QUESTION 1Consider the non-linear regression modelY = log(XTB)+U,where EU|X] = (0With a random sample (Yi, X,) for i = 1, ...,n1,(1) Propose an estimator for B, denoted by B, using the moment condition EX;U = 0.(2) Find the asymptotic distribution of B.

The considered linear regression model: Here There is a random sample

Answered: Consider the non-linear regression…

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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Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…
Some non-linear regressions can also be estimated using a linear regression model (using 'linearization'). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression in the form y = cd* to estimate parameters c and d from the data by linearizing the model through In y In c+ (In d)x = b, + b, x. y y 6381 3 5394 5673 4980 2 5740 4896 (Click the button to copy or download the data.) Using Excel ot other software, the non-linear regression model y = cd can be estimated as: y = D*. (Round c and d to four decimal places, inlcuding any zeros.)
The following table presents the highway gasoline mileage performance (y) and engine displacement (x) for Damler-Chrysler vehicles for model year 2005 (source: U.S. Environmental Protection Agency). Engine Displacement MPG (highway) Carline 300C/SRT-8 215 30.8 CARAVAN 2WD 201 32.5 CROSSFIRE ROADSTER 196 35.4 DAKOTA PICKUP 2WD 226 28.1 DAKOTA PICKUP 4WD 226 24.4 DURANGO 2WD 348 24.1 GRAND CHEROKEE 2WD 226 28.5 GRAND CHEROKEE 4WD 348 24.2 LIBERTY/CHEROKEE 2WD 148 32.8 LIBERTY/CHEROKEE 4WD 226 28 NEON/SRT-4/SX 2.O 122 41.3 PACIFICA 2WD 215 30 PACIFICA AWD 215 28.2 PT CRUISER 148 34.1 RAM 1500 PICKUP 2WD 500 18.7 RAM 1500 PICKUP 4WD 348 20.3 SEBRING 4-DR 165 35.1 STRATUS 4-DR 148 37.9 TOWN & COUNTRY 2WD 148 33.8 VIPER CONVERTIBLE 500 25.9 WRANGLER/TJ 4WD 148 26.4
1
Suppose you obtain the following regression model, E[y]=91+79*x1 +20*x1*x2. What is the impact of a 39 unit change of x1 on the expected value of y when x2 is at its mean of 40?
With t test statistics and its p-value, given in the regression output, we test: O a. a joint hypothesis about significance of all parameters except constant O b. a single hypothesis about insignificance of R^2 O C. a single hypothesis about significance of parameter O d. a joint hypothesis about insignificance of all regression parameters
To examine whether there is any association between the performances on the two tests, T1 and T2 (test T1 was conducted before T2), and whether T2 scores could be predicted in terms of T1 scores. A random sample of 150 students in Statistics major was selected. Let the scores be denoted S1 and S2 for tests T1 and T2, respectively. The tests had different maximum points. The following outputs using R codes were obtained. fit[t]) (Intercept) 0.10152 2.51003 0.04 0.968 S1 0.26723 0.01921 13.91 <2e-16 *** Signif. codes: O ***' 0.001 **' 0.01 (*' 0.05 '.' 0.1 '? 1 Residual standard error: 4.472 on 148 degrees of freedom Multiple R-squared: F-statistic: 193.6 on 1 and 148 DF, 0.5667, Adjusted R-squared: 0.5638 p-value: < 2.2e-16 plot (fit$fitted,fit$residuals, xlab="fitted values", ylab="residuals") qqnorm (fit$residuals) Normal Q-Q Plot oo 00 00 00 O Go a god 00 00 0. of 25 30 35 40 45 -2 2 fitted values Theoretical Quantiles esiduals 15 Score: Sample Quantiles 091
Suppose that n= 195 I.I.d. observations for (Y, X;) yleld the following regression results: v= 32.68 + 67.55Xx, SER= 18.63, R = 0.84 (15.7) (12.5) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 390 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following eatimated parameters change result? (Check all that apply) O A. The estimated intercept and slope. O B. The R of the regression. Yc. The standard error of the regrussion (SER). YD. The standard errors of the estimated coefficients. Using the 390 observations, what results will be produced by his regression program? Ý= 32.68 + 67.55X, SER =.R = 0.84 (Round your responses to two decimal places)
The time needed to find a parking space is normally distributed with a mean of 20 minutes and a standard deviation of 5.18 minutes. 90% of the time, it takes less than how many minutes to find a parking space?
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).

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Consider the non-linear regression model QUESTION 1 Y = log(XB)+U, where EU[X]=0 With a random sample (Y₁, X.) for i = 1,...,n, (1) Propose an estimator for ß, denoted by 8, using the moment condition EXU₁] = 0. (2) Find the asymptotic distribution of B.