3. Consider the following regression model:Yi Bo+B1x1 +=···· + ßpxip + Єi, i = 1, . . ., n,where are i.i.d.~N (0,0²).(i) Give the MLE of ẞ and σ², where ẞ = (Bo, B₁,..., Bp)T.(ii) Derive explicitly the expressions of AIC and BIC for the above linear regressionmodel, based on their general formulae.

Step 1: Maximum Likelihood Estimation (MLE)We consider the multiple linear regression…

Answered: 3. Consider the following 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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Which pair of data points are always on the regression line: Y = a + bx? (0, 0) (0, b) (X, Y) (a,0)
Construct the simple linear regression equation of Y on X if n = 7, x,=113, E Ey-182 and Exy, =3186. =1983,
please answer b and c.
We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form yˆ=b0+b1x1+b2x2 HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars.
Compute the coefficients b₁ and b₂ for the regression model y₁ = 60+ b₁x₁₁ +b2×21 given the summary statistics shown below. a. Tx₁y b. rx₁y c. Tx₁y d. = 0.80, x2y=0.60, =200, Sx2 = 0.40, Sx₁ 0,5x1x2 =-0.80, гx2y=0.60, rx₁x2 = -0.40, Sx₁ = 200, Sx2 = 100, sy = 500 = 100, 0, Sy = 500 100, Sy = 500 =0.80, x2y = -0.20, 0, rx₁x2 = -0.10, Sx₁ =200, Sx2 = 100, Sy = 500 =0.50, rx2y=0.75, x₁x2 = 0.70, Sx₁ =200, Sx2 =
Suppose that you have the following three regression models: Yi B₁ + B₂x₁ + Uj regression) Y₁ = a₁ + a₂x₁ + eį, if i is male male individuals) Yi = ₁ + ₂x₁ + Ei, if i is female (separate regression for female individuals) ESS RSS The error terms satisfies that E[ui] = E[ei] = E[ei] = 0. Then, we find the following RSS and ESS: Pooled Regression 124.3 25 (separate regression for (pooled 71.1 11.4 separate separate regression for regression for male individuals female individuals 56.6 8.6 The number of sample size is given by 18. Select the correct statement(s). The RSS from the pooled regression is always smaller than the sum of RSSS from the separate regression models. In the above setup, Chow test is equal to 2. If e; is correlated with €;, then the OLS estimator of a2 from the separate regression will be is biased. If the variances of e; is different from €;, then the OLS estimator of 3₂ is no longer unbiased estimator. If we add another variable z; to the pooled regression, then the…
You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: = 71.0 – 4.84×BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) Values in parenthesis are standard errors. (a) What is the interpretation of the intercept? What is the interpretation of the coefficient of the dummy variable? How tall are females, on average? (b) Test the hypothesis that females, on average, are shorter than males, at the 1% significance level.
5
Consider the points in the plane: (1,2) (2,3) (3,5) (4,4) (5,7) (7,8) (i) Compute the correlation coefficient. (ii) Compute the equation for the regression line.
Let edu denote years of education, exper years of experience, wage denote wages measured in dollars per hour, and assume that the following model is correct: wage = B1 + B2edu + e where E[eledu, exper] = 0 and the error e is homoskedastic, so that Var(e|edu, exper) = Consider two regressions: (I) A first regression estimates the given model (denote those estimates by b1, b2); (I) A second regression also adds exper as a regressor -- i.e. estimates wage = ß1 + Bzedu + ßzexper + e (denote those estimates by b1, b2, b3). Which of the following statements is true? O a. The estimator b2 may be biased (i.e. we may have E[b2] # B2). O b. If wage and exper are positively correlated, then E[b3] > 0. O c. Var(b2) depends on the correlation between exper and edu (Hint: this is not asking the variance of b2.) O d. If Var(b2) = Var(b2), then the correlation between exper and edu must be zero. Oe. The correlation between wage and exper must be equal to zero. Clear my choice
The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 29.1370 + 0.5103x, + 0.4980x2 (a) Interpret b, in this estimated regression equation. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 29.1370 is an estimate of the change in y corresponding to a 1 unit change in x, when x., is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. Interpret b, in this estimated regression equation. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a…
2. We will show a link between regression and the T-test. Suppose we have data of written of the form (Yij, xj), equal to, (Y11, 1), (12, 1), (Yin, 1) (Y21, 1), (22,-1),..., (2n-1) And assume the model, Yij = Bo+B₁xj + Eij, where Eij id N(0.02) (a) Show that Bo Y. : = == +Y=-12. 2n (b) Show for the fitted values, Y₁₁ = Y₁., and Y2j = Y2. for 1jn (c) Show that ²= 82 for the pooled variance t-test (d) Show that the test statistic for the hypothesis test Ho₁ = 0, HA: B00 can be written as, Y₁. - Y2. T And therefore the pooled variance T-test can be written via the SLR equation

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