4.6 We have five observations on x and y. They are x₁ = 3,2,1,-1,0 with corresponding y values y = 4,2,3,1,0. The fitted least squares line is y, = 1.2 +0.8x, the sum of squared least squares residuals is = 3.6 and Σ(-y)² = 10. Carry out this exercise with a hand calculator. a. Calculate the fitted values y, and their sample mean y. Compare this value to the sample mean of the y values. b. Calculate Σ, (; – 5) and Σ1 ( − 5)/Σ (-5). - i=1 c. The least squares residuals are ê; = 0.4, -0.8, 1, 0.6, and -1.2. Calculate Σ( - ) ê i=1 2 d. Calculate 1 -/-(-)² and compare it to the results in part (b). i=1 e. Show, algebraically, that Σ(-y) (y; - y) = i=1 y; - Ny². Calculate this value. f. Using Σ(x₁ - x)² = 10, and previous results, calculate r= [Σº (9; − 3)(x - 1)] / [√Σ (91 − 5)² √Σ²2, (1; − 5) ²
4.6 We have five observations on x and y. They are x₁ = 3,2,1,-1,0 with corresponding y values y = 4,2,3,1,0. The fitted least squares line is y, = 1.2 +0.8x, the sum of squared least squares residuals is = 3.6 and Σ(-y)² = 10. Carry out this exercise with a hand calculator. a. Calculate the fitted values y, and their sample mean y. Compare this value to the sample mean of the y values. b. Calculate Σ, (; – 5) and Σ1 ( − 5)/Σ (-5). - i=1 c. The least squares residuals are ê; = 0.4, -0.8, 1, 0.6, and -1.2. Calculate Σ( - ) ê i=1 2 d. Calculate 1 -/-(-)² and compare it to the results in part (b). i=1 e. Show, algebraically, that Σ(-y) (y; - y) = i=1 y; - Ny². Calculate this value. f. Using Σ(x₁ - x)² = 10, and previous results, calculate r= [Σº (9; − 3)(x - 1)] / [√Σ (91 − 5)² √Σ²2, (1; − 5) ²
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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Please answer 4.6
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4.5 Using the answer to (d), what is the correlation between WAGE and EDUC? (Hint: Is the correlation between WAGE and the fitted value WAGE?)
c. The sample mean and variance of EDUC are 14.315 and 8.555, respectively. Calculate the leverage of observations with EDUC = 5, 16, and 21. Should any of the values be considered large?
d. Omitting the ninth observation, a person with 21 years of education and wage rate $30.76, and reestimating the model we find ḡ = 14.25 and an estimated slope of 2.470095. Calculate DFBETAS for this observation. Should it be considered large?
e. For the ninth observation, used in part (d), DFFITS = -0.0571607. Is this value large? The leverage value for this observation was found in part (c). How much does the fitted value for this observation change when this observation is deleted from the sample?
f. For the ninth observation, used in parts (d) and (e), the least squares residual is -10.18368. Calculate the studentized residual. Should it be considered large?
4.6 We have five observations on x and y. They are x₁ = 3, 2, 1, -1, 0 with corresponding y values y₁ = 4, 2, 3, 1, 0. The fitted least squares line is
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