Question 1

Graph the line that passes through the given points.
-$(-6,0) \text { and }(1,-1)$

Accepted Answer

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

Question 2

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l r } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
2 . & \text { Stanford } & 665 & 10.2 & 60,000 \
3 . & \text { Penn } & 644 & 19.4 & 55,000 \
4 . & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
6 . & \text { Chicago } & 632 & 30.0 & 55,269 \
7 . & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
9 . & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
24 . & \text { Maryland } & 593 & 28.1 & 42,925 \
25 . & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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 the 25 data points in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948). Interpret this interval for the situation above.

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 increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984. 
C)  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. 
D)  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. 
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 increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984. 
C)  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. 
D)  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.

Question 3

a. Complete the table.
$\begin{array} { | l | c | c | c | c | } 
\hline & x _ { i } & y _ { i } & x _ { i } ^ { 2 } & x _ { i } y _ { i } \
\hline & 2 & 3 & & \
\hline & 5 & 2 & & \
\hline & 3 & 4 & & \
\hline & 8 & 0 & & \
\hline \text { Totals } & \Sigma x _ { i } = & \Sigma y _ { i } = & \Sigma x _ { i } ^ { 2 } = & \Sigma x _ { i } y _ { i } = \
\hline
\end{array}$

b. Find $S S _ { x y } , S S _ { x x } , \beta _ { 1 } , \bar { x } , \bar { y }$, and $\hat { \beta } _ { 0 }$.
c. Write the equation of the least squares line.

Accepted Answer

None

Question 4

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.

$\begin{array}{c|c}
\text { Months on Job } & \begin{array}{c}
\text { Monthly Sales } \
\text { y (\$ thousands) }
\end{array} \
\hline 2 & 2.4 \
4 & 7.0 \
8 & 11.3 \
12 & 15.0 \
1 & .8 \
5 & 3.7 \
9 & 12.0
\end{array}$

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

Question 5

Suppose you fit a least squares line to 23 data points and the calculated value of SSE is $0.495$.
a. Find $s ^ { 2 }$, the estimator of $\sigma ^ { 2 }$.
b. What is the largest deviation you might expect between any one of the 23 points and the least squares line?

Accepted Answer

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

Question 6

Consider the data set shown below. Find the standard deviation 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)  1.5 
B)  1.49045 
C)  0.9003 
D)  0.94643 
A)  1.5 
B)  1.49045 
C)  0.9003 
D)  0.94643

Question 7

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 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 graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's 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 value of the test statistic for testing $\beta _ { 1 }$ is 17.169. Select the proper conclusion.

Accepted Answer

A)  There is sufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary. 
B)  There is insufficient evidence (at $\alpha = .10$ ) to conclude that GPA is a useful linear predictor of starting salary. 
C)  There is insufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary. 
D)  At any reasonable $\alpha$, there is no relationship between GPA and starting salary. 
A)  There is sufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary. 
B)  There is insufficient evidence (at $\alpha = .10$ ) to conclude that GPA is a useful linear predictor of starting salary. 
C)  There is insufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary. 
D)  At any reasonable $\alpha$, there is no relationship between GPA and starting salary.

Question 9

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

$\begin{array}{lccccc}
\text { Predictor}\
\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \
\text { Constant } & -2298.36 & 158.531 & -14.50 & 0.0000 \
\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000
\end{array}$

$\begin{array}{lccc}
\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \
\text { Adjusted R-Squared } & 0.8922 & \text { Standard Deviation } & 1117.56
\end{array}$

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here:
95% confidence interval for E(Y): ($9091.60, $9509.40)
95% prediction interval for Y: ($7091.50, $11,510.00)
Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all 1-carat diamonds?

Accepted Answer

A)  We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. 
B)  We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. 
C)  We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. 
D)  We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. 
A)  We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. 
B)  We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. 
C)  We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. 
D)  We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40.

