Question 1

Choose the one alternative that best completes the statement or answers the question.
-The least squares regression line

Accepted Answer

A)  minimizes the sum of the residuals squared. 
B)  maximizes the sum of the residuals squared. 
C)  minimizes the mean difference between the residuals squared. 
D)  maximizes the mean difference between the residuals squared. 
A)  minimizes the sum of the residuals squared. 
B)  maximizes the sum of the residuals squared. 
C)  minimizes the mean difference between the residuals squared. 
D)  maximizes the mean difference between the residuals squared.

Question 2

Use the scatter diagrams shown, labeled a through f to solve the problem.
-In which scatter diagram is r = -1

Accepted Answer

A)  $a$ 
B)  $b$ 
C)  $\mathrm { f }$ 
D)  $\mathrm { d }$ 
A)  $a$ 
B)  $b$ 
C)  $\mathrm { f }$ 
D)  $\mathrm { d }$

Question 3

Compute the Sum of Squared Residuals
-A calculus instructor is interested the performance of his students from Calculus I that go on to Calculus II. Their final grades in each course (in percent) are given below. Compute the sum of the squared residuals of the least squared line for the given data. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Calculus I } & 88 & 78 & 62 & 75 & 95 & 91 & 83 & 86 & 98 \
\hline \text { Calculus II } & 81 & 80 & 55 & 78 & 90 & 90 & 81 & 80 & 100 \
\hline
\end{array}$

Accepted Answer

A)  $130.14$ 
B)  $30.85$ 
C)  $11.41$ 
D)  $1075.9$ 
A)  $130.14$ 
B)  $30.85$ 
C)  $11.41$ 
D)  $1075.9$

Question 4

Perform Residual Analysis on a Regression Model
-Residual analysis cannot be used to check for outliers.

Accepted Answer

A) True 
 B)False

Question 5

Provide an appropriate response.
-To eliminate the effects of either the row or the column variables in a contingency table, a distribution is created.

Accepted Answer

A)  marginal 
B)  normalized 
C)  χ2 
D)  Studentʹs t 
A)  marginal 
B)  normalized 
C)  χ2 
D)  Studentʹs t

Question 6

Choose the one alternative that best completes the statement or answers the question.
-A residual is the difference between

Accepted Answer

A)  the observed value of y and the predicted value of y. 
B)  the observed value of x and the predicted value of x. 
C)  the observed value of y and the predicted value of x. 
D)  the observed value of x and the predicted value of y. 
A)  the observed value of y and the predicted value of y. 
B)  the observed value of x and the predicted value of x. 
C)  the observed value of y and the predicted value of x. 
D)  the observed value of x and the predicted value of y.

Question 7

Choose the one alternative that best completes the statement or answers the question.
-Use the regression equation to predict the value of $\mathrm { y }$ for $\mathrm { x } = 3.3$.

Accepted Answer

A)  $- 5.462$ 
B)  $6.979$ 
C)  $0.616$ 
D)  $4.386$ 
A)  $- 5.462$ 
B)  $6.979$ 
C)  $0.616$ 
D)  $4.386$

Question 8

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-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.
$$\hat { \beta _ { 0 } } = - 92040 \hat { \beta } 1 = 228 \mathrm {~s} = 3213 \mathrm { R } ^ { 2 } = 0.66 \mathrm { r } = 0.81 \mathrm { df } = 23 \mathrm { t } = 6.67$$
Give a practical interpretation of $\hat { \beta } 1 = 228$.

Accepted Answer

A)  We estimate SALARY to increase $\$ 228$ for every 1 -point increase in GMAT. 
B)  We expect to predict SALARY to within $2 ( 228 ) = \$ 456$ of its true value using GMAT in a straight-line model. 
C)  We estimate GMAT to increase 228 points for every $\$ 1$ increase in SALARY. 
D)  The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. 
A)  We estimate SALARY to increase $\$ 228$ for every 1 -point increase in GMAT. 
B)  We expect to predict SALARY to within $2 ( 228 ) = \$ 456$ of its true value using GMAT in a straight-line model. 
C)  We estimate GMAT to increase 228 points for every $\$ 1$ increase in SALARY. 
D)  The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.

