Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 5.4, Problem 11P
To determine
To find:
The equation of the least squares parabola associated with the given set of data points
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The director of marketing at Reeves Wholesale Products is studying monthly sales. Three independent variables were selected as
estimators of sales: regional population, per capita income, and regional unemployment rate. The regression equation was computed
to be (in dollars):
ŷ = 64,100 + 0.394x, + 9.6x2 – 11,600x3
Note: Here, the variables x1, X2 and x3 refer to regional population, per capita income, and regional unemployment rate respectively.
a. Choose the right option for the full name of the equation:
O Multiple regression equation
O Single linear equation
O single two linear equation
b. Interpret the number 64,100.
X1 intercept
O x2 intercept
O y-intercept
c. What are the estimated monthly sales for a particular region with a population of 796,000, per capita income of $6,940, and an
unemployment rate of 6.0%?
Estimated monthly sales
Please find the general solution of the underlined problem.
Create a quadratic model for the data shown in the table
1
-1
X
-1
-1
y
Oy=0.85r² +0.11 - 1.78
y = 0.98x² -0.74 - 0.82
y = 0.112²1.78x +.9998
X
y = -0.85x² -0.11x +1.78
2
2
5
20
Chapter 5 Solutions
Differential Equations and Linear Algebra (4th Edition)
Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - True-False Review For Questions a-g, decide if the...Ch. 5.1 - Prob. 6TFRCh. 5.1 - Prob. 7TFRCh. 5.1 - Use the standard inner product in 5 to determine...Ch. 5.1 - Prob. 2PCh. 5.1 - If f(x)=sinx and g(x)=x on [0,], use the function...Ch. 5.1 - If f(x)=sinx and g(x)=2cosx+4 on [0,/2], use the...
Ch. 5.1 - Let m and n be positive real numbers. If f(x)=xm...Ch. 5.1 - If v=(2+i,32i,4+i) and w=(1+i,13i,3i), use the...Ch. 5.1 - If v=(63i,4,2+5i,3i) and w=(i,2i,3i,4i), use the...Ch. 5.1 - Let A=[a11a12a21a22] and B=[b11b12b21b22] be...Ch. 5.1 - Referring to A and B in Problem 8, show that the...Ch. 5.1 - Referring to A and B in Problem 8, show that the...Ch. 5.1 - Referring to A and B in Problem 8, show that the...Ch. 5.1 - For Problems 1213, use the inner product (5.1.13)...Ch. 5.1 - For Problems 1213, use the inner product (5.1.13)...Ch. 5.1 - Let p1(x)=a+bx and p2(x)=c+dx be vectors in P1(R)....Ch. 5.1 - Let V=C0[0,1] and for f and g in V, consider the...Ch. 5.1 - Let V=C0[0,1] and for f and g in V, consider the...Ch. 5.1 - Let V=C0[1,0] and for f and g in V, consider the...Ch. 5.1 - Consider the vector space R2. Define the mapping ,...Ch. 5.1 - For Problems 1921, determine the inner product of...Ch. 5.1 - For Problems 1921, determine the inner product of...Ch. 5.1 - For Problems 1921, determine the inner product of...Ch. 5.1 - Prob. 22PCh. 5.1 - Prob. 23PCh. 5.1 - Prob. 24PCh. 5.1 - Prob. 25PCh. 5.1 - Prob. 26PCh. 5.1 - Prob. 27PCh. 5.1 - Prob. 28PCh. 5.1 - Prob. 29PCh. 5.1 - Prob. 30PCh. 5.1 - Prob. 31PCh. 5.1 - Prob. 32PCh. 5.1 - Prob. 33PCh. 5.1 - Prob. 34PCh. 5.1 - Prob. 35PCh. 5.1 - Prob. 36PCh. 5.1 - Prob. 37PCh. 5.2 - Problems For Problems 1-5, determine whether the...Ch. 5.2 - Problems For Problems 1-5, determine whether the...Ch. 5.2 - Problems For Problems 1-5, determine whether the...Ch. 5.2 - Problems For Problems 1-5, determine whether the...Ch. 5.2 - Problems For Problems 1-5, determine whether the...Ch. 5.2 - Problems Let v=(7,2). Determine all non zero...Ch. 5.2 - Problems Let v=(3,6,1). Determine all vectors w in...Ch. 5.2 - Problems Let v1=(1,2,3), v2=(1,1,1). Determine all...Ch. 5.2 - Let v1=(4,0,0,1), v2=(1,2,3,4). Determine all...Ch. 5.2 - Problems For Problems 10-12, show that the given...Ch. 5.2 - Problems For Problems 10-12, show that the given...Ch. 5.2 - Prob. 12PCh. 5.2 - Prob. 13PCh. 5.2 - Prob. 14PCh. 5.2 - Prob. 15PCh. 5.2 - Prob. 16PCh. 5.2 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - Prob. 19PCh. 5.2 - Prob. 20PCh. 5.2 - Prob. 21PCh. