5. Section 13.1A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand,denoted BOD, and various other chemical constituents resulted in the accompanying data on x = BOD massloading and y = BODMR mass removal:3 8 101113 16 27 3047 8 810 11 16 261. Compute the quantities n, Σ x, y, Σx², Cy², Σxy2. Compute the least squares line.3. Compute SSE and estimate σ with this computation.4. Computer² to determine what proportion of observed variation can be explained by the approximatelinear relationship between x and y.6. Section 13.2Given the data of question 5, conduct a hypothesis test of the null hypothesis Hoẞ = 0 at a significancelevel of α = 0.05.

#5 Section 13.1 1. To compute the quantities n, ∑x, ∑y, ∑x², ∑y², and ∑xy, we first need to organize…

Answered: 5. Section 13.1 A study to assess the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
8. Find the equation y = mx + c of the least-square line that best fits the given data points (-1,0), (0,3), (1,3), (2,5), and (3,9).
4. Determine the equation of the least-squares approximating line that is the best fit for the data points (2, 6), (0, 2), and (1, 1).
4. A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand (BOD) and various other chemical constituents resulted in the accompanying data on z = BOD mass loading (kg/ha/d) and y = BOD mass removal (kg/ha/d) ("Subsurface Flow Wetlands-A Performance Evaluation." Water Envir. Res., 1995: 244-247). x Y 11 8 13 16 27 10 11 16 142 35 38 44 103 30 90 75 31 30 26 21 n = 10; Σ | n = 450; Σα" = 37653; Σy = 318; Σ y = 17244; Σ =y = 25344 Answer the following questions: (a) Plot an appropriate graph for the data. (b) Obtain the best lincar prediction equation. (c) For every additional unit change in BOD mass loading, by how much does the BOD mass removal change, on average? (d) Give the value of the statistic that measures the linear association between the BOD mass loading and BOD mass removal. Comment. (e) What percent of variation in the BOD mass removal is explained by the variation by the BOD mass loading? (f) Predict the BOD mass removal,…
4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (in km/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers. From the data, we calculate i = 48.2, j = 107.8, (z:-2)² = 3669.6, (4- û)° = 752.7. The least squares regression line is calculated to be ŷ = 133.198 – 0.527x. It is also determined that 57.5% of the variation in the speed of a vehicle can be accounted for by its regression on the age of the driver. (a) What is the value of the correlation between the age of a driver and the speed of a vehicle? (b) Provide an interpretation of the slope of the least squares regression line. (c) Calculate a 95% confidence interval for the parameter 31 in the simple linear regression model. (d) We would like to conduct a hypothesis test at the 5% level of significance to determine whether a linear relationship exists between the age of a driver and the speed of a vehicle. Could the confidence interval in (c) have been used to conduct…
2. Let consider given points: (1,1), (3,2), (4,3), (5,6). (a) Find the best least square fit by a linear function (linear regression). Compute the sum of square errors. (b) Find a polynomial of degree 3 that interpolates the points. (c) Find the best least squares exponential fit y = piet. Compute the sum of square errors and compare with result from (a).
7. Information regarding a dependent variable y and an independent variable x is provided in the following table: Ex = 90 2y = 340 n = 4 SSR = 1704 S(y-y)(x-x) = -156 Σ(x − x)" = 234 Σ(y- y)² = 1974 a. What are the least squares estimates of b0, b1? b. What are the sum of squares due to error (SSE), and the total sum of squares (SST)? c. What is the coefficient of determination?
Find the equation y = Bo + B₁x of the least-squares line that best fits the given data points. Data points: (5, 1), (2, 2), (4, 3), (5, 1) Select one: O A. 37 1 y O B. 37 4 -31/2-1/2 x X O C. 47 X O D. 37 + 1x y= y = y = X
A regression analysis between demand (y in Kg) and supply (x in kg) resulted in the following least squares line: = 50 - 15 X.
A DIFFERENT WAY Activity No. 2 Directions: Count the unit cubes and find the volume of cach rectangular prism. One U-1 m 10 12 13 Across Down 3. 5. 2. V - V = V = V = m3 8. V = m3 V = m3 10. 10. V = m3 V = m3 m3 Page 21 of 108
EXER 5.1: Given the observations (1,1), (2,3), (4,5), find the least squares estimates for m and b for the best fit line y=mx+b.
2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231

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