O Consider a polynomial regression modelY; = Bo + 31X; + B2X? + ...+ B,X; + u;,where E (u;|X;, X?,..., X;) = 0, observations (Y;, X;) are independentand identically distributed and 0 < E (Y;*) < o, 0 < E (X") < o.How is the OLS estimation affected if we estimate a linear regression(r = 1) when the true form of the regression function is quadratic(r = 2) or cubic (r = 3)?%3D

The polynomial regression model is The observations are i.i.d. and .The way in which OLS estimation…

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

See similar textbooks

Similar questions

Consider the linear regression y, = B, + Bx, + u;, i=1,...,n,n+1,..,n+ p where E(u,) = 0. Is it possible to observe a result that E(B,)+ B,, while E(B) = B,-
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.)
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
Consider a polynomial regression model Y = Bo + BrX + B2X +...+BX + Ui, where E (u₁|X₁, X²,..., X) = 0, observations (Y₁, X;) are independent and identically distributed and 0 < E (Y₂¹) < ∞, 0 < E (X¹¹) < ∞. How is the OLS estimation affected if we estimate a linear regression 1) when the true form of the regression function is quadratic (r = 2) or cubic (r = 3)? (r =
Consider the linear regression model Y; = Bo + B1 X¡ + U¡ for each i in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get: 1,..., n withn = 1,000. X; represents the annual income of individual i (measured Bin = 43.2, SE(§ „) = 10.2, Bon = 700, SE(Bom) = 7.4. Suppose that we want to test Ho : B1 O against H1 : ß1 # 0 at 1% significance level. Assuming that the sample size is large enough, which one of the following is true about the p-value of this test? 43.2 The p-value can be computed as P(-| ), where is the standard Normal CDF 10.2 а. b. None of the answers 43.2 The p-value can be computed as (- ), where O is the standard Normal CDF 10.2 С. 43.2 d. The p-value can be computed as 20(-- ), where O is the standard Normal CDF 10.2
1. Simple Linear Regression Estimation: (а) For the model y; B1 + B2x; + ui, define the fitted value ĝ; and residual û;. (b) x to arrive at estimates for B1 and B2? How does OLS take data on the outcome variable y and the independent variable Suppose you have the OLS estimate of the slope coefficient B2 from regressing ax; is equal to (c) y on x. Show that the slope coefficient if you regressed y on x* for x B2/a, where a is some constant. To be clear, I want you to show that B = B2/a, where B2 is the OLS estimate of B2 from the model Yi = B1 + B2x; + ui, and B is the OLS estimate of B; from the model y; = Bi + B5x + U;.
A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:
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
7. a) What are residual plots and box plots? b) Do the stability analysis of the following model which is formulated to study the effect of toxicant on one competing species where the environmental toxicant concentration is being taken to change w.r.t. time. dN = rN, - α,Ν,N, - d,C,N , dt dN2 = rN, - α,N,., dt dCo = k,P - g,C, – m¡C, dt dP Q- hp – kPN, + gC,N . dt along with the initial conditions. N, (0) = N10,N2 (0)= N20,C, (0)= 0, P(0)= P, > 0 %3D Here, N1 (t) = Density of prey population
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.)
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS