HW8_1Apply least squares fitting to derive the normal equations and solve for the coefficients by hand (using Cramer'srule) for the model y = a,x + azx?. Use the data below to evaluate the values of the coefficients.v, (m/s) 1020304050607080F, (N)257038055061012208301450

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Answered: HW8_1 Apply least squares fitting to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.6: Quadratic Functions

Problem 38E

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Further Verification of Newtons Second LawThis exercise represents a hypothetical implementation of the experiment suggested in the solution of part 6 of Example 3.7. A mass of 15 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newton. Acceleration Force 8 120 11 165 14 210 17 255 20 300 a. Construct a table of differences and explain how it shows that these data are linear. b. Find a linear model for the data. c. Explain in practical terms what the slope of this linear model is. d. Express, using functional notation, the force resulting from an acceleration of 15 meters per second per second, and then calculate that value. e. Explain how this experiment provides further evidence for Newtons second law of motion.
Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
Find a least-squares solution of Ax=b by (a) constructing the normal equations for x(see picture) and (b) solving for x(see picture).
Water Consumption The Old Farmer's Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 25 people and found that they used on average 120.7 gallons per day and s= 5.3. At a = 0.01, is there enough evidence to say that the Old Farmer's Almanac figure might no longer be correct? Use the P-value method. Assume the population is normally distributed. Use a TI-83 Plus/TI-84 Plus calculator. find the p value
Water Consumption The Old Farmer's Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 17people and found that they used on average 118.4 gallons per day and s = 5.3. At α = 0.05, is there enough evidence to say that the Old Farmer's Almanac figure might no longer be correct? Use the P-value method. Assume the population is normally distributed. Use a TI-83 Plus/TI-84 Plus calculator. (a) State the hypotheses and identify the claim. (b) Find the P-value. Round the answer to at least four decimal places. (c) Make the decision. (d) Summarize the results.
Advertising share x and market share y fir a particular brand of cigarettes were sampled at ten randomly selected year. Summary information is: n = 10, Ex = .688, Ex2 = .050072, Ey =.835, Ey2 = 0.079491, Exy = .060861 a) Compute the least squares regression line b) Find the coefficient of determination r2 and explain what it means in the context of this problem. c) Compute a 90% prediction interval for market share when advertising share is .07(7%)
Q.2: The population of the germs grown in a specific lab environment has been measured to be 600, 700, and 1000 at times t 0, 1, and 2 hours. Find the curve which gives the best least squares fit to the given population points. Find the coefficients C and D of the best curve. Also proceed to find the error vector that would demonstrate the measurement error / tolerance in population sizem.
Find a least-squares solution of Ax=b by (a) constructing the normal equations for x(see pic) and (b) solving for x(see pic). Please take ur time to solve as last guy was wrong!!
Riboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data and the calculated straight line. (c) An unknown sample gave an observed fluorescence intensity of 15.4. Calculate the concentration of Riboflavin (Vitamin B2) in the unknown sample (μg/mL). (d) Calculate the coefficient of determination (R2).
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Consider the one-variable regression model Yi = β0 + β1Xi + ui, and suppose it satisfies the least squares assumptions in Key Concept 4.3. Suppose Yi is measured with error, so the data are ?"i = Yi + wi, where wi is the measurement error, which is i.i.d. and independent of Yi. Consider the population regression ?"i = β0 + β1Xi + vi, where vi is the regression error, using the mismeasured dependent variable ?"i.a) Showthatvi =ui +wi.b) Show that the regression ?"i = β0 + β1Xi + vi satisfies the least squares assumptions in KeyConcept 4.3. (Assume that wi is independent of Yj and Xj for all values of i and j and has afinite fourth moment.)c) Are the OLS estimators consistent? part b in another question
fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data aRiboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5).…

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HW8_1 Apply least squares fitting to derive the normal equations and solve for the coefficients by hand (using Cramer rule) for the model y = a,x + azx?. Use the data below to evaluate the values of the coefficients. v, (m/s) 10 20 30 40 50 60 70 80 F, (N) 25 70 380 550 610 1220 830 1450