Q. 26 What is the principle of least squares ?
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A: (3)
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- Q.1) The table below gives the readings from a laboratory experiment. 2 Time (t) Reading (y) 7 Fit: (i) a curve of the form y = ea(t-b), and (ii) a curve of the form y = a(1-bt) to the above data by method of least squares. (iii) determine which of the two (i) and (ii), is a best approximation. 3 17 5 49 6 71 9 161x y 10 8.04 8 6.95 13 7.58 9 8.81 11 8.33 14 9.96 6 7.23 4 4.26 12 10.84 4) Determine the slope of the least squares regression line. A) 10.48 B) 18.05 C) 3.57 D) 0.46The average remaining lifetimes for women of various ages in a certain country are given in the following table.
- Which of the following statements proves the usage of a least squares line? The residual plot shows extreme observations in residuals. Plots of scrambled residuals against the predictor do not show any pattern. The scatterplot of the fitted values against the response shows a linear relationship. Group of answer choices (i) I only (ii) II only (iii) III only (iv) I and II only (v) II and III onlyUse the method of least squares to fit the model to the data. Y hat= _+_xThe data points in ExerciseIn each of Exercises, we have presented two linear equations and a set of data points. For each exercise,a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.b. construct tables for x, y,ŷ e, and e2 like Table (page 626).c. determine which line fits the set of data points better, according to the least-squares criterion.TABLEDetermining how well the data points in Table are fit by (a) Line A and (b) Line Ba. Line A: y= -1 + 2x x y ŷ e e2 1 3 1 2 4 2 1 3 -2 4 3 5 5 0 0 8 b. Line B: y= -1 + x x y ŷ e e2 1 3 2 1 1 2 1 3 -2 4 3 5 4 1 1 6 TABLE Three data points x y 1 3 2 1 3 5 Line A: y=3-0.6x, Line B: y=4-xData Points x 0 2 2 5 6 y 4 2 0 -2 1 ŷ =14-3x x 1 3 4 4 y 13 -1 3 5
- Simulate the solution of the given problem using Excel such that when the given five data points (x and y values) are changed, a new equation is formed. 1. By the method of least squares, fit a line y = a + bx to the points 0 2 y -1 -1 2 9 3 10 5 14Graph the data and observe the relationship between x and y, is it linear or nonlinear? Predict which of least squares approximation P₁(x) (linear) or P₂ (x) (2nd order polynomial) is better? or they are similar? (Do not need to find P₁ or P₂, no calculations are involved in this problem) Xi 1.0 Yi 1.84 1.1 1.96 1.3 1.5 1.9 2.1 2.21 2.45 2.94 3.18Online Sales of Used Autos The amount (in millions of dollars) of used autos sold online in a certain country is expected to grow in accordance with the figures given in the following table (x 0 corresponds to 2011). 0 12.8 y 1 2 13.9 Year, x Sales, y 15.75 (a) Find an equation of the least-squares line for these data. x 3 4 14.75 15.15 (b) Use the result of part (a) to estimate the sales of used autos online in 2016, assuming that the predicted trend continued. x million
- Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 The least-squares estimate of b0 equals [2 decimal points] ________ The least squares estimate of b1 equals [2 decimal points; also don't forget the sign] __________ Develop the least squares estimated regression equation _______ At 95% confidence, perform a t test and determine whether the slope is significantly different from zero. [3 decimals] t = _____________ Based on this information, we Reject H0 Do not reject H0 The coefficient of determination is [keep 3 decimal points] _________When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is log(Area) = 0.490 + 2.004 log(Time). WWhat is the predicted area of the circle, in cm2, 4 seconds after the stone is dropped? O 49.72 cm2 O 199.43 cm2 O 311.89 cm? O 1854.10 cm2Hello there! Can you help me solve a problem with two subparts? Thank you! Question: If a machine learns the least-squares line that best fits the data shown below, what will the machine pick for the value of y when x= 2? How closely does this match the data pt at x = 2 fed into the machine? (0, 2), (1, 2), (2, 5), (3, 5) First subpart When x = 2, the machine will pick a value of __ for y. Second subpart Three options: (a) This is __ away from the y-value fed into the machine for x= 2, which is too large to be expected for the best fit line. (b) This is exactly the same as the data point fed into the machine. (c) This is __ away from the y-value fed into the machine for x= 2, which is reasonably close considering the range of y-values in the data set.