(a) Explanation Formula used: “The least square line Y = m x + b that gives the best fit to the data points ( x 1 , y 1 ) , ( x 2 , y 2 ) , ... , ( x n , y n ) has slope m and y -intercept b given by m = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 and b = ∑ y − m ( ∑ x ) n .” Calculation: Let x = 0 represent the year 1990 and y represent the average number of pupils per teacher. The number of data points is n = 6 . Obtain the least square line for the given data, first find the required sums. The values x , y , x y , x 2 , y 2 and their column totals are calculated in the below table. x y x y x 2 y 2 0 17.2 0 0 295.84 4 17.3 69.2 16 299.29 8 16.4 131.2 64 268.96 12 15.9 190.8 144 252.81 16 15.6 249.6 256 243.36 20 15.3 306 400 234.09 ∑ x = 60 ∑ y = 97.7 ∑ x y = 946.8 ∑ x 2 = 880 ∑ y 2 = 1594 (b) To determine To predict: The pupil-teacher ratio in 2020. (c) To determine To calculate: The correlation coefficient and interpret.

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Question

Chapter 1.3, Problem 20E

(a)

To determine

To find: The equation for the least square line.

(b)

To determine

To predict: The pupil-teacher ratio in 2020.

(c)

To determine

To calculate: The correlation coefficient and interpret.

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Chapter 1.3, Problem 19E

Chapter 1.3, Problem 21E

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Chapter 1 Solutions

Calculus with Applications (11th Edition)

Ch. 1.1 - YOUR TURN 1 Find the slope of the line through (1,...Ch. 1.1 - YOUR TURN 2 Find the equation of the line with...Ch. 1.1 - YOUR TURN 3 Find the slope of the line whose...Ch. 1.1 - YOUR TURN 4 Find the equation of the line through...Ch. 1.1 - Prob. 5YT Ch. 1.1 - YOUR TURN 6 Find the equation of the line passing...Ch. 1.1 - W1. Evaluate . (Sec. R.1) Ch. 1.1 - Solve each equation for y. (Sec. R.4) W2. y − (−3)...Ch. 1.1 - Solve each equation for y. (Sec. R.4) W3. Ch. 1.1 - Prob. 4WE