Question 10

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. 
\[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
2 . & \text { Stanford } & 665 & 10.2 & 60,000 \
3 . & \text { Penn } & 644 & 19.4 & 55,000 \
4 . & \text { Northwestern } & 640 & 22.6 & 54,000 \
5 . & \text { MIT } & 650 & 21.3 & 57,000 \
6 . & \text { Chicago } & 632 & 30.0 & 55,269 \
7 . & \text { Duke } & 630 & 18.2 & 53,300 \
8 . & \text { Dartmouth } & 649 & 13.4 & 52,000 \
9 . & \text { Virginia } & 630 & 23.0 & 55,269 \
10 . & \text { Michigan } & 620 & 32.4 & 53.300 \
11 . & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
14 . & \text { UNC } & 625 & 15.4 & 50,800 \
15 . & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
16 . & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
21 . & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
23 . & \text { Georgetown } & 617 & 31.7 & 45,156 \
24 . & \text { Maryland } & 593 & 28.1 & 42,925 \
25 . & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] 
The 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 the 25 data points in the table are shown below. 
$$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $t = 6.67$.

Accepted Answer

A)  There is evidence (at $\alpha = .05$ ) of at least a positive linear relationship between SALARY and GMAT. 
B)  We estimate SALARY to increase $\$ 6.67$ for every 1-point increase in GMAT. 
C)  There is evidence (at $\alpha = .05$ ) to indicate that $\beta _ { 1 } = 0$. 
D)  Only $6.67 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model. 
A)  There is evidence (at $\alpha = .05$ ) of at least a positive linear relationship between SALARY and GMAT. 
B)  We estimate SALARY to increase $\$ 6.67$ for every 1-point increase in GMAT. 
C)  There is evidence (at $\alpha = .05$ ) to indicate that $\beta _ { 1 } = 0$. 
D)  Only $6.67 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model.

Question 11

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 $\mathrm { y } =$ appraised value of the house (in thousands of dollars) and $x =$ number of rooms. Using data collected for a sample of $n = 74$ houses in East Meadow, the following results were obtained:
$$\hat { y } = 74.80 + 19.72 x$$ Give a practical interpretation of the estimate of ?, the standard deviation of the random error term in the model.

Accepted Answer

A)  We expect to predict the appraised value of an East Meadow house to within about $29,000 of its true value. 
B)  We expect to predict the appraised value of an East Meadow house to within about $58,000 of its true value. 
C)  We expect 95% of the observed appraised values to lie on the least squares line. 
D)  About 29% of the total variation in the sample of y-values can be explained by the linear relationship between appraised value and number of rooms. 
A)  We expect to predict the appraised value of an East Meadow house to within about $29,000 of its true value. 
B)  We expect to predict the appraised value of an East Meadow house to within about $58,000 of its true value. 
C)  We expect 95% of the observed appraised values to lie on the least squares line. 
D)  About 29% of the total variation in the sample of y-values can be explained by the linear relationship between appraised value and number of rooms.

Question 12

A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue $( x )$, measured in \$ million. Data for 21 companies who use the bank's services were used to fit the model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$
The results of the simple linear regression are provided below.
$$\hat { y } = 2,700 + 20 x$$
Interpret the estimate of $\beta _ { 0 }$, the $y$-intercept of the line.

Accepted Answer

A)  All companies will be charged at least $\$ 2,700$ by the bank. 
B)  About $95 \%$ of the observed service charges fall within $\$ 2,700$ of the least squares line. 
C)  For every $\$ 1$ million increase in sales revenue, we expect a service charge to increase $\$ 2,700$. 
D)  There is no practical interpretation since a sales revenue of $\$ 0$ is a nonsensical value. 
A)  All companies will be charged at least $\$ 2,700$ by the bank. 
B)  About $95 \%$ of the observed service charges fall within $\$ 2,700$ of the least squares line. 
C)  For every $\$ 1$ million increase in sales revenue, we expect a service charge to increase $\$ 2,700$. 
D)  There is no practical interpretation since a sales revenue of $\$ 0$ is a nonsensical value.

