Question 1

Plot the line y = 4 - 2x. Then give the slope and y-intercept of the line.

Accepted Answer

The answer of Plot the line y = 4 -...

Question 2

(-6, -6)and (3, 3)

Accepted Answer

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

Question 3

The Method of Least Squares specifies that the regression line has an average error of 0 and has an
SSE that is minimized.

Accepted Answer

A) True 
 B)False

Question 4

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.
What set of hypotheses would you test to determine whether appraised value is positively linearly related to number of rooms?

Accepted Answer

A)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta 1  0$ 
C)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } \neq 0$ 
D)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } > 0$ 
A)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta 1  0$ 
C)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } \neq 0$ 
D)  $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } > 0$

Question 5

A realtor collected the following data for a random sample of ten homes that recently sold
in her area. $$\begin{array} { | c | c | c | } 
\hline \text { House } & \text { Asking Price } & \text { Days on Market } \
\hline \text { A } & \$ 114,500 & 29 \
\hline \text { B } & \$ 149,900 & 16 \
\hline \text { C } & \$ 154,700 & 59 \
\hline \text { D } & \$ 159,900 & 42 \
\hline \text { E } & \$ 160,000 & 72 \
\hline \text { F } & \$ 165,900 & 45 \
\hline \text { G } & \$ 169,700 & 12 \
\hline \text { H } & \$ 171,900 & 39 \
\hline \text { I } & \$ 175,000 & 81 \
\hline \text { J } & \$ 289,900 & 121 \
\hline
\end{array}$$ a. Find a 90% confidence interval for the mean number of days on the market for all
houses listed at $150,000.
b. Suppose a house has just been listed at $150,000. Find a 90% prediction interval for the
number of days the house will be on the market before it sells.

Accepted Answer

a. The regression li

Question 6

A breeder of Thoroughbred horses wishes to model the relationship between the gestation
period and the length of life of a horse. The breeder believes that the two variables may
follow a linear trend. The information in the table was supplied to the breeder from
various thoroughbred stables across the state.  
Summary statistics yield $S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332$, and $\bar { y } = 22.5$.
Calculate $S S E , s ^ { 2 }$, and $s$.

Accepted Answer

\[\begin{array}{l}
\hat { \beta } 1 = \f

Question 7

Suppose you fit a least squares line to 20 data points and the calculated value of SSE is
0.476. a. Find $s ^ { 2 }$, the estimator of $\sigma ^ { 2 }$.
b. What is the largest deviation you might expect between any one of the 20 points and the least squares line?

Accepted Answer

The answer of Suppose you fit a least squares line...

Question 8

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.
$\begin{array} { l l } \hat { y } = 4.25 + 2.75 x , & S S x y = 5.15 , S S x x = 1.87 \ & S S y y = 15.17 , S S E = 1.0075 \ \text { Range of the } x \text {-values: } & 2.23 - 3.85 \ \text { Range of the } y \text {-values: } & 9.3 - 15.6 \end{array}$
Range of the $y$-values: $\quad 9.3 - 15.6$
Suppose a $95 \%$ prediction interval for $y$ when $x = 3.00$ is $( 16,21 )$. Interpret the interval.

Accepted Answer

A)  We are $95 \%$ confident that the starting salary of a Business School graduate will increase between $\$ 16,000$ and $\$ 21,000$ for every 3 -point increase in GPA. 
B)  We are $95 \%$ confident that the mean starting salary of all Business School graduates with GPAs of $3.00$ will fall between $\$ 16,000$ and $\$ 21,000$. 
C)  We are $95 \%$ confident that the starting salary of a Business School graduate will fall between $\$ 16,000$ and $\$ 21,000$. 
D)  We are $95 \%$ confident that the starting salary of a Business School graduate with a GPA of $3.00$ will fall between $\$ 16,000$ and $\$ 21,000$. 
A)  We are $95 \%$ confident that the starting salary of a Business School graduate will increase between $\$ 16,000$ and $\$ 21,000$ for every 3 -point increase in GPA. 
B)  We are $95 \%$ confident that the mean starting salary of all Business School graduates with GPAs of $3.00$ will fall between $\$ 16,000$ and $\$ 21,000$. 
C)  We are $95 \%$ confident that the starting salary of a Business School graduate will fall between $\$ 16,000$ and $\$ 21,000$. 
D)  We are $95 \%$ confident that the starting salary of a Business School graduate with a GPA of $3.00$ will fall between $\$ 16,000$ and $\$ 21,000$.

