(a) Answer The equation of the best fit of the line is y = 7 x − 95 . Explanation Given: Formula Used: The line of fit is the line that most closely goes through the points of data. The equation of a line is written as y = m x + b where m is the slope and b is the y -intercept. m = y 2 − y 1 x 2 − x 1 Calculation: Given is − Plotting the above points on the graph, we have: Considering the below two points as they fall on the same straight line, we have: ( 26 , 87 ) and ( 27 , 94 ) Thus, we have: Slope = m = y 2 − y 1 x 2 − x 1 m = 94 − 87 27 − 26 m = 7 Thus, the equation of the line is y − y 1 = m ( x − x 1 ) y − 87 = 7 ( x − 26 ) y − 87 = 7 x − 182 y = 7 x − 95 Thus, the equation of the best fit of the line is y = 7 x − 95 . Conclusion: The equation of the best fit of the line is y = 7 x − 95 . (b) To determine To identify and interpret the correlation co-efficient - Answer The correlation co-efficient is 0.9357 . Explanation Given: Formula Used: The formula to calculate correlation co-efficient is - r = n ( ∑ x y ) − ( ∑ x ) ( y ) [ n ∑ x 2 − ( ∑ x ) 2 ] [ n ∑ y 2 − ( y ) 2 ] Calculation: Given is − Using the above formula to calculate correlation co-efficient, we have - r = n ( ∑ x y ) − ( ∑ x ) ( y ) [ n ∑ x 2 − ( ∑ x ) 2 ] [ n ∑ y 2 − ( y ) 2 ] x y x y x 2 y 2 27 94 2538 729 8836 18 56 1008 324 3136 25 58 1450 625 3364 32 123 3936 1024 15129 18 60 1080 324 3600 26 87 2262 676 7569 36 145 5220 1296 21025 Thus, we have: r = n ( ∑ x y ) − ( ∑ x ) ( y ) [ n ∑ x 2 − ( ∑ x ) 2 ] [ n ∑ y 2 − ( y ) 2 ] r = 0.9357 Conclusion: The correlation co-efficient is 0.9357 . (c) To determine To interpret the slope and y-intercept of the line of the best fit- Answer The slope is 7 and y -intercept is − 95 . Explanation Given: Formula Used: The line of fit is the line that most closely goes through the points of data. The equation of a line is written as y = m x + b where m is the slope and b is the y -intercept. m = y 2 − y 1 x 2 − x 1 Calculation: Given is − Equation of the best fit of the line is y = 7 x − 95 . m = 7 y -intercept = − 95 Thus, Slope is 7 and y -intercept is − 95 . Conclusion: The slope is 7 and y -intercept is − 95 . (d) To determine To find the cost of sailboat that is 20 feet long. Answer The cost of sailboat that is 20 feet long is 45 (thousands of dollars). Explanation Given: Formula Used: The line of fit is the line that most closely goes through the points of data. The equation of a line is written as y = m x + b where m is the slope and b is the y -intercept. m = y 2 − y 1 x 2 − x 1 Calculation: Given is − Equation of the best fit of the line is y = 7 x − 95 . Since, x = 20 y = 45 Conclusion: The cost of sailboat that is 20 feet long is 45 (thousands of dollars). (e) To determine To find the length of sailboat that costs $ 147000 . Answer The length of sailboat that costs $ 147000 is 34.57 feet. Explanation Given: Formula Used: The line of fit is the line that most closely goes through the points of data. The equation of a line is written as y = m x + b where m is the slope and b is the y -intercept. m = y 2 − y 1 x 2 − x 1 Calculation: Given is − Equation of the best fit of the line is y = 7 x − 95 . Since, y = 147 x = 34.57 Thus, the length of sailboat that costs $ 147000 is 34.57 feet. Conclusion: The length of sailboat that costs $ 147000 is 34.57 feet.

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 4.5, Problem 20E

(a)

To determine

To find the equation of the line of the best fit for the dataand plot the data-

(a)

Expert Solution

Answer to Problem 20E

The equation of the best fit of the line is $y=7x−95$ .

