Suppose that the response y is generated byy = f(x) + €,where e is a zero-mean Gaussian noise with variance 1.a) Suppose that f(x) = x. Randomly generate 10 x's and generate the corresponding y's; youneed to generate two random numbers (i.e., x and e for each of the 10 points). Fit the datawith linear regression and plot the scatter points.b)Suppose that f(x) = x². Randomly generate 10 (x, y) pairs. Fit the data with linearregression and plot the scatter points.c)Suppose that f(x) = 1/x. Randomly generate 10 (x, y) pairs. Fit the data with linearregression and plot the scatter points.

Given Information: Consider the response y which is generated by: y=fx+ε Where ε is a zero mean…

Answered: Suppose that the response y is…

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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Consider a regression with two variables, in which X1i is the variable of interest and X2i is the control variable. The zero conditional mean assumption requires Group of answer choices E(ui|X1i) = E(ui|X2i) E(ui|X1i, X2i) = E(ui|X1i) E(ui|X1i, X2i) = 0 E(ui) = E(ui|X2i)
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?
Bxi + €i, where €; are independently and Consider a simple linear regression model Y; = identically distributed with mean 0 and variance o?, and i = 1,..., n. Note: this model does not have a intercept term. Derive the Best Linear Unbiased Estimator (BLUE) for B. Denote this by BBLUE. Make sure to state why this is the BLUE.
1. Consider two least-squares regressions and y = Xíễ tế y = Xí$i+ XzB2 tê Let R2 and R2 be the R-squared from the two regressions. Show that R22 R2.
1. When estimating the parameters of a linear regression model, the OLS estimator is a scalar value and the OLS estimate is a random variable. 2. For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable. 3. If the error term in a linear regression model is normally distributed, then the distribution of the OLS estimator, conditional on explanatory variables, is also normal. 4. The value of the coefficient of determination, R2 of Model 1: In yi = a + Bx; + E; (M1) is different from the value of R2 of the Model 2: Yi = a+ Bx; + Ei. (M2) 5. Consider an earnings function In wage = 0.6 + 0.16 · educ estimated on a sample of n = 1000 individuals. The standard error of the estimated slope coefficient equals 0.11. This allows us to interpret the estimated slope coefficient as: ceteris paribus expected returns to schooling are 16%.
Below are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excel

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