Question 13

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

$\begin{array}{lcccll}
\text {Predictor}\
\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & {\text { P }} \
\text { Constant } & -2298.36 & 158.531 & -14.50 & 0.0000 \
\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000
\end{array}$

$\begin{array}{lccc}
\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \
\text { Adjusted R-Squared } & 0.8922 & \text { Standard Deviation } & 1117.56
\end{array}$

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here:

95% confidence interval for E(Y): ($9091.60, $9509.40)
95% prediction interval for Y: ($7091.50, $11,510.00)

Which of the following interpretations is correct if you want to use the model to determine the price of a single 1-carat diamond?

Accepted Answer

A)  We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. 
B)  We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. 
C)  We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. 
D)  We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. 
A)  We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. 
B)  We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. 
C)  We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. 
D)  We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00.

Question 14

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 15

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

Question 16

What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from $0.18$ to $1.1$ carats) 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

$\begin{array}{l}
\text { Predictor }\
\begin{array}{lccccl}
\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \
\text { Constant } & -2298.36 & 158.531 & & -14.50 & 0.0000 \
\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000
\end{array}
\end{array}$

$\begin{array}{llll}
\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950\
\text { Adiusted R-Souared } & 08920 & \text { Standard Deviation } & 111756
\end{array}$
 Interpret the estimated y-intercept of the regression line.

Accepted Answer

A)  No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled. 
B)  When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36. 
C)  When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36. 
D)  When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90. 
A)  No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled. 
B)  When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36. 
C)  When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36. 
D)  When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90.

Question 17

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 determination.

Accepted Answer

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

Question 18

Consider the data set shown below. Find the coefficient of determination for the simple linear regression model. $$\begin{array} { c | c | c | c | c | c | c | c } 
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$

Accepted Answer

A)  0.9003 
B)  0.9489 
C)  0.8804 
D)  0.9383 
A)  0.9003 
B)  0.9489 
C)  0.8804 
D)  0.9383

Question 19

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 $\bar { y } = 7.4571$. Using SSE $= 12.435$, find and interpret the coefficient of determination.

Accepted Answer

@#LAT-DLM&
@#LAT-DLM& of the variation in the samp

Question 20

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

Accepted Answer

@#IMG-DLM&

slope: 3

Graph the line that passes through the given points. - $(-6,0) \text { and }(1,-1)$ $Graph the line that passes through the given points. - (-6,0) \text { and }(1,-1)$

a. Complete the table. 2 3 5 2 3 4 8 0 Totals \Sigma= \Sigma= \Sigma= \Sigma= b. Find $S S _ { x y } , S S _ { x x } , \beta _ { 1 } , \bar { x } , \bar { y }$ , and $\hat { \beta } _ { 0 }$ . c. Write the equation of the least squares line.

Suppose you fit a least squares line to 23 data points and the calculated value of SSE is $0.495$ . a. Find $s ^ { 2 }$ , the estimator of $\sigma ^ { 2 }$ . b. What is the largest deviation you might expect between any one of the 23 points and the least squares line?

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

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

Consider the data set shown below. Find the coefficient of determination for the simple linear regression model. 0 3 2 3 8 10 11 -2 0 2 4 6 8 10

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

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

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

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Exam 11: Simple Linear Regression

Graph the line that passes through the given points. - (−6,0) and (1,−1)(-6,0) \text { and }(1,-1)(−6,0) and (1,−1)

Suppose you fit a least squares line to 23 data points and the calculated value of SSE is 0.4950.4950.495 . 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 23 points and the least squares line?

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

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

Consider the data set shown below. Find the coefficient of determination for the simple linear regression model. 0 3 2 3 8 10 11 -2 0 2 4 6 8 10

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

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

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

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Graph the line that passes through the given points. - $(-6,0) \text { and }(1,-1)$ $Graph the line that passes through the given points. - (-6,0) \text { and }(1,-1)$

Suppose you fit a least squares line to 23 data points and the calculated value of SSE is $0.495$ . a. Find $s ^ { 2 }$ , the estimator of $\sigma ^ { 2 }$ . b. What is the largest deviation you might expect between any one of the 23 points and the least squares line?

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