When a signal is produced from a sequence of measurements made on a process (a chemical reaction, a flow of heatthrough a tube, a moving robot arm, etc.), the signal usually contains random noise produced by measurement errors. Astandard method of preprocessing the data to reduce the noise is to smooth or filter the data. One simple filter is a movingaverage that replaces each yk by its average with the two adjacent values:yk+1 +Yk +Yk-1 = Zkfor k = 1, 2, ...= Z.kSuppose a signal yk, for k = 0, ..., 14, is9, 5, 7, 3, 2, 4, 6, 5, 7, 6, 8, 10, 9, 5, 7Use the filter to compute 7,1, ..Z,13. . Make a broken-line graph that superimposes the original signal andthe smoothed signal.

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Answered: When a signal is produced from a…

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 wants to develop a model to describe the relationship between the average daily temperature, x °C, and her household’s daily energy consumption, y kWh, in winter. A random sample of the average daily temperature and her household’s daily energy consumption are taken from 10 winter days and shown in the table. x -0.4 -0.2 0.3 0.8 1.1 1.4 1.8 2.1 2.5 2.6 y 28 30 26 25 26 27 26 24 22 21 You may use: Sy=255 Sxy=283.8 Syy= 64.5 Find a value for the product moment correlation coefficient r for this data Explain what the value of the product moment corelation tells you about the relationship between daily temperature and the household energy consumption.
The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). X1 = money spent on television advertising (in 1000's of dollars) X2 money spent on promotion (i.e., free samples) X3 = money spent on newspaper advertising (in 1000's of dollars) X4 average discounts offered to retail outlets (in %) Using data from the previous 18 months, the company decides to collect data on 6 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R´ for this model is 0.93, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places.
Ensure the RaceResults worksheet is active, then use the FREQUENCY function to calculate the frequency distribution of the race results in column D. Place your results in the range G4:G9. Enter a function in cell F22 to calculate the correlation between age (Columns C) and race time (Column D). Enter a function in cell G22 to calculate the covariance between age and race time. Enter a function in cell H22 to calculate the variance of the ages in the data set. Note this is a sample of data not a population. Enter a function in cell 122 to calculate the standard deviation of the ages in the data set.
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. Σx = 476, Σy = 87.1, Σx2 = 62,290, Σy2 = 2046.87, Σxy = 11121.3,and r ≈ 0.94367. x days 72 76 32 91 205y km/100 14.7 19.6 5.3 11.7 35.8 a) Use a 1% level of significance to test the claim ? > 0.(Use 2 decimal places.)t =critical t= b) Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2 decimal places.)________ km/100 c) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limit = _____…
c. Which of the following is the correct graph of the given data? -ОА. 10 1012 12 10 O C. 12- 81012 1012 Using the graph, explain the dramatic difference between the answers to parts (a) and (b). Choose the correct answer below. OA. The point (10,10) is not an outier, but it does have a strong effect on the least squares line and the correlation coefficient. OB. The point (10,10) does not have any effect on the least squares line and the correlation coefficient. OC. The point (10,10) is an outler that has a weak effect on the least squares line and the correlation coefficient. OD. The point (10,10) is an outlier that has a strong effect on the least squares line and the correlation coefficient.
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.
The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). X 1 = money spent on television advertising (in 1000's of dollars) X2 = money spent on promotion (i.e., free samples) X3 money spent on newspaper advertising (in 1000's of dollars) = average discounts offered to retail outlets (in %) Using data from the previous 16 months, the company decides to collect data on 2 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R for this model is 0.81, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places.
The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). x = money spent on television advertising (in 1000's of dollars) X2 = money spent on promotion (i.e., free samples) x3 = money spent on newspaper advertising (in 1000's of dollars) X = average discounts offered to retail outlets (in %) Using data from the previous 26 months, the company decides to collect data on 3 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R´ for this model is 0.5, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places. Source of variation Degrees of freedom Sums of Mean F statistic squares squares Regression Error Total 4+
A movie studio wishes to determine the relationship between the revenue from the streaming rental of comedies and the revenue generated from the theatrical release of such comedies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming rentals (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Also given is the product of the theater revenue and the rental revenue for each of the fifteen movies. (These products, written in the column labelled "xy", may aid in calculations.) Theater Rental revenue, y revenue, x xy (in millions of (in millions of dollars) dollars) 61.7 9.7 598.49 15.1 1.7 25.67 45.3 6.3 285.39 28.1 12.1 340.01 49.1 16.1 790.51 xx 12.9 10.2 131.58 28.1 2.4 67.44 66.0 9.7 640.2 20.6 5.8 119.48 7.5 2.8 21 25.8 6.9 178.02 Theater revenue 36.2 12.8…

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