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.2 - Prob. 24PCh. 5.2 - Problems For Problems 22-27, find the distance...Ch. 5.2 - Prob. 26PCh. 5.2 - For Problems 2227, find the distance from the...Ch. 5.2 - Problems For Problems 29-32, use result of problem...Ch. 5.2 - Problems For Problems 29-32, use result of problem...Ch. 5.2 - Prob. 31PCh. 5.2 - Problems For Problems 29-32, use result of problem...Ch. 5.2 - Problems Let {u1,u2,u3} be linearly independent...Ch. 5.2 - Prob. 34PCh. 5.3 - Problems For Problems 110, use the Gram-Schmidt...Ch. 5.3 - Problems For Problems 110, use the Gram-Schmidt...Ch. 5.3 - Problems For Problems 110, use the Gram-Schmidt...Ch. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 8PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 15PCh. 5.3 - Prob. 16PCh. 5.3 - For problems 17-20, determine an orthogonal basis...Ch. 5.3 - For problems 17-20, determine an orthogonal basis...Ch. 5.3 - Prob. 25PCh. 5.4 - True-False Review For Questions a-f, decide if the...Ch. 5.4 - True-False Review For Questions a-f, decide if the...Ch. 5.4 - Prob. 3TFRCh. 5.4 - Prob. 4TFRCh. 5.4 - Prob. 5TFRCh. 5.4 - Prob. 6TFRCh. 5.4 - Prob. 1PCh. 5.4 - Prob. 2PCh. 5.4 - For problems 1-7, find the equation of the least...Ch. 5.4 - Prob. 4PCh. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.4 - Prob. 7PCh. 5.4 - Prob. 8PCh. 5.4 - For Problems 8-9, find the equation of the least...Ch. 5.4 - Prob. 10PCh. 5.4 - Prob. 11PCh. 5.4 - Prob. 12PCh. 5.4 - Prob. 13PCh. 5.4 - Prob. 14PCh. 5.4 - If the size P(t) of a culture of bacteria measured...Ch. 5.4 - Prob. 16PCh. 5.4 - Prob. 17PCh. 5.4 - Prob. 18PCh. 5.5 - For Problem 1-2, determine the angle between the...Ch. 5.5 - Prob. 2APCh. 5.5 - Prob. 3APCh. 5.5 - Prob. 4APCh. 5.5 - Prob. 6APCh. 5.5 - For Problems 69, find an orthogonal basis for the...Ch. 5.5 - For Problems 69, find an orthogonal basis for the...Ch. 5.5 - For Problems 69, find an orthogonal basis for the...Ch. 5.5 - Prob. 11APCh. 5.5 - Prob. 12APCh. 5.5 - Prob. 13APCh. 5.5 - Prob. 14APCh. 5.5 - Prob. 15APCh. 5.5 - Prob. 16APCh. 5.5 - Prob. 17APCh. 5.5 - Prob. 18AP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Please provide all of the work so that i could properly understand the problem. Thank you !arrow_forwardPlease give me a detailed solution on both problemsarrow_forwardIf the equation of the regression line for hours a spent cycling in the summer and hours y spent working in the summer is ŷ = - 0.7x + 42 , then as the number of cycling hours increases, the number of work hours tends to decrease. true O falsearrow_forward
- Answer the following questions. 1. A tea company wants to make 7 pounds of a blend of tea costing $4 per pound by combining a tea that costs $3 per pound and tea that costs $6 per pound. How many pounds of each grade of tea should be used? Which of the following equations represents a possible model for this problem? A. 6 x + 7(7) = 3 (4 - x)^() B. 6 x + 4 x = 7 (7 - x)^() C. 3 x + 6(4 - x) = 7 x D. 3 x + 6(7 - x) = 4(7) E. 3 x + 6 x = 7 2. How many ounces of a brand of coffee that costs $8 an ounce must be mixed with 14 ounces of another brand that costs $10 an ounce to make a mixture that costs $9.50 an ounce? Which of the following equations represents a possible model for this problem? A. 8 x + 10(14 - x)^() = 9.5(14)^() B. 8 x + 10 x = 9.5(14) C. 8 x + 10(14) = 9.5(x + 14) 3. How many gallons of a solution that is 18% acidic must be mixed with 7 gallons of a solution that is 25% acidic to make a solution that is 21% acidic? Which of the following equations…arrow_forwardYou are the Filipino analyst hired by the multinational company to study the sales data of its more than 75 stores worldwide. You used regression analysis between $ sales (y) and $ advertising (x1) and $ salary of sales representatives (x2) across all the branches. You obtained the