Question 1

(2, -6)and (-1, 3)

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA)of a graduating student can be used to predict the graduateʹs starting
Salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting
Salaries. Records for 23 of last yearʹs Business School graduates are selected at random, and data
On GPA (x)and starting salary (y, in $thousands)for each graduate were used to fit the model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } ^ { x }$$
The results of the simple linear regression are provided below.
$$\begin{aligned}
\hat { y } = 4.25 + 2.75 x , & S S _ { x y } = 5.15 , S S _ { x x } = 1.87 \
S S _ { y y } = 15.17 , S S E = 1.0075
\end{aligned}$$
Compute an estimate of $\sigma$, the standard deviation of the random error term.

Accepted Answer

A)  $1.0075$ 
B)  $.048$ 
C)  $0.219$ 
D)  $.689$ 
A)  $1.0075$ 
B)  $.048$ 
C)  $0.219$ 
D)  $.689$

Question 3

For the situation above, give a practical interpretation of $\hat { \beta } _ { 0 } = - 92040$.

Accepted Answer

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

Question 4

Plot the line y = 1.5 + .5x. Then give the slope and y-intercept of the line.

Accepted Answer

The answer of Plot the line y = 1.5 +...

Question 5

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \mathrm { df } = 23 \quad t = 6.67$$
Give a practical interpretation of $r = .81$.

Accepted Answer

A)  $81 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 
B)  We can predict SALARY correctly $81 \%$ of the time using GMAT in a straight-line model. 
C)  There appears to be a positive correlation between SALARY and GMAT. 
D)  We estimate SALARY to increase $81 \%$ for every 1 -point increase in GMAT. 
A)  $81 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 
B)  We can predict SALARY correctly $81 \%$ of the time using GMAT in a straight-line model. 
C)  There appears to be a positive correlation between SALARY and GMAT. 
D)  We estimate SALARY to increase $81 \%$ for every 1 -point increase in GMAT.

Question 6

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's)charged by the program.
The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary
Predictor
$\begin{array} { l r r c l } \text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \ \text { Constant } & 18.1849 & 10.3336 & 1.76 & 0.0826 \ \text { Size } & 1.47494 & 0.14017 & 10.52 & 0.0000 \end{array}$

R-Squared $ \quad 0.6027 \quad $ Resid. Mean Square (MSE) $ 532.986 $
Adjusted R-Squared $ 0.5972 $ Standard Deviation $ \quad 23.0865 $

The model was then used to create $95 \%$ confidence and prediction intervals for $y$ and for $\mathrm { E } ( \mathrm { Y } )$ when the tuition charged by the MBA program was $\$ 75,000$. The results are shown here:
95\% confidence interval for $\mathrm { E } ( \mathrm { Y } )$ : $( \$ 123,390 , \$ 134,220 )$
$95 \%$ prediction interval for $Y$ : $( \$ 82,476 , \$ 175,130 )$
Which of the following interpretations is correct if you want to use the model to estimate $E ( Y )$ for all MBA programs?

Accepted Answer

A)  We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$. 
B)  We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$. 
C)  We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$. 
D)  We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$. 
A)  We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$. 
B)  We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$. 
C)  We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$. 
D)  We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$.

Question 7

Consider the following pairs of observations: $\begin{array}{|l|l|l|l|l|l|}
\hline x & 2 & 0 & 3 & 3 & 5 \
\hline y & 1 & 3 & 4 & 6 & 7 \
\hline
\end{array}$

a. Construct a scattergram for the data.
b. Find the least squares line, and plot it on your scattergram.
c. Find a $99 \%$ confidence interval for the mean value of $y$ when $x = 1$.
d. Find a $99 \%$ prediction interval for a new value of $y$ when $x = 1$.

Accepted Answer

a.
@#IMG-DLM&

b. @#LAT-DLM&
c. For @#LAT-DLM&.
For 3 degrees of freed

Question 8

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT was created from a set of 25 data points.
Which of the following is not an assumption required for the simple linear regression analysis to
Be valid?

Accepted Answer

A) The errors of predicting SALARY are normally distributed. 
B) SALARY is independent of GMAT. 
C) The errors of predicting SALARY have a mean of 0. 
D) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. 
A) The errors of predicting SALARY are normally distributed. 
B) SALARY is independent of GMAT. 
C) The errors of predicting SALARY have a mean of 0. 
D) The errors of predicting SALARY have a variance that is constant for any given value of GMAT.

