Question 2. Show that, for a simple linear regression, R² = ry, where R² is thecoefficient of determination and rxy is the sample correlation between Y and X.Hint:Σ" (Υ - Y)2Σ1(Y₁-Y)²¹SxY√SXXSYY'where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)².R²="XY =

Answered: Image /qna-images/answer/d3050a4b-6be2-444f-8d2b-1329a3ceef8c.jpg

Answered: Question 2. Show that, for a simple…

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

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?
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.
I need answers for A, B, C The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.14 + 0.091x. (a) What is the true average flow rate for a pressure drop of 10 in.? and A drop of 15 in.? (b) What is the true average change in flow rate associated with a 1-inch increase in pressure drop? (c) What is the average change in flow rate when pressure drop decreases by 5 in.?
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
A residual plot from a simple linear regression analysis is shown to the right. Use the plot to answer the question below. residuals 0 X Which of the following statements regarding the plot is true? OA. The condition that the residuals are normally distributed is not met since not all of the residuals fall on the reference line in the residual plot. OB. The condition that the residuals have constant variation is met since the lines connecting the largest positive residuals and largest negative residuals are parallel. Oc. The condition that the residuals are normally distributed is not met since there is a diamond shape to the residuals in the residual plot. OD. The condition that the residuals have constant variation is not met since the variation increases and then decreases as x gets larger.
If 0 is the angle between the two regression lines. Show that sin 0 < 1 - r? (r is the correlation coefficient )
Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?

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