  Detecting  Detecting Nonlinear Patterns [Objective: Recognize the presence of curved patterns in models and data and pick an appropriate transformation.] 1.  Based on the scatterplot, does it appear appropriate to fit a regression line to this data? Explain why or why not. Section 20.2  –  Transformations  Transformations 2.  The manager has decided to transform the response variable from TIME (hours/unit) to 1/TIME (units/hour).  Note: This is a reciprocal transformation. The scatterplot of 1/TIME versus YRS is shown on the next page. Using the fitted line provided with the data, determine the prediction of the number of hours per unit required on average for a worker with 1.75 years of experience. (Remember to convert back to TIME in ho hours urs per unit.)

 

 

Units  .015      .096  Years  Estimated  hour  r 2   0.897  se   0.029  

 

 

(a)  0.183 (b) 5.464 (c)   5.796 (d)  0.571

Section 20.3  –  Reciprocal  Reciprocal Transformation [Objective: Explain the impact of nonlinear patterns on how the explanatory variable and response are related to each other.] 3.  Use the fitted line above question 1 to predict the number of hours per unit required on average for a worker with 1.75 years of experience. (a)  7.068 (b)  20.157 (c)  3.158 (d)  11.518 4.  Looking at the scatterplot of TIME versus years and the points corresponding to YRS=1.75, which o off the two  predictions that you have computed appears to be more accurate? Explain your answer.

[Objective: Interpret the slope and intercept in an equation that uses logs or reciprocals to capture the pattern in data] 5.  In question 2, the fitted line is given as  Estimated units per hour  .015    .096  Years , with the standard 029 . What are the units for  s e ? deviation of the residuals given by  se  .029 (a)  Years (b)  1/years (c)  Units per hour (d)  Hours per unit

A medium-sized business has a policy that keeps its weekly advertising budget within the range from $1000 to $5000. The marketing manager has collected data from a sample of weeks, recording the amount spent on  

 

advertising (ADV) and the revenue (REV) for each week. The amounts spent on advertising are recorded in thousands of dollars (for example, an actual amount of $3500 $3 500 corresponds to ADV=3.5). Revenue amounts are in actual dollars. After examining the data, the manager decides to use a log log transformation (using log e    ln  or natural logs) on both variables in order to derive a regression line. The log-log equation is determined to be: Estimated Estim ated log REV = 7.1 2.4 2.4log log ADV    Section 20.4  –  Logarithm  Logarithm Transformations 6.  Interpret the slope b      2.4, addressing the effect on the predicted revenue associated with a change in the 1

amount spent on advertising. (a)  For every 1% increase in revenue (REV) it is predicted to result in an average 2.4% iincrease ncrease in advertising (ADV). (b)  For every 2.4% increase in revenue (REV) it is predicted to result in an average 7.1% increase in advertising (ADV). (c)  For every 1% increase in advertising (ADV) it is predicted to result in aan n average 2.4% increase in revenue (REV). (d)  For every 1% increase in advertising (ADV) it is predicted to result in aan n average 7.1% increase in revenue (REV).

[Objective: Predictions using logs or reciprocal transformation equations] 7.  Use the log-log  equation  equation to estimate the t he average revenue for a week in which the actual amount spent on advertising is $2500. (a)  $6007 (b)  $13,100 (c)  $3150 (d)  $10,928

Section 20.4  –  Logarithm  Logarithm Transformation [Objective: Interpret the slope and intercept in an equation that uses logs or reciprocals to capture the pattern in data.] 8.  Give the value of the elasticity for the log-log equation to estimate the average revenue for a week from amount spent on advertising. (a)  7.1 (b)  2.4 (c)  0.71 (d)  0.88 9.  What are the units on the residual standard deviation

 se for this log-log  equation?  equation?

(a)  Revenue Dollars (b)   Log( Revenue Revenue Dollars) (c)   Log (Advertising (Advertising Dollars) (d)  Advertising Dollars

[Objective: Recognize the presence of curved patterns in models and data and pick an appropriate transformation.] 10.  Suppose the marketing manager decided to compare this log-log  model  model with a log model using the log of only the Advertising money spent. Is it appropriate to compare the r 2 values of these two models? Explain.

 

 

Answers:

1.  It does not appear appropriate to fit the data with a regression line. The fitted line passes below most points on the left and right, and above most points in the mid-range. The curved pattern in the data indicates that the linear condition for regression is not being satisfied. 2.  B 3.  A 4.  From the scatterplot, when YRS = 1.75, the fitted line predicts 7.068 hours per unit, which overestimates each of the actual times. The lower estimate of 5.46 hours per unit appears to be more accurate as the curve

would more closely follow the pattern in the data. 5.  C 6.  C 7.  D 8.  B 9.  A 10.   No, the two models have different response variables. It makes no sense to compare the proportion of variation in the log revenue to revenue itself.