27. Given X= 4Y+ 5 and Y= KX + 4 are the lines of regression of X on Y and Y on Xrespectively. If K is positive, prove that it cannot exceed 4. If K= 1/16, find the means of two variables[D.U., B. Com. (Hons.) 2006]and the coefficient of correlation between them.

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Answered: 27. Given X= 4Y+5 and Y= KX + 4 are the…

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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The manufacturer of Beanie Baby dolls used quarterly price data for 2012/-2020/V (t = 1, ..., 36) and the regression equation Pt= a + bt+c₁D1 t + c2 D2 + + c3 D3 t to forecast doll prices in the year 2021. Pt is the quarterly price of dolls, and D1, D2t, and D3+ are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE P-VALUE ON F 0.0001 OBSERVATIONS: F-RATIO 76.34 STANDARD 36 0.9078 PARAMETER VARIABLE ESTIMATE ERROR T-RATIOP-VALUE INTERCEPT 24.0 6.20 3.87 0.0005 T 0.8 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.0 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 The estimated quarterly increase in price is and the estimated annual increase in price is Multiple Choice O O $1.50; $6.00 $1.40; $4.00 $0.60; $2.40 $0.80; $3.20 None of the choices are correct.
69 Q1. [6 points] :From the following data set 3\ 9. 1 6. 5. 4 11 16 1.find correlation coefficients 2. Estimate the simple linear regression model 3. Find the predicted value of y when x-10
Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is: kids; = Bo + B1educ; + uż. 1. What are the parameters in the model? 2. What kinds of factors are contained in u? Are these likely to be cor- related with level of education? 3. Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 83.3 + 2.24x, + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST 25.2 and SSR = 23.455. %D (a) Compute and interpret R² and R,. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R = 0.653 and R, = 0.595. Do you prefer the multiple regression results? Explain. %3D 2 Multiple regression analysi v ---Select--- ipreferred since both R2 and R, show ---Select--- O…
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?
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is

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27. Given X= 4Y+5 and Y= KX + 4 are the lines of regression of X on Y and Y on X respectively. If K is positive, prove that it cannot exceed 4. If K= 1/16, find the means of two variables [D.U., B. Com. (Hons.) 2006] and the coefficient of correlation between them.