Explanation of Solution

Given:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 2

Formula Used:

The line of fit is the line that most closely goes through the points of data.

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

$m=y2−y1x2−x1$

Calculation:

Given is −

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 3

Plotting the above points on the graph, we have:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 4

Considering the below two points as they fall on the same straight line, we have:

$(26,87)$ and $(27,94)$

Thus, we have:

Slope $=$ $m=y2−y1x2−x1$

$m=94−8727−26m=7$

Thus, the equation of the line is

$y−y1=m(x−x1)$

$y−87=7(x−26)y−87=7x−182y=7x−95$

Thus, the equation of the best fit of the line is $y=7x−95$ .

Conclusion:

The equation of the best fit of the line is $y=7x−95$ .

(b)

To determine

To identify and interpret the correlation co-efficient -

(b)

Expert Solution

Answer to Problem 20E

The correlation co-efficient is $0.9357$ .

Explanation of Solution

Given:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 6

Formula Used:

The formula to calculate correlation co-efficient is -

$r=n(∑xy)−(∑x)(y)[n∑x2−(∑x)2][n∑y2−(y)2]$

Calculation:

Given is −

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 7

Using the above formula to calculate correlation co-efficient, we have -

$r=n(∑xy)−(∑x)(y)[n∑x2−(∑x)2][n∑y2−(y)2]$

$x$	$y$	$xy$	$x2$	$y2$
$27$	$94$	$2538$	$729$	$8836$
$18$	$56$	$1008$	$324$	$3136$
$25$	$58$	$1450$	$625$	$3364$
$32$	$123$	$3936$	$1024$	$15129$
$18$	$60$	$1080$	$324$	$3600$
$26$	$87$	$2262$	$676$	$7569$
$36$	$145$	$5220$	$1296$	$21025$

Thus, we have:

$r=n(∑xy)−(∑x)(y)[n∑x2−(∑x)2][n∑y2−(y)2]$

$r=0.9357$

Conclusion:

The correlation co-efficient is $0.9357$ .

(c)

To determine

To interpret the slope and y-intercept of the line of the best fit-

(c)

Expert Solution

Answer to Problem 20E

The slope is $7$ and $y$ -intercept is $−95$ .

Explanation of Solution

Given:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 9

Formula Used:

The line of fit is the line that most closely goes through the points of data.

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

$m=y2−y1x2−x1$

Calculation:

Given is −

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 10

Equation of the best fit of the line is $y=7x−95$ .

$m=7$

$y$ -intercept $=$ $−95$

Thus, Slope is $7$ and $y$ -intercept is $−95$ .

Conclusion:

The slope is $7$ and $y$ -intercept is $−95$ .

(d)

To determine

To find the cost of sailboat that is $20$ feet long.

(d)

Expert Solution

Answer to Problem 20E

The cost of sailboat that is $20$ feet long is $45$ (thousands of dollars).

Explanation of Solution

Given:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 12

Formula Used:

The line of fit is the line that most closely goes through the points of data.

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

$m=y2−y1x2−x1$

Calculation:

Given is −

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 13

Equation of the best fit of the line is $y=7x−95$ .

Since, $x=20$

$y=45$

Conclusion:

The cost of sailboat that is $20$ feet long is $45$ (thousands of dollars).

(e)

To determine

To find the length of sailboat that costs $$147000$ .

(e)

Expert Solution

Answer to Problem 20E

The length of sailboat that costs $$147000$ is $34.57$ feet.

Explanation of Solution

Given:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 15

Formula Used:

The line of fit is the line that most closely goes through the points of data.

The equation of a line is written as $y=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

$m=y2−y1x2−x1$

Calculation:

Given is −

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 4.5, Problem 20E , additional homework tip 16

Equation of the best fit of the line is $y=7x−95$ .

Since, $y=147$

$x=34.57$

Thus, the length of sailboat that costs $$147000$ is $34.57$ feet.

Conclusion:

The length of sailboat that costs $$147000$ is $34.57$ feet.

Chapter 4.5, Problem 19E

Chapter 4.5, Problem 21E

Chapter 4 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

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