Question 9

Change the exponential expression to an equivalent expression involving a logarithm.
-$\log _ { 3 } 9 = 2$

Accepted Answer

A)  $3 ^ { 2 } = 9$ 
B)  $2 ^ { 3 } = 9$ 
C)  $3 ^ { 9 } = 2$ 
D)  $9 ^ { 2 } = 3$ 
A)  $3 ^ { 2 } = 9$ 
B)  $2 ^ { 3 } = 9$ 
C)  $3 ^ { 9 } = 2$ 
D)  $9 ^ { 2 } = 3$

Question 10

Compute the Sum of Squared Residuals
-The regression line for the given data is $\hat { y } = - 2.75 x + 96.14$. Determine the residual of a data point for which $x =$ 2 and $y = 92$.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\hline \text { Number of absences, } \mathrm{x} & 0 & 3 & 6 & 4 & 9 & 2 & 15 & 8 & 5 \
\hline \text { Final grade, } \mathrm{y} & 98 & 86 & 80 & 82 & 71 & 92 & 55 & 76 & 82
\end{array}$

Accepted Answer

A)  $1.36$ 
B)  $182.64$ 
C)  $90.64$ 
D)  $158.86$ 
A)  $1.36$ 
B)  $182.64$ 
C)  $90.64$ 
D)  $158.86$

Question 11

Change the exponential expression to an equivalent expression involving a logarithm.
-$$9 ^ { x } = 134$$

Accepted Answer

A)  $\log _ { 9 } 134 = x$ 
B)  $\log _ { 134 } 9 = x$ 
C)  $\log _ { 134 } x = 9$ 
D)  $\log _ { 9 } x = 134$ Change the logarithmic expression to an equivalent expression involving an exponent. 
A)  $\log _ { 9 } 134 = x$ 
B)  $\log _ { 134 } 9 = x$ 
C)  $\log _ { 134 } x = 9$ 
D)  $\log _ { 9 } x = 134$ Change the logarithmic expression to an equivalent expression involving an exponent.

Question 12

Choose the one alternative that best completes the statement or answers the question.
-In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Which is the best predicted value for $\mathrm { y }$ given $\mathrm { x } = 15.9$ ?
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Rainfall (in inches), } \mathrm{x} & 10.5 & 8.8 & 13.4 & 12.5 & 18.8 & 10.3 & 7.0 & 15.6 & 16.0 \
\hline \text { Yield (bushels per acre), y } & 50.5 & 46.2 & 58.8 & 59.0 & 82.4 & 49.2 & 31.9 & 76.0 & 78.8
\end{array}$

Accepted Answer

A)  $73.9$ 
B)  $74.2$ 
C)  $73.7$ 
D)  $74.4$ 
A)  $73.9$ 
B)  $74.2$ 
C)  $73.7$ 
D)  $74.4$

Question 13

Provide an appropriate response.
-In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient.

Accepted Answer

A)  $0.981$ 
B)  $0.998$ 
C)  $0.900$ 
D)  $0.899$ 
A)  $0.981$ 
B)  $0.998$ 
C)  $0.900$ 
D)  $0.899$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The following data represent the compound yield in grams for a chemical reaction for various temperatures of the reaction. Determine the "best" model to describe the relationship between temperature and compound yield.
$\begin{array}{l|l}
\text { Temperature }\left({ }^{\circ} \mathrm{C}\right), & \text { Compound Yield (grams), } \mathrm{y} \
\hline 50 & 4 \
60 & 12 \
70 & 14 \
80 & 21 \
90 & 26
\end{array}$

Accepted Answer

A)  linear model: $\mathrm { y } = - 21.7 + 0.53 \mathrm { x }$ 
B)  exponential model: $\hat { y } = - 0.195 + 0.019 x$ 
C)  power model: $\mathrm { y } = - 4.392 + 2.999 \mathrm { x }$ 
D)  power model: $\hat { y } = 4.392 + 2.999 x$ 
A)  linear model: $\mathrm { y } = - 21.7 + 0.53 \mathrm { x }$ 
B)  exponential model: $\hat { y } = - 0.195 + 0.019 x$ 
C)  power model: $\mathrm { y } = - 4.392 + 2.999 \mathrm { x }$ 
D)  power model: $\hat { y } = 4.392 + 2.999 x$

Question 15

The scatter diagram shows the relationship between average number of years of education and births per woman ofchild bearing age in selected countries. Use the scatter plot to determine whether the statement is true or false.
-There is a strong positive correlation between years of education and births per woman.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 16

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Find the equation of the regression line for the given data.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Rainfall (in inches), } x & 10.5 & 8.8 & 13.4 & 12.5 & 18.8 & 10.3 & 7.0 & 15.6 & 16.0 \
\hline \text { Yield (bushels per acre), y } & 50.5 & 46.2 & 58.8 & 59.0 & 82.4 & 49.2 & 31.9 & 76.0 & 78.8
\end{array}$

