Question 1

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

Accepted Answer

A)    =0.522x-2.097 
B)    =-0.552x+2.097 
C)    =2.097x-0.552 
D)    =2.097x+0.552 
A)    =0.522x-2.097 
B)    =-0.552x+2.097 
C)    =2.097x-0.552 
D)    =2.097x+0.552

Question 2

The regression line for the given data is   = -1.885x + 0.758. Determine the residual of a data point for which x = 4 and y = -6.

Accepted Answer

A)  -12.782 
B)  -8.068 
C)  0.782 
D)  -6.782 
A)  -12.782 
B)  -8.068 
C)  0.782 
D)  -6.782

Question 3

Given the equation of a regression line is   = -5.5x - 0.7, what is the best predicted value for y given x= 7.4?

Accepted Answer

A)  40.00 
B)  41.40 
C)  -41.40 
D)  -40.00 
A)  40.00 
B)  41.40 
C)  -41.40 
D)  -40.00

Question 4

Use the scatter diagrams shown, labeled a through f to solve the problem.
-In which scatter diagram is r = 0.01?

Accepted Answer

A)  d 
B)  c 
C)  e 
D)  f 
A)  d 
B)  c 
C)  e 
D)  f

Question 5

A traffic officer is compiling information about the relationship between the hour or the day and the speed over the limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tell the officer?

Accepted Answer

A)  There is a moderate negative linear correlation. 
B)  There is insufficient evidence to make any conclusions about the relationship between the variables. 
C)  There is a weak positive linear correlation. 
D)  There is a moderate positive linear correlation. 
A)  There is a moderate negative linear correlation. 
B)  There is insufficient evidence to make any conclusions about the relationship between the variables. 
C)  There is a weak positive linear correlation. 
D)  There is a moderate positive linear correlation.

Question 6

Make a scatter diagram for the data. Use the scatter diagram to describe how, if at all, the variables are related.
-

Accepted Answer

A)  The variables do not appear to be linearly related.   
B)  The variables appear to be positively, linearly related.   
C)  The variables do not appear to be linearly related.   
D)  The variables appear to be negatively, linearly related.   
A)  The variables do not appear to be linearly related.   
B)  The variables appear to be positively, linearly related.   
C)  The variables do not appear to be linearly related.   
D)  The variables appear to be negatively, linearly related.

Question 7

Choose the coefficient of determination that matches the scatterplot. Assume that the scales on the horizontal and vertical axes are the same.
-

Accepted Answer

A)    =0.76 
B)    =0.41 
C)    =-0.31 
D)    =0.097 
A)    =0.76 
B)    =0.41 
C)    =-0.31 
D)    =0.097

Question 8

The regression line for the given data is   = 4.379x + 4.267. Determine the residual of a data point for which x = 10.5 and y = 50.5.

Accepted Answer

A)  50.2465 
B)  100.7465 
C)  0.2535 
D)  -214.9065 
A)  50.2465 
B)  100.7465 
C)  0.2535 
D)  -214.9065

Question 9

A scatter diagram is given with one of the points labeled "A." In addition, there are two least-squares regression lines drawn. The solid line excludes the point A. The dashed line includes the point A. Based on the graph, is the point A influential?
-

Accepted Answer

A) True 
 B)False

Question 10

To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, an experimenter divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows:   Summary statistics yield SSxx = 10.5, SSyy = 112, and SSxy = 25. Calculate the coefficient of determination rounded to the nearest ten-thousandth.

Accepted Answer

The answer of To investigate the relationship between yield of...

Question 11

The data below are the average one-way commute times (in minutes) for selected students and the number of absences for those students during the term. Find the equation of the regression line for the given data. What would be the predicted number of absences if the commute time was 95 minutes? Is this a reasonable question? Round the predicted number of absences to the nearest whole number. Round the regression line values to the nearest hundredth.

Accepted Answer

A)    =0.45x-30.27; 12 absences; No, it is not reasonable. 95 minutes is well outside the scope of the model. 
B)    =0.45x+30.27; 73 absences; Yes, it is reasonable. 
C)    =0.45x+30.27; 73 absences; No, it is not reasonable. 95 minutes is well outside the scope of the model. 
D)    =0.45x-30.27; 12 absences; Yes, it is reasonable. 
A)    =0.45x-30.27; 12 absences; No, it is not reasonable. 95 minutes is well outside the scope of the model. 
B)    =0.45x+30.27; 73 absences; Yes, it is reasonable. 
C)    =0.45x+30.27; 73 absences; No, it is not reasonable. 95 minutes is well outside the scope of the model. 
D)    =0.45x-30.27; 12 absences; Yes, it is reasonable.

