a) In regression analysis, to obtain the least square estimators of a and B, the SSRof Squares of the errors (Y: – a - Bx;)2 is minimised.i) Given thatasSR-2y: +2a+ 28x;)dai-1show by minimising thata = y – Bxii) Given thatasSR-2x,Yi + 2ax; + 2Bx)i=1show by minimising thatB= -n1 - (E, ¤i)²

Answered: Image /qna-images/answer/a55ae41f-b895-4c7b-a428-fc909ac8bf07.jpg

Answered: a) In regression analysis, to obtain…

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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c) Give the expression of R˜^2 in terms of R^2 , and justify your answer.
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 X
The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm
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.
Need only handwritten solution only (not typed one).
Experimenters wants to assess the association between X and Y, the scatter plot of X and Y showed a quadratic pattern. After applying the appropriate regression model, experimenters want to produce a prediciton interval for X = 20. Using StatCrunch with 95% confiendence, the result interval is 223 to 267. Provide the most appropriate interpretation of this interval.
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.

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