Accepted Answer

A)  $\hat  { y } = 4.379 \mathrm { x } + 4.267$ 
B)  $\hat  { y } = - 4.379 \mathrm { x } + 4.267$ 
C)  $\hat  { y } = 4.267 \mathrm { x } + 4.379$ 
D)  $\hat { y } = 4.267 x - 4.379$ 
A)  $\hat  { y } = 4.379 \mathrm { x } + 4.267$ 
B)  $\hat  { y } = - 4.379 \mathrm { x } + 4.267$ 
C)  $\hat  { y } = 4.267 \mathrm { x } + 4.379$ 
D)  $\hat { y } = 4.267 x - 4.379$

Question 17

Write the expression as a sum of logs. Express powers as factors.
-$\log _ { b } yz ^ { 2 } 2$

Accepted Answer

A)  $\log _ { b } y + 2 \log _ { b } z$ 
B)  $2 \log _ { b } y + 2 \log _ { b } z$ 
C)  $2 \log _ { b } y z$ 
D)  $\log _ { b } y + \log _ { b } 2 z$ 
A)  $\log _ { b } y + 2 \log _ { b } z$ 
B)  $2 \log _ { b } y + 2 \log _ { b } z$ 
C)  $2 \log _ { b } y z$ 
D)  $\log _ { b } y + \log _ { b } 2 z$

Question 18

Perform Residual Analysis on a Regression Model
-To determine if there are outliers in a least squares regression modelʹs data set, we could construct a boxplot of the

Accepted Answer

A)  residuals. 
B)  response variables. 
C)  predictor variables. 
D)  lurking variables. 
A)  residuals. 
B)  response variables. 
C)  predictor variables. 
D)  lurking variables.

Question 19

Choose the one alternative that best completes the statement or answers the question.
-If the coefficient of determination is close to 1, then

Accepted Answer

A)  the least squares regression line equation explains most of the variation in the response variable. 
B)  the least squares regression line equation has no explanatory value. 
C)  the sum of the square residuals is large compared to the total variation. 
D)  the linear correlation coefficient is close to zero. 
A)  the least squares regression line equation explains most of the variation in the response variable. 
B)  the least squares regression line equation has no explanatory value. 
C)  the sum of the square residuals is large compared to the total variation. 
D)  the linear correlation coefficient is close to zero.

Question 20

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Find the equation of the regression line for the given data. What would be the predicted pressure if the age was 60 ? Round the predicted pressure to the nearest whole number.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\text { Age, } \mathrm{x} & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm{y} & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$

Accepted Answer

A)  $\hat { y } = 1.488 x + 60.46 ; 150 \mathrm {~mm}$ 
B)  $\hat {y} = 60.46 x - 1.488 ; 3626 \mathrm {~mm}$ 
C)  $\hat {y} = 1.448 \mathrm { x } - 60.46 ; 29 \mathrm {~mm}$ 
D)  $\hat {y} = 60.46 x + 1.488 ; 3629 \mathrm {~mm}$ 
A)  $\hat { y } = 1.488 x + 60.46 ; 150 \mathrm {~mm}$ 
B)  $\hat {y} = 60.46 x - 1.488 ; 3626 \mathrm {~mm}$ 
C)  $\hat {y} = 1.448 \mathrm { x } - 60.46 ; 29 \mathrm {~mm}$ 
D)  $\hat {y} = 60.46 x + 1.488 ; 3629 \mathrm {~mm}$

Choose the one alternative that best completes the statement or answers the question. -The least squares regression line

Use the scatter diagrams shown, labeled a through f to solve the problem. -In which scatter diagram is r = -1

Perform Residual Analysis on a Regression Model -Residual analysis cannot be used to check for outliers.

Provide an appropriate response. -To eliminate the effects of either the row or the column variables in a contingency table, a distribution is created.

Choose the one alternative that best completes the statement or answers the question. -A residual is the difference between

Change the exponential expression to an equivalent expression involving a logarithm. - $\log _ { 3 } 9 = 2$

Compute the Sum of Squared Residuals -The regression line for the given data is $\hat { y } = - 2.75 x + 96.14$ . Determine the residual of a data point for which $x =$ 2 and $y = 92$ . Number of absences, 0 3 6 4 9 2 15 8 5 Final grade, 98 86 80 82 71 92 55 76 82

Change the exponential expression to an equivalent expression involving a logarithm. - $9 ^ { x } = 134$

Provide an appropriate response. -In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient.

Write the expression as a sum of logs. Express powers as factors. - $\log _ { b } yz ^ { 2 } 2$

Perform Residual Analysis on a Regression Model -To determine if there are outliers in a least squares regression modelʹs data set, we could construct a boxplot of the

Choose the one alternative that best completes the statement or answers the question. -If the coefficient of determination is close to 1, then

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Probability

Discrete Probability Distributions

The Normal Probability Distribution

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 and Multiple Regression

Nonparametric Statistics

Filters

Exam 4: Describing the Relation Between Two Variables