QI. Write the following models using matrix notation, Y = XB +e :(a) Multiple regression,Y = Bo +BXin + B2xi2 + B3X13 + ei; i=1, 2, 3, ..., 7.(b) Multiple polynomial regression,Y; = Bo + Bxi1 + B2Xi2 + B3x + B4x + B5X11X12 + ei; i= 1, 2, 3, ..., 7(c) Two-way ANCOVA with no interaction and common slope,Yi = µ+a; + Bj + yxijk + ei; i=1, 2, 3; j= 1, 2; k= 1, 2.

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Answered: QI. Write the following models using…

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 help me to solve questions a and b, using matrix
2. Express the system of linear equations as a matrix equation in the form Ax =b. - lx1+ 2x2+ x3- X4 = 1 2x1 – x2– x3+2x4 = 0 lxi+x2+2x3 = 2
The following data are the average annual repair cost (in O.R.) and the age of automobiles ( in years). Car age (x) 1 2 3 4 5 Repair Cost (y) 100 150 320 350 380 Find the equation of Y on X by least-squares regression method.
Consider the model Y = ß0 + B₁X1 + ß₂X2 + B3X³ + B4X4 + €. If it is suggested to you that the two variables Z₁ = X₁ + X3 and Z2 = X₂ + X4 might be adequate to represent the data, what hypothesis, in the form C3 = 0, would you need to test? (Give the form of C.)
One of the key tasks in metropolitan area transportation planning is to estimate the total number of trips made by households during a typical day. The dependent variable is the number of trips made by a household per day, known as the trip generation rate. One of the most important determinants of variations in household trip generation rates is household income. Consider a hypothetical city, values of the trip generation rates and household income are listed in the following table. (a) Find the regression coefficients (the intercept and the slope coefficients). Interpret the meaning of the slope coefficient.(b) Write out the regression line formula.(c) Calculate the coefficient of determination for this problem.
H1.
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…
In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in °F (y) and air pressure in psi (x). Three models were fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, and the cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for each model are presented in the following table. Plot the residuals versus the fitted values for each model. For each model, state whether the model is appropriate, and explain. %3D Quadratic Model Fit Linear Model Cubic Model Residual Fit Residual Residual Fit -56.2 125.6 11.2 58.2 3.3 66.1 -34.0 153.1 -7.4 126.5 -6.7 125.7 8.4 179.8 4.9 183.4 9.2 179.0 21.4 207.2 -3.6 232.2 0.9 227.8 28.6 234.7 -8.2 271.5 -5.9 269.2 46.9 260.9 8.1 299.7 7.3 300.5 47.2 288.1 15.7 319.6 12.1 323.2 8.5 314.4 -7.0 329.8 -11.7 334.6 -7.1 342.0 4.0 330.9 1.0 333.9 -47.1 139.3 -1.3 93.6 -4.1 96.4 -1.6 166.2 9.1 155.5 12.1 152.5 38.0 220.9 5.9 253.0 9.5 249.4…
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
3. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁?
Find the equation of the line .that best fits, in the least squares sense, the data in the following table: xy 55 6 10 8 13 9 20 12 28 Form the system for m and b by substituting the points in the model, e.g. substituting the first point leaves the equation : 5 m + b = 5 Report the value of m:
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 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if: one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) ) QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity'…

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