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

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True or false: 1. Standard regression models are appropriate for modeling non-linear relationships between continuous variables 2. r2 calculated for a regression model tells you something about the directionality of the relationship
State true or false: 1. One of the assumptions in regression analysis is that the errors have a mean of 0. 2. A multiple regression model differs from a simple linear regression model because the multiple regression model has more than one dependent variable. 3. If the coefficient of determination for some data is 0.7 , then the correlation coefficient is ±0.84 (round to 2 significant digits). 4.In the Linear regression equation y = 7 + 5x, the slope of the regression line is 7.
41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
The following data on x= maternal age in years of the young birth mothers and y weight of baby born in grams summarizes the result of a study. Assume that a simple linear regression model y = Bo + B1x + e is an appropriate model for the study. x-bar 17 (avg of y-bar 3004.1 x's) (avg of y's) SSXX = 20 SS= 4903 SSyw = 1539182.9 n- 10 Calculate the estimated for Bo and B correct to T WO decimal places. Using your results, predict the average weight of a baby born for a value of x = 18. Enter your answer correct to TWO DECIMAL PLACES.
12
Q#2: (a) Calculate the estimated multiple linear regression equation for the following data using the multiplication in deviation form ΣΥ- 89, ΣΧ30 ΣΧ52 ΣX 238, EX = 582 £X¡Y = 619, EX1X2 %3| %3D 351, EX2Y = 1007,n = 5 %3D
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.?
Q2: For the raw data shown in Table below: 1) Find out which of the x₁ or x₂ variables is better correlated to y. 2) Find out the linear regression lines: y₁ = f(x₁) and y2 = f(x₂) depending on the results of 1) above. X1 1 3 4 11 14 X2 1 2 3 12 15 y 1 2 4 9 65 87 99 4 5 сл 7 12 8
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.
Show that the following relationship on the simple linear regression class notebook is true: (Refer the image)
Calculate the standard error of the estimate of Y from the regression of Y on X for the following data: n= 10 E y- 90, Σw- 120. Ex - 200 where x-X-X, y-Y Y.
45. Calculate the correlation coefficient from the following results : N- 10, Σ X= 350 Σ Υ- 310 Σ (X-35= 162, Σ (Y- 31)? = 222 E (X-35) (Y-31) = 92. erlw %3D %3D Also find the regression line of Y on X

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