Question 9

A high value of the correlation coefficient r implies that a causal relationship exists between x and
y.

Accepted Answer

A) True 
 B)False

Question 10

Probabilistic models are commonly used to estimate both the mean value of y and a new
individual value of y for a particular value of x.

Accepted Answer

A) True 
 B)False

Question 11

$$\text { Calculate SSE and } s ^ { 2 } \text { for } n = 25 , \sum y ^ { 2 } = 950 , \sum y = 65 , \mathrm { SS } _ { \mathrm { xy } } = 3000 \text {, and } \hat { \beta } 1 = .2$$

Accepted Answer

\[\begin{array} { l } 
\mathrm { SS } _

Question 12

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: MANHRS: $\quad y =$ Number of man-hours required to erect the drum
PRESSURE: $\quad x =$ Boiler design pressure (pounds per square inch, i.e., psi)
The simple linear model $E ( y ) = \beta 1 + \beta 1 x$ was fit to the data. A printout for the analysis appears below:
UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS
$\begin{array}{c|c|c|c|c}
\text { PREDICTOR } & & & & \
\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENTST } & \text { P } \
\hline \text { CONSTANT } & 1.88059 & 0.58380 & 3.22 & 0.0028 \
\text { PRESSURE } & 0.00321 & 0.00163 & 2.17 & 0.0300
\end{array}$

$\begin{array}{l|r|c|c|c|c}
\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \mathrm{F} & \mathrm{P} \
\hline \text { REGRESSION } & 1 & 111.008 & 111.008 & 5.19 & 0.0300 \
\text { RESIDUAL } & 34 & 144.656 & 4.25160 & & \
\text { TOTAL } & 35 & 255.665 & & &
\end{array}$

Give a practical interpretation of the coefficient of determination, $r ^ { 2 }$.

Accepted Answer

A)  Approximately $95 \%$ of the actual man-hours required to build a drum will fall within 43 hours of their predicted values. 
B)  We are $43 \%$ confident that the design pressure will be a useful predictor of number of man-hours required to build a steam drum. 
C)  About $43 \%$ of the sample variation in number of man-hours can be explained by the simple linear model. 
D)  About $2.06 \%$ of the sample variation in number of man-hours can be explained by the simple linear model. 
A)  Approximately $95 \%$ of the actual man-hours required to build a drum will fall within 43 hours of their predicted values. 
B)  We are $43 \%$ confident that the design pressure will be a useful predictor of number of man-hours required to build a steam drum. 
C)  About $43 \%$ of the sample variation in number of man-hours can be explained by the simple linear model. 
D)  About $2.06 \%$ of the sample variation in number of man-hours can be explained by the simple linear model.

Question 13

(-9, 0)and (-4, -1)

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Is the number of games won by a major league baseball team in a season related to the
teamʹs batting average? Data from 14 teams were collected and the summary statistics
yield: $$\sum y = 1,134 , \sum x = 3.642 , \sum y ^ { 2 } = 93,110 , \sum x ^ { 2 } = .948622 , \text { and } \sum x y = 295.54$$
Assume $\hat { \beta } 1 = 455.27$. Estimate and interpret the estimate of $\sigma$.

Accepted Answer

\[\begin{array} { l } 
S S E = S S _ { y

Question 15

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
A $95 \%$ prediction interval for SALARY when GMAT $= 600$ is approximately $( \$ 37,915 , \$ 51,984 )$. Interpret this interval.

Accepted Answer

A)  We are $95 \%$ confident that the SALARY of a top business school graduate will fall between $\$ 37,915$ and \$51,984. 
B)  We are $95 \%$ confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $\$ 37,915$ and $\$ 51,984$. 
C)  We are $95 \%$ confident that the increase in SALARY for a 600 -point increase in GMAT will fall between $\$ 37,915$ and $\$ 51,984$. 
D)  We are $95 \%$ confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $\$ 37,915$ and $\$ 51,984$. 
A)  We are $95 \%$ confident that the SALARY of a top business school graduate will fall between $\$ 37,915$ and \$51,984. 
B)  We are $95 \%$ confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $\$ 37,915$ and $\$ 51,984$. 
C)  We are $95 \%$ confident that the increase in SALARY for a 600 -point increase in GMAT will fall between $\$ 37,915$ and $\$ 51,984$. 
D)  We are $95 \%$ confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $\$ 37,915$ and $\$ 51,984$.