Question 9

Is there a relationship between the raises administrators at County University receive and their performance on the job? A faculty group wants to determine whether job rating $( x )$ is a useful linear predictor of raise ( $y$ ). Consequently, the group considered the linear regression model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$
The faculty group obtained the following prediction equation:
$$\hat { y } = 14,000 - 2,000 x$$
Which of the following statements about the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } ^ { x }$ is correct?

Accepted Answer

A)  The model hypothesizes that, on average, administrators make more money than professors. 
B)  The model hypothesizes that the raises for the administrators fall in a perfect straight line. 
C)  The model hypothesizes a line of means; as rating $( x )$ increases, the mean raise $E ( y )$ moves up or down along a straight line. 
D)  The model hypothesizes that knowing an administrator's rating $( x )$ will determine exactly the administrator's raise $( y )$. 
A)  The model hypothesizes that, on average, administrators make more money than professors. 
B)  The model hypothesizes that the raises for the administrators fall in a perfect straight line. 
C)  The model hypothesizes a line of means; as rating $( x )$ increases, the mean raise $E ( y )$ moves up or down along a straight line. 
D)  The model hypothesizes that knowing an administrator's rating $( x )$ will determine exactly the administrator's raise $( y )$.

Question 10

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 number of grunts and and the age of the warthog (in days)are listed below: $\begin{array}{cc}
\hline \text { Number of Grunts } & \text { Age (days) } \
\hline 82 & 117 \
60 & 133 \
31 & 147 \
36 & 152 \
55 & 159 \
32 & 166 \
54 & 175 \
9 & 181 \
12 & 187 \
\hline
\end{array}$

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 $\hat { \beta } _ { 0 }$, if possible.
d. Give a practical interpretation of the value of $\hat { \beta } _ { 1 }$, if possible.

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. We would expect approximately

Question 11

Consider the data set shown below. Find the estimate of the y-intercept of the least squares regression line. $$\begin{array} { c | c | c | c | c | c | c | c } 
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$

Accepted Answer

A) 0.9003 
B) 0.94643 
C) 1.49045 
D) 1.5 
A) 0.9003 
B) 0.94643 
C) 1.49045 
D) 1.5

Question 12

Consider the following pairs of measurements: $\begin{array}{|c|c|c|c|c|c|}
\hline x & 5 & 8 & 3 & 4 & 9 \
\hline y & 6.2 & 3.4 & 7.5 & 8.1 & 3.2 \
\hline
\end{array}$

a. Construct a scattergram for the data.
b. Use the method of least squares to model the relationship between $x$ and $y$.
c. Calculate $S S E , s ^ { 2 }$, and s.
d. What percentage of the observed $y$-values fall within $2 s$ of the values of $\hat { y }$ predicted by the least squares model?

Accepted Answer

a. @#IMG-DLM&
b. @#LAT-DLM&
c.

Question 13

The probabilistic model allows the E(y)values to fall around the regression line while the actual
values of y must fall on the line.

Accepted Answer

A) True 
 B)False

Question 14

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars)and x = size of
The diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE
Predictor

Which of the following assumptions is not stated correctly?

