Find the least-squares solution of Az = b for A = 'o 1 1 17 and b = = 112
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- 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.Each of 25 teenage girls with one brother was asked to provide her own height (y), in inches, and the height (x), in inches, of her brother. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of the (x,y) pairs were the same. The equation of the least-squares regression line is ŷ = 35.1 + 0.427x.*Girls are on the y-axis and brothers are on the x-axis* a.) Draw the least-squares regression line on the scatterplot above. b.) One brother’s height was x = 67 inches and his sister’s height was y = 61 inches. Circle the point on the scatterplot above that represents this pair and draw the segment on the scatterplot that corresponds to the residual for it. Give a numerical for the residual. c.) Suppose the point x = 84 , y = 71 is added to the data set. Would the slope of the least squares regression line increase, decrease, or remain about the same?Explain. Would the correlation increase, decrease, or remain about the same? Explain.Suppose the least squares regression line for predicting weight (in pounds) from height (in inches) is given by Weight= -110+3.5*(height) Which of the following statements is correct? l. A person who is 61 inches tall will weigh 103.5 pounds ll. For each additional inch of height, weight will decrease on average by 3.5 pounds. lll. There is a negative linear relationship between height and weight. a) l and lll only b) l and ll only c) ll only d) l only e) ll and lll only
- A lab received a new instrument to measure pH. To compare the new instrument to the old lab instrument, 11 samples were measured with both pieces of equipment. Using the data (below), find the least squares equation (x = "pH old" and Y = "pH new") and then predict the value on the new instrument if the old instrument gave a pH of 6.30. Enter your answer using 3 significant digits. pH Old pH New 6.35 6.16 6.01 5.95 6.15 6.05 6 6.01 6.11 6.06 5.93 5.83 5.84 5.81 5.63 5.71 5.63 5.74 6.11 6.1 6.07 6.01When a least squares line is fit to the 8 observations in the fuel consumption data, we obtain SSE = 3.264. Calculate s? and s. (Round your answers to 3 decimal places.)In a study, nine tires of a particular brand were driven on a track under identical conditions. Each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. Tread depth is measured in "mils." Here, 1 mil is 0.001 inch. The equation of the least-squares regression line is: y-hat 360.64 - 11.39x Also, r = 0.9762. For every 1,000 miles driven, the decrease in tread depth (in mils) can be estimated as: 246.74 mils. 11.39 mils. 275.6 mils. O 360.64 mils.
- An engineer found that by including small amounts of a compound in rechargeable batteries for portable computers, she could extend their lifetimes. She experimented with different amounts of the additive and the data are Amount of additive Life (hours) 1 4 2. 3 3 4 a) Obtain the least squares fit of a straight line to the amount of additive. b) Test whether or not the slope B-0. Take a = 0.10 as your level of significance.Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 XE) Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years. F) why does your answer for part (e) differ so much from the average gestation period of a human (280 days)?
- Assume: qi= β0 + β1pi + ui Please derive the estimated values (b0 and b1) based on the equation using OLS (ordinary least squares regression). Show that they are unbiased estimators of β0 and β1.The proiessur of an introductory statistics course has found something interesting: there may be a relationship between scores on his first midterm and the number of years the test-takers have spent at the university. For the 64 students taking the course, the professor found that the least-squares regression Español equation relating the two variables number of years spent by the student at the university (denoted by x) and score on the first midterm (denoted by y) is y = 82.52- 2.53x. The standard error of the slope of the least-squares regression line is approximately 1.55. %3D Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B,: (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two- tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) Aa…Find a least squares solution of Ax = b by constructing and solving the normal equations.