following regression function : y = 6000 + 8.5x1-1.6x2 If the advertising budgets of one of the branches of the corporation is $12,000 and the salary of sales representatives is $2,500, then what will be the predicted sales? A. $112,000 B. $6000 C. $104,000 D. $102,000arrow_forwardYou are the Filipino analyst hired by the multinational company to study the sales data of its more than 75 stores worldwide. You used regression analysis between $ sales (y) and $ advertising (x1) and $ salary of sales representatives (x2) across all the branches. You obtained the following regression function : y = 6000 + 8.5x1-1.6x2 If the advertising budgets of one of the branches of the corporation is $12,000 and the salary of sales representatives is $2,500, then what will be the predicted sales? If the advertising budgets of one of the branches of the corporation is now $45,000 (which is 10% more than before) and the salary of sales representatives is now $8,500 (which is 20% less than before), then the predicted sales before in that branch is?arrow_forward
- Use the following linear regression equation to answer the questions. x3 = -18.8 + 4.0x, + 9.3x4 - 1.3x7 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. (c) If X1 X3? = 10, X4 = -4, and x7 = 4, what is the predicted value for (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. Suppose x1 and X7 were held at fixed but arbitrary values. If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be? If x4 increased by 3 units, what would be the corresponding expected change in x3? If x4 decreased by 2 units, what would we expect for the corresponding change in x3? (e) Suppose that n = 11 data points were used to construct the given regression equation and that the standard error for the is 0.857. Construct a 90% confidence coefficient of X4 interval for the coefficient of x4.…arrow_forwardIf the equation for the regression line is y1=-8x+3 , then the slope of this line is a.3 b.6 c.-5 d.-8arrow_forwardAt the start of the millennium, State A was the third most populous state in the country, followed by State B. Since that time, State B has experienced faster growth. The population y (in millions) of the given state in year x is approximated by the following equations, where x = 0 corresponds to the year 2000. In what year did State B overtake State A in population? To the nearest million, what was the population of these states at that time? State B: 7y - 2x = 101 State A: 12y – x = 212 The year State B overtook State A was (Type a whole number.) A The population at that time was million. (Type a whole number.)arrow_forward
- At the start of the millennium, State A was the third most populous state in the country, followed by State B. Since that time, State B has experienced faster growth. The population y (in millons) of the given state in year x is approximated by the following equations, where x = 0 corresponds to the year 2000, In what year did State B overtake State A in population? To the nearest million, what was the population of these states at that time? State B: 8y - 2x = 160 State A 13y - x = 296 The year State B overtook State A was (Type a whole number.) Clear all Check answ Help me solve this View an example Get more help - 7:3 3/2/2 delete horne brt sc Tum & 8. 5 Rarrow_forwardIf the equation of the regression line for hours, xx, spent cycling in the summer and hours, yy, spent working in the summer is y=38−0.77xy=38-0.77x . Then as the number of cycling hours increases, the number of work hours tends to decrease. a. What is the best prediction for the number of hours someone works in the summer who does not cycle? b. What is the best prediction for the number of hours someone works in the summer who cycles 8 hours per week? c. What is the best prediction for the number of hours someone works in the summer who cycles 15 hours per week?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY