For the line of best fit in the least-squaresmethod,O althe sum of the squares of theresiduals has the greatest possiblevaluethe sum of the squares of theresiduals has the least possiblevalueO c)the sum of the residuals is equal tooneO d) both b) and c)O b)

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Answered: For the line of best fit in the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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When the predicted overnight temperature is between 15°F and 32°F, roads in northern cities are salted to keep water from freezing on the roadways. Suppose that a small city was trying to determine the average amount of salt y (in tons) needed per night at temperature x. They found the following least squares prediction equation: y = 20,000 - 2,500x Interpet the slope. a) 2,500 tons is the decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the increase in the amount of salt needed for a 1 degree increase in temperature. c) 20,000 is the increase in the amount of salt needed for a 1 degree increase in temperature. d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.
Consider the data points (2,7) and (3,4). (a) Find the straight line that provides the best least-squares fit to these data. (b) Use the slope and point-slope form to find the equation of the straight line passing through the two points. (c) Explain why it could have been predicted that the straight line in (b) would be the same as the straight line (a)
If we have a series of experimental data of 2 variables A and B, with both sets of data related by the expression: A = B + C, where C is a constant. If by plotting A against B we obtain a straight line with a theoretical slope m and ordinate at the origin C, and by applying the least squares method we could determine C. But, as the previous expression can be transformed into B = A - C, we could also plot B against A and obtain C from the ordinate at the origin with a changed sign. Should the same value of C be obtained by both methods?(A). Yes, because the step from "A = B + C" to "B = A - C" is an exact algebraic transformation(B). Only in the case where A and B are equal(C). Only in the case where the errors of A and B are high, since the least squares method compensates for them(D). The most normal thing is that the same value is not obtained
State the least squares criterion, Q.
Explain the Extended Least Squares Assumptions?
For a linear regression problem, the least squares line is y = 2x+2. Determine the predicted value of y when x = 5 19 not enough information 12 oooo
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ŷ = 25x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 5. When amount of schooling increases by one year, the number of pregnancies tends to increase by 2. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 2.
In the least-squares line = 5 – 9x, what is the value of the slope?When x changes by 1 unit, by how much does y change? When x increases by 1 unit, y decreases by 9 units. When x decreases by 1 unit, y decreases by 9 units. When x increases by 1 unit, y decreases by −9 units. When x increases by 1 unit, y increases by 9 units.
A farmer has 800 meters of fencing and needs to fence off a rectangular paddock that borders a straight river. He doesn't need to fence along the river. Set up and solve an appropriate optimisation problem to find the dimensions of the paddock that has the largest area.
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation,…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…
Explain the concept and use of the method of Least Squares

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For the line of best fit in the least-squares method,