Accepted Answer

A)  The variance of the probability distribution of $\varepsilon$ is constant for all settings of the independent variable. 
B)  The values of $\varepsilon$ associated with any two observations are dependent on one another. 
C)  The probability distribution of $\varepsilon$ is normal. 
D)  The mean of the probability distribution of $\varepsilon$ is 0 . 
A)  The variance of the probability distribution of $\varepsilon$ is constant for all settings of the independent variable. 
B)  The values of $\varepsilon$ associated with any two observations are dependent on one another. 
C)  The probability distribution of $\varepsilon$ is normal. 
D)  The mean of the probability distribution of $\varepsilon$ is 0 .

Question 15

Plot the line y = 3x. Then give the slope and y-intercept of the line.

Accepted Answer

The answer of Plot the line y = 3x. Then...

Question 16

A company keeps extensive records on its new salespeople on the premise that sales
should increase with experience. A random sample of seven new salespeople produced
the data on experience and sales shown in the table. $\begin{array}{c|c}
\text { Months on Job } & \begin{array}{c}
\text { Monthly Sales } \
y \text { (\$ thousands) }
\end{array} \
\hline 2 & 2.4 \
4 & 7.0 \
8 & 11.3 \
12 & 15.0 \
1 & .8 \
5 & 3.7 \
9 & 12.0
\end{array}$

Summary statistics yield $S S _ { x x } = 94.8571 , S S _ { x y } = 124.7571 , S S _ { y y } = 176.5171 , \bar { x } = 5.8571$, and $\bar { y } = 7.4571$. State the assumptions necessary for predicting the monthly sales based on the linear relationship with the months on the job.

Accepted Answer

The assumptions necessary are: 1. The ra

Question 17

A company keeps extensive records on its new salespeople on the premise that sales
should increase with experience. A random sample of seven new salespeople produced
the data on experience and sales shown in the table. $\begin{array}{c|c}
\text { Months on Job } & \begin{array}{c}
\text { Monthly Sales } \
y \text { (\$ thousands) }
\end{array} \
\hline 2 & 2.4 \
4 & 7.0 \
8 & 11.3 \
12 & 15.0 \
1 & .8 \
5 & 3.7 \
9 & 12.0
\end{array}$

Summary statistics yield $S S _ { x x } = 94.8571 , S S _ { x y } = 124.7571 , S S _ { y y } = 176.5171 , \bar { x } = 5.8571$, and $\bar { y } = 7.4571$. Calculate a $90 \%$ confidence interval for $E ( y )$ when $x = 5$ months. Assume $s = 1.577$ and the prediction equation is $\hat { y } = - .25 + 1.315 x$.

Accepted Answer

For @#LAT-DLM&
The confidence interval i

Question 18

In a comprehensive road test on new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is
Conducted on a random sample of 129 new cars. TIME60: $\quad y =$ Elapsed time (in seconds) from $0 \mathrm { mph }$ to $60 \mathrm { mph }$
MAX $\quad x =$ Maximum speed attained (miles per hour)
The simple linear model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ was fit to the data. Computer printouts for the analysis are given below:
NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60
$\begin{array}{l|c|c|c|c}
\text { PREDICTOR } & & & & \
\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENTS T } & \mathrm{P} \
\hline \text { CONSTANT } & 18.7171 & 0.63708 & 29.38 & 0.0000 \
\text { MAX } & -0.08365 & 0.00491 & -17.05 & 0.0000
\end{array}$

$\begin{array}{llll}
\text { R-SQUARED } & 0.6960 & \text { RESID. MEAN SQUARE (MSE) } & 1.28695 \
\text { ADJUSTED R-SQUARED } & 0.6937 & \text { STANDARD DEVIATION } & 1.13444
\end{array}$

$\begin{array}{l|r|r|r|c|c}
\text { SOURCE } & \text { DF } &{\text { SS }} & \text { MS } & \text { F } & \text { P } \
\hline \text { REGRESSION } & 1 & 374.285 & 374.285 & 290.83 & 0.0000 \
\text { RESIDUAL } & 127 & 163.443 & 1.28695 & & \
\text { TOTAL } & 128 & 537.728 & & &
\end{array}$

CASES INCLUDED 129 MISSING CASES 0
Approximately what percentage of the sample variation in acceleration time can be explained by the simple linear model?

