Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.)(-1, 1), (1, -2), (3, -3)-0.33 - 1xXGraph the points and the line on the same set of axes.y

Solution-: Let, X=be the independent variable and Y= be the dependent variable Given data: X:…

Answered: Find the least squares regression line…

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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For a linear regression problem, the least squares line is y = 2x+2. Determine the predicted value of y when x = 5 19 not enough information 12 oooo
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 28 Suppose your estimated MLR model is: Y_hat = -30 + 2*X1 + 10*X2 Suppose the standard error for the estimated coefficient associated with X2 is equal to 5. Now, suppose that for some reason we multiply X2 by 5 and we re-estimate the model using the rescaled explanatory variable. What will be the value of the estimated coefficient of X2 and its standard error? The estimated coefficient of X2 will be equal to 50 and its standard error will be…
q4. Linear regression
How do I go about these two questions followin this asnwer above: B) Ater removing the point with coordinates (2,9), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b).
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5% QUESTION 17 In an MLR…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (c) The printout gives the value of the…
Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent varia (-1, 1), (1, -1), (3,-2) 2 X

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Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) (-1, 1), (1, -2), (3, -3) -0.33 - 1x X