Problem 1. In a general linear regression set-up of the type Y = XB+€ where ~ Nn(0, 02In). Further assume€that X has a column of 1's, i.e., an intercept term, and the linear combination Aß does not involve the interceptparameter.(i) Show that imposing a restriction H : Aß = c will always result in an increase (or no change) in RSS, i.e.,that RSSH ≥ RSS.(ii) Show that imposing the restriction H : Aß = = c will result in a decrease (or no change) in R².(iii) Show that the F-test of hypothesis H (versus the alternative of not H) is equivalent to a GeneralizedLikehihood Ratio test.(iv) Express the F-test of hypothesis H as a test on R², i.e., a test statistic that compares the unrestricted tothe restricted R².

ANSWER: (i) Residual sum of squares (RSS) is defined as RSS = e'e, where e is a vector of residuals.…

Answered: Problem 1. In a general linear…

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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19. We are interested in the relationship between years of post-secondary education (x), and annual salary (y), so a survey is put together and the linear regression analysis yields an R2 value of .79 the following regression line: ŷ = 4,500x + 40,000 b) What is the correct interpretation of the slope? Group of answer choices A person with 0 years of post-secondary education can expect a salary of $40,000 79% of the variation found in salary can be explained by variation in years of post-secondary education For every additional year of post-secondary education, the expected annual salary increases by $4,500 There is a strong, positive, linear correlation between years of post-secondary education and annual salary.
he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 10 9 7 8 5 4 4 Cups of coffee (n) 1 1 2 3 3 4 5 5 Unless otherwise stated, you can round values to two decimal places.a) Using regression to find a linear equation for P(n)P(n) = b) Interpret the meaning of the slope of your formula in the context of the problemc) Interpret the meaning of the P intercept in the context of the problemd) Use your model to predict the number of people that will complain about his attitude if he drinks 8 cups of coffee.(Round to 2 decimals) e) Is the answer to part d reasonable? Why or why not?f) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.
17. The equation of the regression line used in statistics is O A. x = a +by O B. y = bx +a %3D O C. y' = a + bx O D. x = ay +b
A particular professor has noticed that the number of people, y, who complain about his attitude is dependent on the number of cups of coffee, x, he drinks. From eight days of tracking he compiled the following data: People (y) 11 11 8 7 9 6 4 5 Cups of coffee (x) 1 1 2 3 3 4 5 5 Unless otherwise stated, you can round values to two decimal places.a) Using regression to find a linear equation for ˆy . Round to three decimal places.ˆy = b) Find the correlation coefficient. Round to three or four decimals.r =
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: Реople (P) 13 13 10 7 7 7 3 4 Cups of coffee (n) 1 1 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. a) Using regression to find a linear equation for P(n) P(n) = %3D b) Interpret the meaning of the slope of your formula in the context of the problem c) Interpret the meaning of the P intercept in the context of the problem d) Use your model to predict the number of people that will complain about his attitude if he drinks 8 cups of coffee.(Round to 2 decimals) e) Is the answer to part d reasonable? Why or why not?
Finish times (to the nearest hour) for 10 dogsled teams are shown below. Find the class width. Use five classes. 243 255 314 312 326 355 357 238 307 298
Town A B C D E F GPopulation (lakh) (X ) 11 14 14 17 17 21 25No. of TV sets demanded ('000) (Y ) 15 27 27 30 34 38 46Fit a linear regression of Y on X and estimate the demand for TV sets for a city with apopulation of (a) 20 lakh and (b) 32 lakh.
Suppose the analyst constructs the simple linear regression model In(y) = a + Bx+e. She estimates it to be In() = -1- 1.3x. What is the residual in Excel output for the pair of observations x= 1.5 and y = 27 O a. 6. O b. 1.98 O c. -2. O d. 403.43 e. 4.29
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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