Using the method of Least Squares, determine to 4-decimal place thenecessary values of the coefficient (A, B and C) in the equation y A-from the given data points:Bo-Cz²X2.078.6014.4215.80y4

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Answered: Using the method of Least Squares,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A scientist collected data on the mating call frequency of frogs and temperature. They found the least squares line to be: y = 3 + 5x where x is the temperature (in Celsius) and y is mating call frequency. The slope of the regression line can be interpreted in the following way: OWhen temperature decreases by one degree, the mating call frequency increases by 5. When temperature increases by one degree, the mating call frequency increases by 3. O When temperature increases by one degree, the mating call frequency increases by 5. O When temperature decreases by one degree, the mating call frequency increases by 3. OWhen temperature increases by one degree, the mating call frequency decreases by 5. Submit Question
The symbol for the intercept of a least squares line is O A. b, О В. г OC. Sy O D. y O E. bo
x 5.50 6.50 7.50 7.75 8.75 y 15 32 55 39 72 a) Find a for the equation of the least-squares line y = ax+b: choose one: –75.923 42.698 –42.068 –42.698 75.923
Consider the following data: Fit a line, y = x1 + x2t, to the data using the least squares approach.
The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Please answer the all 3 subparts Height (in feet) Stories 1050 55 428 27 362 26 529 40 790 60 401 22 380 38 1454 110 1127 100 700 46 Part (c) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) Part (d) Find the correlation coefficient r. (Round your answer to four decimal places.)r = Part (e) Find the estimated height for 34 stories. (Use your equation from part (c). Round your answer to one decimal place.) ftFind the estimated height for 92 stories. (Use your equation from part (c). Round your answer to one decimal place.)
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.
The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Stories (x) Height (y) 56 1050 29 428 26 362 40 529 60 790 22 401 38 380 110 1454 100 1127 46 700 Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.)ŷ = + x
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…
I need the right answer to d, e, and f ASAP, please.
The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Stories (x) Height (y) 56 1050 29 428 26 362 40 529 60 790 22 401 38 380 110 1454 100 1127 46 700 Calculate the least squares line. Put the equation in the form of: ý = a + bx. (Round your answers to three decimal places.) 86.7405 12.195

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Using the method of Least Squares, determine to 4-decimal place the necessary values of the coefficient (A, B and C) in the equation A+ B₂ - Cz² from the given data points: X 2.07 8.60 14.42 15.80 2 3 y 4