b.Suppose y, and x, exist a linear population relationship, y, = Bo + B₁x, +u,, with arandomy drawn sample of n observations of y, and x,. u, is i.i.d. normal with mean 0 andvariance o². Let 3, be the OLS intercept and slope estimators from the regression.a.Show that B₁ =B₁+ku,, where k (x₁ - x)=i=1-. Under the assumption thatrespectively.nΣ(x₁ - x)²i=1X₁nonrandom, please show that the expected value and variance of ₁ is ₁ and0²nΣ(x₁ - x)²i=1Please explain why , is a random variable and normal distributed.is

The question at hand delves into the properties of the OLS (Ordinary Least Squares) estimator,…

Answered: b. Suppose y, and x, exist a 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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3. The relationship between variables Y (RM billion), X (%) and Z (million tons) can be illustrated by the following linear regression model. Yi = Bot BiXit BeZit Hi A summary of the data for the three variables from year 1988 to 2018 is as follows: Σκ. = 192.734 Σy² = 55,541.86 [vix = 403.937 Sy = 4.304 Where y₁=Y₁ - Y x₁ = X₁ - X Z₁ = Z₁ - Z (a) Use the Ordinary Least Squares Method (OLS) to estimate all the parameters in the model. Ex= [x² = 3.029 = 1.899 Yi Zi Στις Ez = 535.562 = 5,112.319 Σχ Sz = 0.423 Sx = 0.032 = 39.522 XZ₁ = 39.492 (b) Use the standardized regression coefficients to compare the effect of X and Z on Y respectively. (c) Calculate the elasticity of Y with respect to Z at the mean value. Explain the meaning of the elasticity value obtained.
29) Two variables are measured on a random sample of n = 23. The sample data results ina sample correlation of 0.393. If you fit a simple regression model to the data, whatvalue would the coefficient of determination (or R-squared) take on?A) 0.627B) 0.393C) 0.154D) 0.000E) 0.296
A researcher collected data on ( X, Y ), and wanted to test if the true relationship is linear. Therefore, she collected replicated values of X. Here is a summary of the data, and some results: Xi No. of replicates yi SSE = 312. 1 3 9 10 5 11 8. 3 2 12 14 4 4. 15 13 3 9 6 6 5 11 10 7 1 8 4 8 3 7 5 At significance level a = 0.05, carry out the test of Lack-of-Fit for linearity of the model. No need to show an ANOVA Table. Calculations: Test statistic: T = Critical value = Conclusion: Since we 2.
18. 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 a) What is the correct interpretation of the coefficient of determination? Group of answer choices There is a strong, positive, linear correlation between years of post-secondary education and annual salary. 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
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
Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.867 and the equation of the regression line is y = 3.57 + 0.97x, where x represents the IQ score of the younger child. Also, the 20 x values have a mean of 96.75 and the 20 y values have a mean of 97.1. What is the best predicted IQ of the older child, given that the younger child has an IQ of 95? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the older child is (Round to two decimal places as needed.)
27) The total blood cholesterol concentrations, in mg/dL, are shown below for a random sample of six people. In the table below, x is the age of the subject and y is the subject's total cholesterol concentration. Find the 95% prediction interval when x = 58 years. 27) x (age) 36 49 58 69 63 71 204 256 194 257 245 y (mg/dL) 209 A) Regression line: y = 1.82x +122.5 Standard error of the estimate: s est = 16.51184 Prediction interval for y(58): 159
116). With 77.4 and y 77.2, you You run a regression analysis on a bivariate set of data (n obtain the regression equation y -1.848z+56.533 0.092. You want to predict what value (on average) for the with a correlation coefficient of r= response variable will be obtained from a value of 180 as the explanatory variable. What is the predicted response value? %3D (Report answer accurate to one decimal place.)
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.
The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y. Mathematics score (X) 70 92 80 74 65 83 English score (Y) 74 84 63 87 78 90 ∑x=464, ∑y=476,∑x^2=36354,∑y^2=38254, ∑xy=36926. Estimate the regression parameters and also write the prediction equation.
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. A) Find the regression equation for predicting GPA from SAT scores. B) What percentage of the variance in GPAs is accounted for by the regression equation (i.e., compute the correlation, r, then find r2)? C) Does the regression equation account for a significant portion of the variance in GPA? Use a = .05 to evaluate the F-ratio.
Attempt any three questions. Q1. The regression line between height (X) in inches and weight (Y) in Ibs of male students are: 2y – 5x = 17 7x + 3y = 21 Determine which is regression of Y on X and X on Y. Obtain also correlation coefficient 'r'. Q2. The following table gives the ages and blood pressure of 9 women. Age (X): 56 42 36 47 49 42 60 72 63 Blood Pressure(Y) 147 125 118 128 145 140 155 160 149 Find the correlation coefficient between X and Y. (i) Determine the least square regression equation of Y on X. Q3. Find out the regression coefficients of Y on X and of X on Y on the basis of following data: ΣΧ 50 X = 5. ΣΥ-6 , Y= 6, EXY = 350 Variance of X= 4, Variance of Y= 9 Q4. The equations of two regression lines between two variables are expressed as 2X – 3Y= 0 and 4Y– 5X-8 = 0. (i) Identify which of the two can be called regression line of Y on X and of X on Y. (ii) Find X and Y and correlation coefficientr from the equations

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