Question 12

Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools." An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Total GMAT scores range from 200 to 800. A simple linear regression of SALARY versus GMAT using 25 data points shown below.   
-Give a practical interpretation of   = -92040.

Accepted Answer

A)  We expect to predict SALARY to within 2(92040) = $184,080 of its true value using GMAT in a straight-line model. 
B)  We estimate the base SALARY of graduates of a top business school to be $-92,040. 
C)  We estimate SALARY to decrease $92,040 for every 1-point increase in GMAT. 
D)  The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. 
A)  We expect to predict SALARY to within 2(92040) = $184,080 of its true value using GMAT in a straight-line model. 
B)  We estimate the base SALARY of graduates of a top business school to be $-92,040. 
C)  We estimate SALARY to decrease $92,040 for every 1-point increase in GMAT. 
D)  The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.

Question 13

In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the weekly number of grunts and the age of the warthog (in days) are listed below:   a. Write the equation of a straight-line model relating number of grunts (y) to age (x).
b. Give the least squares prediction equation.
c. Give a practical interpretation of the value of   if possible.
d. Give a practical interpretation of the value of   if possible.

Accepted Answer

a. E(y) = @#IMG-DLM& + @#IMG-DLM& x
b. @#IMG-DLM& = @#IMG-DLM& + @#IMG-DLM& x = 181.16 - 0

Question 14

Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools." An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points shown below.

Accepted Answer

A)  We can predict SALARY correctly 66% of the time using GMAT in a straight-line model. 
B)  66% of the differences in SALARY are caused by differences in GMAT scores. 
C)  66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 
D)  We estimate SALARY to increase $.66 for every 1-point increase in GMAT. 
A)  We can predict SALARY correctly 66% of the time using GMAT in a straight-line model. 
B)  66% of the differences in SALARY are caused by differences in GMAT scores. 
C)  66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 
D)  We estimate SALARY to increase $.66 for every 1-point increase in GMAT.

Question 15

Analyze the residual lot below. Does it violate any of the conditions for an adequate linear model?
-

Accepted Answer

A)  No, the plot of residuals is random. 
B)  Yes, the residuals do not display constant error variance. 
C)  Yes, there is a discernable pattern in the residuals. 
A)  No, the plot of residuals is random. 
B)  Yes, the residuals do not display constant error variance. 
C)  Yes, there is a discernable pattern in the residuals.

Question 16

The data below are the average one-way commute times (in minutes) for selected students and the number of absences for those students during the term. Find the equation of the regression line for the given data. What would be the predicted number of absences if the commute time was 40 minutes? Is this a reasonable question? Round the predicted number of absences to the nearest whole number. Round the regression line values to the nearest hundredth.

Accepted Answer

A)    =0.45x+30.27; 48 absences; No, it is not reasonable. 40 minutes is well outside the scope of the model. 
B)    =0.45x-30.27;-12 absences; No, it is not reasonable. 40 minutes is well outside the scope of the model. 
C)    =0.45x+30.27; 48 absences; Yes, it is reasonable. 
D)    =0.45x-30.27;-12 absences; Yes, it is reasonable. 
A)    =0.45x+30.27; 48 absences; No, it is not reasonable. 40 minutes is well outside the scope of the model. 
B)    =0.45x-30.27;-12 absences; No, it is not reasonable. 40 minutes is well outside the scope of the model. 
C)    =0.45x+30.27; 48 absences; Yes, it is reasonable. 
D)    =0.45x-30.27;-12 absences; Yes, it is reasonable.

Question 17

Construct a scatter diagram for the data.
-The data below are the number of absences and the final grades of 9 randomly selected students from a literature class.

Accepted Answer

The answer of Construct a scatter diagram for the data.
-The...

Question 18

Calculate the linear correlation coefficient for the data below.

Accepted Answer

A)  -0.132 
B)  -0.549 
C)  -0.104 
D)  -0.581 
A)  -0.132 
B)  -0.549 
C)  -0.104 
D)  -0.581

Question 19

A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables:   Give a practical interpretation of the coefficient of determination,   . Express   to the nearest whole percent.

