Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold x and the total production cost y . Tyler's results are shown in the table. x 25 40 65 53 46 30 50 74 70 y 200 260 350 360 260 250 310 600 450 Use your regression line as a model to find and interpret the meaning of the gradient

Given data, x 25 40 65 53 46 30 50 74 70 y 200 260 350 360 260 250 310 600 450 From the given table we can find the value of variables:- Serial number x y x y x 2 1 25 200 5000 625 2 40 260 10400 1600 3 65 350 22750 4225 4 53 360 19080 2809 5 46 260 11960 2116 6 30 250 7500 900 7 50 310 15500 2500 8 74 600 44400 5476 9 70 450 31500 4900 Total ∑ x = 453 ∑ y = 3040 ∑ x y = 168090 ∑ x 2 = 25151 The line of regression of y on x be y = b + a x Now, ∑ y = n b + a ∑ x ⇒ 3040 = 9 b + 453 a ∑ x y = b ∑ x + 9 ∑ x 2 ⇒ 168090 = 453 b + 25151 a Solving the both equation we get, a = 6 . 416 and b = 14 . 859 Then the line of regression be y = 14 . 859 + 6 . 416 x . The gradient (a) of the line represent the change in the product cost depend on change of number of pizzas sold. Here, gradient is a = 6 . 42 . Thus, each pizza produced raises costs by 6 . 42 .

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold x and the total production cost y . Tyler's results are shown in the table. x 25 40 65 53 46 30 50 74 70 y 200 260 350 360 260 250 310 600 450 Use your regression line as a model to find and interpret the meaning of the y -intercept.

Given data, x 25 40 65 53 46 30 50 74 70 y 200 260 350 360 260 250 310 600 450 From the given table we can find the value of variables:- Serial number x y x y x 2 1 25 200 5000 625 2 40 260 10400 1600 3 65 350 22750 4225 4 53 360 19080 2809 5 46 260 11960 2116 6 30 250 7500 900 7 50 310 15500 2500 8 74 600 44400 5476 9 70 450 31500 4900 Total ∑ x = 453 ∑ y = 3040 ∑ x y = 168090 ∑ x 2 = 25151 The line of regression of y on x be y = b + a x Now, ∑ y = n b + a ∑ x ⇒ 3040 = 9 b + 453 a ∑ x y = b ∑ x + 9 ∑ x 2 ⇒ 168090 = 453 b + 25151 a Solving the both equation we get, a = 6 . 416 and b = 14 . 859 Then the line of regression be y = 14 . 859 + 6 . 416 x . The y-intercept represent the value of production cost when the recorded number of pizza sold is zero. Here, y -intercept is 4 . 859 . Thus, the cost to the shop when no pizzas are produced is $ 14 . 86 .

The value, y thousand Yen, of a used car changes as the age of the car ( x years ) increases. This able shows the age and value of Chan's car over 10 years. x 1 2 3 4 5 8 9 10 y 115 110 92 89 80 63 59 54 The relationship between x and y can be modelled by the regression equation y = a x + b . Write down the values of a and b .

Given data, x 1 2 3 4 5 8 9 10 y 115 110 92 89 80 63 59 54 The relationship between x and y can be modelled by the regression equation y = a x + b . Serial number x y x y x 2 1 1 115 115 1 2 2 110 220 4 3 3 92 276 9 4 4 89 356 16 5 5 80 400 25 6 8 63 504 64 7 9 59 531 81 8 10 54 540 100 Total ∑ x = 42 ∑ y = 662 ∑ x y = 2942 ∑ x 2 = 300 The linear equation of y o n x be y = b + a x Now, ∑ y = n b + a ∑ x ⇒ 662 = 8 b + 42 a and ∑ x y = b ∑ x + a ∑ x 2 ⇒ 2942 = 42 b + 300 a b = 117 . 981 , a = - 6 . 711 The line of regression is y = 117 . 981 - 6 . 711 x

The value, y thousand Yen, of a used car changes as the age of the car ( x years ) increases. This able shows the age and value of Chan's car over 10 years. x 1 2 3 4 5 8 9 10 y 115 110 92 89 80 63 59 54 Use the regression equation to estimate the value of Chan's car after six years. Give your answer to the nearest ¥ 1000

