6. The data are given by the table:
x= 0.50 1.0 1.5 2.0 2.5
y= 0.29 0.35 0.51 0.73 0.81
Find the best linear fit ? = ? + ?? for these data.
1. Problem 1. Given a data set (X, Y), use the least squares techniques to find the best ftting curve y-/() within the exponential family v ab) where a,b ER. The data set is given by, where, χ-io, 0.2, 0.4, 0.6, 08, 09, 1, 12, 14, 1.6] y 2, 2.5, 3.1, 3.9, 4.8, 5.4, 6, 7.5, 9.3, 11.6] In particular: a) Going from the original data (x,Y) set to the transformed data set (X, Z) with z(Y)-In (Y), verify that...
Match the graphs with their parametric equations. II y 2.0 kor 1.51 0.5 1.01 -1.0 -0.5 0.5 1.0 0.5 -0.51 -1.0 -0.5 0.5 1.0 ho IV 8 III у 0.21 6 0.1 х 40.2 -0.1 0.1 0.2 -0.1 -0.2 VI v у 11.06 у 0 0.B os 0.6 0.4 |-ho -0.5 0.5 102 -0.5 0.5 1.0 1.5 2.0 2.5 3.0 (a) x = 44 - t + 1, y = 42 Х IV = 42 – 2t, y = VE...
Question 11 5 pts Electronegativities 2.1 Li 1.0 2.5 4.0 Be 1.5 Mg 1.2 Na 2.0 Al 1.5 Si СІ Ν Ι Ο 3.0 3.5 PS 2.1 2.5 As 2.0 2.4 0.9 1.8 3.0 са Ga Ge Se Br 0.8 1.0 1.6 1.8 2.8 Given the electronegativites above, which element would form a polar covalent bond with sulfur that results in the sulfur being slightly negative? oc Si none of these
1. (25 points) The figure below shows the contour plot of f(x,y)-3 -1 - 2y+y. (Credit for the figure is due to UMich instructors.) 6.00U 6.000 1.5 1.0 0.5 0.0 0.5 1.0 1.5 6.000 2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 (a) Find all critical points of f. There should be six. Mark them on the contour plot. (Think, but don't write, about how to guess the critical points from the contour plot.) (b) Find f-,) v(,),and fp()-fy(, y) (c) Try to...
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5 2 1.5 1/4 2.5 4 1/4 3.0 1/8 Determine the following: In your intermediate calculations, round all fractions to three decimal places. Round your answers to three decimal places (e.g 98.765) (a) Conditional probability distribution of Y qiven that X = 1,5. у Fуus 0) 1 2 3 5 (b) Conditional probability distribution of X given that Y 2. 1.0 1.5 2.5 (c) E(YIX...
Data for a force sensor is given in the table below (Force is the input, x, Voltage is the output, y.). a. Find the slope and y-intercept of the least-squares best-fit line through the data. b. Estimate the standard error of the fit. C. Find the 95% confidence interval of the best-fit line. Force (N) Vout (V) 62.0 1.05 63.0 1.41 64.0 1.93 65.0 2.46 66.0 3.03 67.0 3.59 68.0 3.88 69.0 4.48 70.0 5.04 71.0 5.51
Given the following reaction and the table of rate data, determine orders and then the rate constant (k) for this reaction: 2NO(g)Cl2g)-»2NOCIg) Rate Data [C (M) [NO] (M) Rate (M/h) 0.70 1.00 1.14 0.50 0.35 0.29 0.70 0.50 0.56
4. The following table presents data on x- the number of oil changes per year and y the cost of repairs for a sample of 10 cars from a given region: Number of oil changes per year (x ost of Repairs S( e) Put the points into your calculator list. (d) Use your calculator to perform linear regression. a. What is the correlation? Is it positive, negative, or neither? Is it strong or weak? b. Find the equation of the...
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit the given data with a quadratic spline. (b) Find an approximate value of f(3) using the first-degree spline. 6. (20) Consider the table X 0 | 2 | y = f(x) | 7 11 | 3 5 (a) Fit the given data with a quadratic spline. YE (b) Find an approximate value of f (3) using the first-degree spline.
Use nonlinear regression to estimate α4 and β4 based on the following data. y= α4Xe^(β4X) x 0.1 0.2 0.4 0.6 0.9 1.3 1.5 1.7 1.8 y 0.75 1.25 1.45 1.25 0.85 0.55 0.35 0.28 0.14 If you were to use linear regression to find α4 and β4, how would you make the model linear? Plot the data points, the fit to the data using linear and nonlinear regression. What method produces the better estimate