7. For simple linear regression, we assume that Y = Bo + BIX +e, where e - N(0,0?) and X isfixed (not random). We collect n i.i.d, training sample (x),y1)....(XYn)). Prove that the (Bo.B1)estimated through minimizing RSS equals to the one through maximizing likelihood.

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Answered: 7. For simple linear regression, we…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: β1 = 0 and the alternative hypothesis Ha: β1 ≠ 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.
2
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.
Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)
I need this question completed in 10 minutes with full handwritten working out
Below are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excel
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

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7. For simple linear regression, we assume that Y = Bo + BIX +e, where e - N(0,0?) and X is fixed (not random). We collect n i.i.d, training sample (x),y1)....(Yn)). Prove that the (Bo.B1) estimated through minimizing RSS equals to the one through maximizing likelihood.