2. Zerox SERVICE TIMEThe Service Time Data and the Least Squares LineNumber of CopiersServiced, xNumber of MinutesServiceCallCopiers Line Fit PlotRequired, y2001092581505138471891001378250Minutes = 11.4641 + 24.6022 Copiers4103134268Copiers1011211154Zerox-Copiers, Ic., sells and services the Accu-500 copying machine. As part of its standard servicecontract, the company agrees to perform routine service on this copier. To obtain information about thetime it takes to perform routine service, Zerox Copiers has collected data for 11 service calls. The dataand Excel output from fitting a least squares regression line to the data are given on the Table above.b. Use the least squares line to compute a point estimate of the mean time to service four copiersand a point prediction of the time to service four copiers on a single call.Minutes

Consider the data that contains the information of the time to service the copiers. The least-square…

Answered: Zerox-Copiers, Inc., sells and services…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 34EQ

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Various doses of a poisonous substance were givento groups of 25 mice and the following results wereobserved: Dose (mg) Number of deathsx y4 16 38 610 812 1414 1616 20 (a) Find the equation of the least squares line fit tothese data.(b) Estimate the number of deaths in a group of 25 micethat receive a 7-milligram dose of this poison.
Suppose 5 out of 25 data points in a weighted least-squares problem have a y-measurement that is less reliable than the others, and they are to be weighted half as much as the other 20 points. One method is to weight the 20 points by a factor of 1 and the other 5 by a factor of 1/2. A second method is to weight the 20 points by a factor of 2 and the other 5 by a factor of 1. Do the two methods produce different results? Explain.
The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.
Percentages of public school students in fourth and eighth grades who were above the proficiency level were given for 8 western states 4th Grade Proficiency 8th Grade Proficiency Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 Construct a scatterplot and comment on any interesting characteristics Find the least squares equation. If Nevada had a 4th grade proficiency of 14%, what would you expect the 8th grade proficiency to be?
In a study of the causes of bearing wear, a machine was run 24 times, with various loads (denoted x1), oil viscosities (x2), and ambient temperatures (x3). The wear, denoted y, was modeled as y = β0 + β1x1 + β2x2 + β3x3 + ε. When this model was fit to the data, the sum of squares for error was SSE = 9.37. Then the reduced model y = β0 + β1x1 + β2x2 + β3x3 was fit, and the sum of squares for error was SSE = 27.49. Is it reasonable to use the reduced model, rather than the model containing all the interactions, to predict wear? Explain.
Find the best-fitting least-squares linear and quadratic approximations to the data set{(1,2),(3,4),(5,7),(7,9),(9,12)}.
When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?
Let x be the number of different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs. x 10 12 14 16 18 20 y 1.7 1.6 1.6 1.4 1.0 0.7 (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x =? y =? = ?+ ?x (f) Suppose a pharmaceutical company has 12 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.) ? patents per program
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
The accompanying table is used to make the preliminary computations forfinding the least squares line for the given pairs of x and y values.
When using the least-squares line for prediction, are results more reliable for extrapolation or interpolation? a. Interpolation, because we are predicting from data outside the range used to create the least-squares line. b. Extrapolation, because we are predicting from data outside the range used to create the least-squares line. c. Extrapolation, because we are predicting from data in the range used to create the least-squares line. d. Interpolation, because we are predicting from data in the range used to create the least-squares line.
Find the curve of best-fit y = axb to the following data by using the method of least square.

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