o determine a functional relationship between the attenuation ample of taconite, V. P. Singh [Si] fits a collection of data by usin The following collection of data is taken from a graph in that olynomial fitting these data. Thickness (cm) Attenuation coefficien 26.5 28.1 0.040 0.041
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- Find the curve of best-fit y = axb to the following data by using the method of least square.Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.It is known that the tensile strength of a plastic increases as a function of the time it is subjected to heat treatment. The table below shows the data of the plastic subjected to heat treatment. Determine these data by using the "lagrange interpolation" method by approximating the functions of the lagrange multipliers of L0 , L1 , L2 , L3 and L4 to a 4th order curve. Calculate the tensile strengths of 1.7321 and 2.2361 seconds for each lagrange factor in the function equations of the lagrange multipliers.
- 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 programThe population of Botswana (in millions) for the years 1970to 2020 is given in the table.Year 1970 1980 1990 2000 2010 2020Population, P 0.628 0.898 1.287 1.643 1.987 2.254(a) Make a scatter plot (population versus years) for the data. (b) Using the scatter plot determine the data trend and law of the curve ofbest fit for the data. (c) Use the least squares method find the curve of best fit for the data. (d) Hence estimate the population of Botswana in the year 2036Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (6, 6), (7, 7), (9, 10); y = x − 1
- When an object is thrown straight up into the air, Newton's Second Law of Motion states that its height s (t) at time tis given by s(t) = s0 + v0t + tgt2 where v0 is its initial velocity and g is the constant of acceleration due to gravity. Suppose we take the measurements shown in Table . (a) Find the least squares approximating quadratic for these data. (b)Estimate the height at which the object was released (in m), its initial velocity (in mis), and its acceleration due to gravity (in m/s2). (c) Approximately when will the object hit the groundCompute the sum of squares error (SSE) by hand for the given set of data and linear model: (6,6),(7,7),(8,9); Y = x - 1The following data show the number of hurricanes to directly strike a certain country each decade. A major hurricane is one with a strength rating of 3, 4 or 5. DecadeTotal Number of HurricanesNumber of Major Hurricanes1941 – 195021111951 – 19601881961 – 19701361971 – 19801241981 – 19901551991 – 20001452001 – 200493 Using only completed decades (1941 – 2000), calculate the least squares line for the number of major hurricanes expected based on the total number of hurricanes. (Round your answers to three decimal places.) ŷ = + x
- The following are the scores that 12 students obtainedon the midterm and final examinations in a course instatistics:Midterm examination Final examinationx y71 8349 6280 7673 7793 8985 7458 4882 7864 7632 5187 7380 89 (a) Find the equation of the least squares line that willenable us to predict a student’s final examination score inthis course on the basis of his or her score on the midtermexamination.(b) Predict the final examination score of a student whoreceived an 84 on the midterm examination.An issue of USA Today reported the average fees charged to use another bank's ATM for 2000-2005. Year ATM Fee 2000 $2.65 2001 $2.54 2002 $2.76 2003 $2.87 2004 $2.69 2005 $2.93 (a) Use these data to find a least squares line of ATM fees as a function of years since 2000. (Round your coefficients to three decimal places.)y = (b) Estimate the average ATM fee for 2019. (Round your answer to the nearest cent.)A researcher collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.