An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3,6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residualsy – ŷ and plot the residuals against their corresponding value of x.An obvious megaphone pattern is apparent in the residuals y – ŷ. Calculatethe line of best fit between a and y – ŷ|. (y – ŷ = mx + b.The value of the residual for a given value of x predicted by this linearrelationship is an estimate of o(x), the standard deviation of the y variable(which increases with x). Compute0,1, 2, 3, 4, 5 and use themfor xo(x)?as weights in a matrix W to run a weighted regression on the original x, y data.6.

We will use the basic knowledge of curve fitting by the "least square approximations" method.

Answered: An ordinary least squares regression on…

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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An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second city
For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
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The table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 13 12 11 10 9 a. 15 b. 8 c. 7 d. 20
5. Write the equation of the least-squares regression line defining any variables used. Round coefficients to 4 decimal places .
Need only handwritten solution only (not typed one).
Find the least-squares regression line ŷ bo+ b₁z through the points For what value of is y = 0? H= (-2,0), (1, 6), (4, 14), (8, 19), (10, 27).
Find the least squares regression line for the points: (0,0), (1,1), (2,5).
An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y data on rainfall and runoff volume (n = runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to 15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21. = x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) Ŷ 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. OYes, precise information is available because the resulting interval is very wide. 34.46 Yes, precise information is available because the resulting interval is very…
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.
Find the least-squares regression line ŷ = bo + bịx through the points (-3, 1), (0, 6), (4, 15), (8, 19), (10, 23). For what value of x is ŷ = 0?

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An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3, 6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residuals y – ŷ and plot the residuals against their corresponding value of x.