Given data, x 1 2 3 4 5 8 9 10 y 115 110 92 89 80 63 59 54 The relationship between x and y can be modelled by the regression equation y = a x + b . Serial number x y x y x 2 1 1 115 115 1 2 2 110 220 4 3 3 92 276 9 4 4 89 356 16 5 5 80 400 25 6 8 63 504 64 7 9 59 531 81 8 10 54 540 100 Total ∑ x = 42 ∑ y = 662 ∑ x y = 2942 ∑ x 2 = 300 The linear equation of y o n x be y = b + a x Now, ∑ y = n b + a ∑ x ⇒ 662 = 8 b + 42 a and ∑ x y = b ∑ x + a ∑ x 2 ⇒ 2942 = 42 b + 300 a On solving the equations, we get b = 117 . 981 , a = - 6 . 711 The line of regression is y = 117 . 981 - 6 . 711 x Put, x = 6 , ∴ y = 117 . 981 - 6 . 711 × 6 ⇒ y = 77 . 715 ≈ 77 . 7 ⇒ y = 77 . 7 × 10000 = 777000 Thus, the value of chans's car after six years is 777000 .

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D

Attempt the practice questions on Chapter 7: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D with Hints & Solutions

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 9

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold $x$ and the total production cost $y$ . Tyler's results are shown in the table.

$x$	$25$	$40$	$65$	$53$	$46$	$30$	$50$	$74$	$70$
$y$	$200$	$260$	$350$	$360$	$260$	$250$	$310$	$600$	$450$

Use your regression line as a model to find and interpret the meaning of the gradient

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 9

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold $x$ and the total production cost $y$ . Tyler's results are shown in the table.

$x$	$25$	$40$	$65$	$53$	$46$	$30$	$50$	$74$	$70$
$y$	$200$	$260$	$350$	$360$	$y = b + a x$	$250$	$310$	$600$	$450$

Use your regression line as a model to find and interpret the meaning of the $y$ -intercept.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 9

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold $x$ and the total production cost $y$ . Tyler's results are shown in the table.

$x$	$25$	$40$	$65$	$53$	$46$	$30$	$50$	$74$	$70$
$y$	$200$	$260$	$350$	$360$	$260$	$250$	$310$	$600$	$450$

Estimate the cost of producing $60$ pizzas.(Answer up to one decimal value)

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 9

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold $x$ and the total production cost $y$ . Tyler's results are shown in the table.

$x$	$25$	$40$	$65$	$53$	$46$	$30$	$50$	$74$	$70$
$y$	$200$	$260$	$350$	$360$	$260$	$250$	$310$	$600$	$450$

Comment on the appropriateness of using your model to estimate the cost of producing $5000$ pizzas

Estimate the cost of producing $60$ pizzas.(Answer up to one decimal value)

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 9

Tyler manages a pizza shop. Over a nine-day period, Tyler recorded the number of pizzas sold $x$ and the total production cost $y$ . Tyler's results are shown in the table.

$x$	$25$	$40$	$65$	$53$	$46$	$30$	$50$	$74$	$70$
$y$	$200$	$260$	$350$	$360$	$260$	$250$	$310$	$600$	$450$

Comment on the appropriateness of using your model to estimate the number of pizzas produced when the total cost is $100$ .(Write the answer to a near whole number)

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 10

The value, y thousand Yen, of a used car changes as the age of the car $(x$ years $)$ increases. This able shows the age and value of Chan's car over $10$ years.

$x$	$1$	$2$	$3$	$4$	$5$	$8$	$9$	$10$
$y$	$115$	$110$	$92$	$89$	$80$	$63$	$59$	$54$

Find the value of $r$ for this data.(Answer up to two decimal values)

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 10

The value, y thousand Yen, of a used car changes as the age of the car $(x$ years $)$ increases. This able shows the age and value of Chan's car over $10$ years.

$x$	$1$	$2$	$3$	$4$	$5$	$8$	$9$	$10$
$y$	$115$	$110$	$92$	$89$	$80$	$63$	$59$	$54$

The relationship between $x$ and $y$ can be modelled by the regression equation $y = a x + b$ .

Write down the values of $a$ and $b$ .

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 7 - Modelling Relationships between Two Data Sets: Statistics for Bivariate Data>Exercise 7D>Q 10

The value, $y$ thousand Yen, of a used car changes as the age of the car $(x$ years $)$ increases. This able shows the age and value of Chan's car over $10$ years.

$x$	$1$	$2$	$3$	$4$	$5$	$8$	$9$	$10$
$y$	$115$	$110$	$92$	$89$	$80$	$63$	$59$	$54$

Use the regression equation to estimate the value of Chan's car after six years. Give your answer to the nearest $¥ 1000$

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships between Two Data Sets: Statistics for Bivariate Data, Exercise 18: Exercise 7D with Hints & Solutions

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