Accepted Answer

A)  About 43% of the sample variation in number of man-hours can be explained by the simple linear model. 
B)  About 2.06% of the sample variation in number of man-hours can be explained by the simple linear model. 
C)  Man hours needed to erect drums will be associated with boiler design pressure 43% of the time. 
D)    =1.88+0.00321x will be correct 43% of the time. 
A)  About 43% of the sample variation in number of man-hours can be explained by the simple linear model. 
B)  About 2.06% of the sample variation in number of man-hours can be explained by the simple linear model. 
C)  Man hours needed to erect drums will be associated with boiler design pressure 43% of the time. 
D)    =1.88+0.00321x will be correct 43% of the time.

Question 20

Civil engineers often use the straight-line equation,   =   +   x, to model the relationship between the mean shear strength of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 triplet tests is shown in the accompanying table followed by a SAS printout of the regression analysis.   
-Give a practical interpretation of the estimate of the slope of the least squares line.

Accepted Answer

A)  For a triplet test with a precompression stress of 1 ton, we estimate the shear strength of the joint to be 0.987 ton. 
B)  For every 0.987 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 1 ton. 
C)  For a triplet test with a precompression stress of 0 tons, we estimate the shear strength of the joint to be 1.19 tons. 
D)  For every 1 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 0.987 ton. 
A)  For a triplet test with a precompression stress of 1 ton, we estimate the shear strength of the joint to be 0.987 ton. 
B)  For every 0.987 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 1 ton. 
C)  For a triplet test with a precompression stress of 0 tons, we estimate the shear strength of the joint to be 1.19 tons. 
D)  For every 1 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 0.987 ton.

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

The regression line for the given data is = -1.885x + 0.758. Determine the residual of a data point for which x = 4 and y = -6.

Given the equation of a regression line is = -5.5x - 0.7, what is the best predicted value for y given x= 7.4?

Use the scatter diagrams shown, labeled a through f to solve the problem. -In which scatter diagram is r = 0.01?

A traffic officer is compiling information about the relationship between the hour or the day and the speed over the limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tell the officer?

Make a scatter diagram for the data. Use the scatter diagram to describe how, if at all, the variables are related. -

Choose the coefficient of determination that matches the scatterplot. Assume that the scales on the horizontal and vertical axes are the same. -

The regression line for the given data is = 4.379x + 4.267. Determine the residual of a data point for which x = 10.5 and y = 50.5.

A scatter diagram is given with one of the points labeled "A." In addition, there are two least-squares regression lines drawn. The solid line excludes the point A. The dashed line includes the point A. Based on the graph, is the point A influential? -

Analyze the residual lot below. Does it violate any of the conditions for an adequate linear model? -

Construct a scatter diagram for the data. -The data below are the number of absences and the final grades of 9 randomly selected students from a literature class.

Calculate the linear correlation coefficient for the data below.

Data Collection

Organizing and Summarizing Data

Numerically Summarizing Data

Probability

Discrete Probability Distributions

The Normal Probability Distributions

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model

Filters

Exam 4: Describing the Relation Between Two Variables

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

The regression line for the given data is = -1.885x + 0.758. Determine the residual of a data point for which x = 4 and y = -6.

Given the equation of a regression line is = -5.5x - 0.7, what is the best predicted value for y given x= 7.4?

Use the scatter diagrams shown, labeled a through f to solve the problem. -In which scatter diagram is r = 0.01?

A traffic officer is compiling information about the relationship between the hour or the day and the speed over the limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tell the officer?

Make a scatter diagram for the data. Use the scatter diagram to describe how, if at all, the variables are related. -

Choose the coefficient of determination that matches the scatterplot. Assume that the scales on the horizontal and vertical axes are the same. -

The regression line for the given data is = 4.379x + 4.267. Determine the residual of a data point for which x = 10.5 and y = 50.5.

A scatter diagram is given with one of the points labeled "A." In addition, there are two least-squares regression lines drawn. The solid line excludes the point A. The dashed line includes the point A. Based on the graph, is the point A influential? -

Analyze the residual lot below. Does it violate any of the conditions for an adequate linear model? -

Construct a scatter diagram for the data. -The data below are the number of absences and the final grades of 9 randomly selected students from a literature class.

Calculate the linear correlation coefficient for the data below.

Data Collection

Organizing and Summarizing Data

Numerically Summarizing Data

Probability

Discrete Probability Distributions

The Normal Probability Distributions

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model

Filters