Consider a linear regression modely = Bo + B1xwith N data points D = {Xi, yi}, i= 1, 2, 3, ..., NShow that the unbiased estimate of the model parameters are given byE) (E) – (E) ENE - (E .)"Bo(E-.) (EM, ».) – N (E, )(E)* - N (E,)vi=1 *ivi=1 YiB1

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Answered: Show that the unbiased estimate of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A computer engineer needs to know how the efficiency of a new computerprogram depends on the size of incoming data. Efficiency will be measuredby the number of processed requests per hour. Applying the program todata sets of different sizes with the following results. The response variableis the number of processed requests (Y) and to predict it from the size of adata set (X). Estimate the quadratic regression model and use it to find theprocessed requests when the data size is 14 GB.Data size (GB) X 6 7 7 8 10 10 15Processed requests Y 50 43 44 37 25 26 15
A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
One of the standard curves used is harmonic decline model, that is: Q = bx/(1+ ax²) where Q is the rate of production and x is the time, b and a are the constants of the regression model. If we apply linear least squares fit for estimating b and a, what will be the value of the summation of squared errors.S Sr x, Months 11 16 18 22 90 75 65 Q, Barrels/Day 1 9 44 100 50 Sr= {(y- P(x)} 2 - (9,- #2) ²
Determine the orthogonal trajectories to the given family of curves. y² = cx²
Over the years Olympic racers have been getting fasterin most events, and the women’s singles 500-meter kayakrace is no exception. A scatterplot displaying the data foryears since 1948 (x) and time in seconds (y) suggests thata linear model is appropriate. The equation of the leastsquares regression line is, yn = 144.627 - 0.776x, andr2 = 0.932.a) Interpret the value of r2 in this context.b) Compute and interpret the value of r in context.c) The Olympics are held every 4 years. What changein the winning time does this model predict from oneOlympics to the next?d) The residual for the winning time in 1980 was-1.795 seconds. Find this gold medal time.
Please solve 12.7 and dont use any programme like minitab.
While shopping for an air conditione, a buyer bonsulted the following table giving a machine's BTUS and the square footage ( that it would cool t' (x) BTUS (y) 5100 5400 6350 6700 7275 7825 8300 8550 9750 9900 150 175 230 250 285315 350 360 435 | 450 (a) Find a linear model for the data. (b) Use the results from part (a) to find the number of BTUS required to cool rooms of 360 ft, 435 r, and 450 (c) Suppose a room measures 215 Use the results from part (a) to decide how many BTUS it requires if the air conditioners are available only with the BTU cholces in the table, which is the best choice? (a) Find a linear model for the data Find the least-aquares regression ine Once you have found the line in ynix+b form, input the values of m and b into the appropriate boxes below A linear model for the data is y (Round to the nearest whole number as needed) %3D
Find the orthogonal trajectories of the family of curves y3 = 3(x – c). Draw a few representative curves of each family.

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