Accepted Answer

A)  $0 \%$ 
B)  $70 \%$ 
C)  $- 17 \%$ 
D)  $8 \%$ 
A)  $0 \%$ 
B)  $70 \%$ 
C)  $- 17 \%$ 
D)  $8 \%$

Question 19

For the situation above, write the equation of the probabilistic model of interest.

Accepted Answer

A)  GMAT $= \beta _ { 0 } + \beta _ { 1 }$ (SALARY) 
B)  Salary $= \beta _ { 0 } + \beta _ { 1 } ($ GMAT $) + \epsilon$ 
C)  Salary $= \beta _ { 0 } + \beta _ { 1 } ($ GMAT $)$ 
D)  GMAT $= \beta _ { 0 } + \beta _ { 1 } ($ SALARY $) + \epsilon$ 
A)  GMAT $= \beta _ { 0 } + \beta _ { 1 }$ (SALARY) 
B)  Salary $= \beta _ { 0 } + \beta _ { 1 } ($ GMAT $) + \epsilon$ 
C)  Salary $= \beta _ { 0 } + \beta _ { 1 } ($ GMAT $)$ 
D)  GMAT $= \beta _ { 0 } + \beta _ { 1 } ($ SALARY $) + \epsilon$

Question 20

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

Interpret the estimated slope of the regression line.

Accepted Answer

A)  For every $\$ 1000$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $\$ 1474.94$. 
B)  For every $\$ 1000$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $\$ 1474.94$. 
C)  For every $\$ 1474.94$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $\$ 18,184.90$. 
D)  For every $\$ 1000$ increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $\$ 1474.94$. 
A)  For every $\$ 1000$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $\$ 1474.94$. 
B)  For every $\$ 1000$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $\$ 1474.94$. 
C)  For every $\$ 1474.94$ increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $\$ 18,184.90$. 
D)  For every $\$ 1000$ increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $\$ 1474.94$.

Plot the line y = 4 - 2x. Then give the slope and y-intercept of the line.

(-6, -6)and (3, 3)

The Method of Least Squares specifies that the regression line has an average error of 0 and has an SSE that is minimized.

Suppose you fit a least squares line to 20 data points and the calculated value of SSE is 0.476. a. Find $s ^ { 2 }$ , the estimator of $\sigma ^ { 2 }$ . b. What is the largest deviation you might expect between any one of the 20 points and the least squares line?

Consider the data set shown below. Find the estimate of the y-intercept of the least squares regression line. 0 3 2 3 8 10 11 -2 0 2 4 6 8 10

The probabilistic model allows the E(y)values to fall around the regression line while the actual values of y must fall on the line.

Plot the line y = 3x. Then give the slope and y-intercept of the line.

For the situation above, write the equation of the probabilistic model of interest.

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

Plot the line y = 4 - 2x. Then give the slope and y-intercept of the line.

(-6, -6)and (3, 3)

The Method of Least Squares specifies that the regression line has an average error of 0 and has an SSE that is minimized.

Suppose you fit a least squares line to 20 data points and the calculated value of SSE is 0.476. a. Find s2s ^ { 2 }s2 , the estimator of σ2\sigma ^ { 2 }σ2 . b. What is the largest deviation you might expect between any one of the 20 points and the least squares line?

Consider the data set shown below. Find the estimate of the y-intercept of the least squares regression line. 0 3 2 3 8 10 11 -2 0 2 4 6 8 10

The probabilistic model allows the E(y)values to fall around the regression line while the actual values of y must fall on the line.

Plot the line y = 3x. Then give the slope and y-intercept of the line.

For the situation above, write the equation of the probabilistic model of interest.

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

Suppose you fit a least squares line to 20 data points and the calculated value of SSE is 0.476. a. Find $s ^ { 2 }$ , the estimator of $\sigma ^ { 2 }$ . b. What is the largest deviation you might expect between any one of the 20 points and the least squares line?