Question 16

To investigate the relationship between yield of potatoes, y, and level of fertilizer
application, x, a researcher 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: $\begin{array}{l|cccccccc}
\hline x & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 & 4.5 \
\hline y & 25 & 31 & 27 & 28 & 36 & 35 & 32 & 34 \
\hline
\end{array}$

Summary statistics yield $S S _ { x x } = 10.5 , S S _ { y y } = 112 , S S _ { x y } = 25$, and $S S E = 52.476$. Calculate the coefficient of correlation.

Accepted Answer

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

Question 17

The least squares model provides very good estimates of y for values of x far outside the range of x
values contained in the sample.

Accepted Answer

A) True 
 B)False

Question 18

For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?

Accepted Answer

A) The errors of predicting SALARY are normally distributed. 
B) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. 
C) SALARY is independent of GMAT. 
D) The errors of predicting SALARY have a mean of 0. 
A) The errors of predicting SALARY are normally distributed. 
B) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. 
C) SALARY is independent of GMAT. 
D) The errors of predicting SALARY have a mean of 0.

Question 19

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model: $$E ( y ) = \beta _ { 0 } + \beta 1 ^ { x }$$
where $y =$ appraised value of the house (in thousands of dollars) and $x =$ number of rooms. Using data collected for a sample of $n = 84$ houses in East Meadow, the following results were obtained:
$$\hat { y } = 84.80 + 19.72 x$$
What are the properties of the least squares line, $y = 84.80 + 19.72 x ?$

Accepted Answer

A)  Average error of prediction is 0 , and $S S E$ is minimum. 
B)  It will always be a statistically useful predictor of $y$. 
C)  All 84 of the sample $y$-values fall on the line. 
D)  It is normal, mean 0 , constant variance, and independent. 
A)  Average error of prediction is 0 , and $S S E$ is minimum. 
B)  It will always be a statistically useful predictor of $y$. 
C)  All 84 of the sample $y$-values fall on the line. 
D)  It is normal, mean 0 , constant variance, and independent.

Question 20

$$\text { Construct a } 90 \% \text { confidence interval for } \beta 1 \text { when } \hat { \beta } 1 = 49 , s = 4 , \mathrm { SS } _ { \mathrm { XX } } = 55 \text {, and } n = 15 \text {. }$$

Accepted Answer

The answer of \[\text { Construct a } 90 \%...

(2, -6)and (-1, 3)

For the situation above, give a practical interpretation of $\hat { \beta } _ { 0 } = - 92040$ .

Plot the line y = 1.5 + .5x. Then give the slope and y-intercept of the line.

A high value of the correlation coefficient r implies that a causal relationship exists between x and y.

Probabilistic models are commonly used to estimate both the mean value of y and a new individual value of y for a particular value of x.

$\text { Calculate SSE and } s ^ { 2 } \text { for } n = 25 , \sum y ^ { 2 } = 950 , \sum y = 65 , \mathrm { SS } _ { \mathrm { xy } } = 3000 \text {, and } \hat { \beta } 1 = .2$

(-9, 0)and (-4, -1)

The least squares model provides very good estimates of y for values of x far outside the range of x values contained in the sample.

For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?

$\text { Construct a } 90 \% \text { confidence interval for } \beta 1 \text { when } \hat { \beta } 1 = 49 , s = 4 , \mathrm { SS } _ { \mathrm { XX } } = 55 \text {, and } n = 15 \text {. }$

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics Available Online

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Exam 11: Simple Linear Regression

(2, -6)and (-1, 3)

For the situation above, give a practical interpretation of β^0=−92040\hat { \beta } _ { 0 } = - 92040β^​0​=−92040 .

Plot the line y = 1.5 + .5x. Then give the slope and y-intercept of the line.

A high value of the correlation coefficient r implies that a causal relationship exists between x and y.

Probabilistic models are commonly used to estimate both the mean value of y and a new individual value of y for a particular value of x.

(-9, 0)and (-4, -1)

The least squares model provides very good estimates of y for values of x far outside the range of x values contained in the sample.

For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics Available Online

Filters

For the situation above, give a practical interpretation of $\hat { \beta } _ { 0 } = - 92040$ .