Consider a polynomial regression modelY = Bo + BrX + B2X +...+BX + Ui,where E (u₁|X₁, X²,..., X) = 0, observations (Y₁, X;) are independentand identically distributed and 0 < E (Y₂¹) < ∞, 0 < E (X¹¹) < ∞.How is the OLS estimation affected if we estimate a linear regression1) when the true form of the regression function is quadratic(r = 2) or cubic (r = 3)?(r=

Given: Let's consider the given binomial equation,…

Answered: Consider a polynomial regression model…

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.
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
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
Find the least square regression line.
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.
)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.
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

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Consider a polynomial regression model Y = Bo+31X + B,X? +...+BX + lin where E (u₂X₁, X²,..., X) = 0, observations (Yi, X;) are independent and identically distributed and 0