Ch. 1.1 - Find the slope of each line. 1. Through (4, 5) and...Ch. 1.1 - Prob. 2E Ch. 1.1 - Find the slope of each line. 3. Through (8, 4) and...Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Find the slope of each line. 6. y = 3x − 2 Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Find the slope of each line. 13. A line parallel...Ch. 1.1 - Find the slope of each line. 14. A line...Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - 38. Use slopes to show that the square with...Ch. 1.1 - Prob. 39E Ch. 1.1 - For the lines in Exercises 39 and 40, which of the...Ch. 1.1 - Prob. 41E Ch. 1.1 - In Exercises 41 and 42, estimate the slope of the...Ch. 1.1 - 43. To show that two perpendicular lines, neither...Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Graph each equation. 46. y = 4x + 5 Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Graph each equation. 59. x + 4y = 0 Ch. 1.1 - Prob. 60E Ch. 1.1 - Prob. 61E Ch. 1.1 - 62. Cost The total cost for a bakery to produce...Ch. 1.1 - Prob. 63E Ch. 1.1 - Prob. 64E Ch. 1.1 - Prob. 65E Ch. 1.1 - Life Sciences 66. HIV Infection The time interval...Ch. 1.1 - Prob. 67E Ch. 1.1 - Prob. 68E Ch. 1.1 - Prob. 69E Ch. 1.1 - Prob. 70E Ch. 1.1 - 71. Immigration In 1950, there were 249,187...Ch. 1.1 - 72. Marriage The following table lists the U.S....Ch. 1.1 - Prob. 73E Ch. 1.1 - Prob. 74E Ch. 1.1 - Prob. 75E Ch. 1.2 - Prob. 1YT Ch. 1.2 - Prob. 2YT Ch. 1.2 - Prob. 3YT Ch. 1.2 - YOUR TURN 4 Repeat Example 5, using a marginal...Ch. 1.2 - Prob. 5YT Ch. 1.2 - Prob. 6YT Ch. 1.2 - Prob. 1WE Ch. 1.2 - Prob. 2WE Ch. 1.2 - Prob. 1E Ch. 1.2 - Prob. 2E Ch. 1.2 - Prob. 3E Ch. 1.2 - Prob. 4E Ch. 1.2 - Prob. 5E Ch. 1.2 - Prob. 6E Ch. 1.2 - Prob. 7E Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Prob. 10E Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - In Exercises 11–14, decide whether the statement...Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Assume that each situation can be expressed as a...Ch. 1.2 - Prob. 24E Ch. 1.2 - Prob. 25E Ch. 1.2 - Prob. 26E Ch. 1.2 - Prob. 27E Ch. 1.2 - Prob. 28E Ch. 1.2 - 29. Supply and Demand Let the supply and demand...Ch. 1.2 - Prob. 30E Ch. 1.2 - Prob. 31E Ch. 1.2 - Prob. 32E Ch. 1.2 - Prob. 33E Ch. 1.2 - 34. Break-Even Analysis To produce x units of a...Ch. 1.2 - Prob. 35E Ch. 1.2 - Prob. 36E Ch. 1.2 - Prob. 37E Ch. 1.2 - Prob. 38E Ch. 1.2 - Prob. 39E Ch. 1.2 - Prob. 40E Ch. 1.2 - Prob. 41E Ch. 1.2 - Prob. 42E Ch. 1.2 - 43. Break-Even Analysis Suppose that the fixed...Ch. 1.2 - Prob. 44E Ch. 1.2 - Life Sciences 45. Deer Ticks Deer ticks are of...Ch. 1.2 - Prob. 46E Ch. 1.2 - Prob. 47E Ch. 1.2 - Prob. 48E Ch. 1.2 - Prob. 49E Ch. 1.2 - Prob. 50E Ch. 1.3 - YOUR TURN 1 Calculate the least squares line for...Ch. 1.3 - Prob. 2YT Ch. 1.3 - Prob. 1E Ch. 1.3 - Prob. 2E Ch. 1.3 - Prob. 3E Ch. 1.3 - The following problem is reprinted from the...Ch. 1.3 - 5. Consider the following table of...Ch. 1.3 - 6. Consider the following table of...Ch. 1.3 - Prob. 7E Ch. 1.3 - Prob. 8E Ch. 1.3 - 9. The formulas for the least squares line were...Ch. 1.3 - 10. Consumer Durable Goods The total value of...Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - 14. Consumer Credit The total amount of consumer...Ch. 1.3 - 15. Mean Earnings The mean earnings (in dollars)...Ch. 1.3 - Prob. 16E Ch. 1.3 - Prob. 17E Ch. 1.3 - Prob. 18E Ch. 1.3 - Prob. 19E Ch. 1.3 - Prob. 20E Ch. 1.3 - Prob. 21E Ch. 1.3 - Prob. 22E Ch. 1.3 - Prob. 23E Ch. 1.3 - Prob. 24E Ch. 1.3 - Prob. 25E Ch. 1.3 - Prob. 26E Ch. 1.3 - Prob. 29E Ch. 1 - Prob. 1RE Ch. 1 - Determine whether each statement is true or false,...Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - 46. U.S. Exports to China U.S. exports to China...Ch. 1 - Prob. 47RE Ch. 1 - Prob. 48RE Ch. 1 - Prob. 49RE Ch. 1 - Prob. 50RE Ch. 1 - Prob. 51RE Ch. 1 - Prob. 52RE Ch. 1 - Prob. 53RE Ch. 1 - Prob. 54RE Ch. 1 - Prob. 55RE Ch. 1 - Prob. 56RE Ch. 1 - Prob. 57RE Ch. 1 - Prob. 58RE Ch. 1 - Prob. 59RE Ch. 1 - Life Sciences 60. World Health In general, people...Ch. 1 - Prob. 61RE Ch. 1 - Prob. 62RE Ch. 1 - Prob. 63RE Ch. 1 - Prob. 65RE

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