5) State any theorems that you use in determining your solution.a) By using partial differentiation derive the equations that a and ß satisfy in yt = a +Bxt + ut where symbols have their usual meaning.b) Suppose you are given the following information for an OLS regression:Xxi yi = 830102, T = 22, x = 416.5, y = 86.65,Yix² = 3919654, RSS = 130.6i)Calculate the ordinary least square regression line.ii)Calculate SE (a) and SE (B)iii)Perform the hypothesis test such that Ho: a = -60 versus H₁: a ‡ -60iv)Perform the hypothesis test such that Ho: P = 0.4 versus H₁: ß # 0.4In both cases use a significance of 5%.c) Discuss using appropriate mathematics the properties and assumptions underlyingthe OLS technique, you should mention and discuss all 5 assumptions.

a) Suppose we have n pairs of values yt, xt t=1,2,...,n yt=α+βxt+ut where yt=Dependent…

Answered: 5) State any theorems that you use in…

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 particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.
The annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!
Use the linear regression model yˆ=−24.8x+564.38 to predict the y-value for x=63.
If the linear equation between Height and Gestational Age is given as: Height=a + b Gest x What is the value of a from the output above What is the value of b from the output above
A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds), Two variables thought to affect weight loss are client's length of time on the weight-loss program and time of session These variables are described below: Y-BO+B1'X+82'D 83'X'D+E Y-Weight loss (in pounds) X- Length of time in weight-loss program (in months) D-1 if morning session. O if not in terms of the Bs in the model, what is the difference between the weight loss of an individual who has spent 3 months in the program when attending the morning session, and an individual who has spent 2 months in the program when attending the evening session? OB1+83 OB1+82-83 OB1+82+283 O81+82+383
A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?
The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.8 + 0.3x, +4.5x,, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values for the values of the independent variables. x, = 70, x, = 8.6 The predicted volume is cubic feet. (Round to one decimal place as needed.)

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