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1) Consider n data points with 3 covariates and observations {xil, Гіг, xī,3, yi); i-1,.,n, and y...
linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of t...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of the mean at covariate value Xh . (f) Suppose we estimate ơ2 by 82-SSE/(n-2). Derive the distribution for You can use the fact that SSE/σ2 ~ X2-2 without proof. (g) What is a (1-a)100% confidence interval for y? (h) Suppose we observe a new observation Ynet at covariate value X =...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n,...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n, where yi 's are indicator variable for the experiment that is if a particular medicine is effective on some individual. Here, xi1 and ri.2 are age and blood pressure of i th individual, respectively. Our assumption is that the log odds ratio follows a linear model. That is p-P(i-1) and 10i b) What should be a good estimator for ?,A, e) Suppose. On, A,n...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points i...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
1. Ten steel rods of nominally the same composition and diameter were subjected to various tensile forces (x, in thousands of pounds), and elongation (y, in thousands of an inch) of the steel rods wa...
1. Ten steel rods of nominally the same composition and diameter were subjected to various tensile forces (x, in thousands of pounds), and elongation (y, in thousands of an inch) of the steel rods was observed. The following data was observed: Σ!! Xi-458, Σ i X- 260.46, 201y630, 1 48735.1, 21 ry 3558.42. (a) Fit the least squares line that will enable us to predict elongation in terms of tensile force. For (b) and (c), assume independent normally distributed errors...
1. Choose a data set of your own:?Response or dependent variable (Y)?At least 3 or more...
1. Choose a data set of your own:?Response or dependent variable (Y)?At least 3 or more independent variables (X1, X2, X3, ... etc.) that you believe has an influence on Y.?At least 40 observations or data points?If there are categorical variables, model them appropriately2. Fit a multiple regression model. ?Interpret the model equation?Are all the chosen variables significant? Discuss.?Check for model assumptions and make appropriate comments.?How good is the model? Comment on R2 , R , se, F-value etc and...
(i) Show that 15 (ii) Show that (X) 5/12 and E(Y) 5/8 3(1 - 2X2 +X4)...
(i) Show that 15 (ii) Show that (X) 5/12 and E(Y) 5/8 3(1 - 2X2 +X4) 4(2- 3X +X3) (iii) Show that 3(y|X) (iv) Verify thatE(Y)E(Y) 14] 7. (a) State Chebyshev's inequality and prove it using Markov's inequality 15] (b) Let (2, P) be a probability space representing a random experiment that can be repeated many times under the same conditions, and let A C S2 be a random event. Suppose the experiment is repeated n times (i) Write down...
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a...
Section 12.3 Multiple Linear Regression:
Number ONE:
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a through h EEB Click the icon to see the software output. Data Table The regression equation is Y-1738.93 - 384.54x1 517.39x2 Predictor Constant X1 X2 Coef 1738.93 - 384.54 -517.39 SE Coef 369.06 101.65 - 3.78 0.002 353.04 - 1.47 0.162 4.71 0.000 s-172.003 R-sq-55.0% R-sq(adj):49.0% Analysis of Variance MS Source Regression Residual Error 17...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of the mean at covariate value Xh . (f) Suppose we estimate ơ2 by 82-SSE/(n-2). Derive the distribution for You can use the fact that SSE/σ2 ~ X2-2 without proof. (g) What is a (1-a)100% confidence interval for y? (h) Suppose we observe a new observation Ynet at covariate value X =...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n, where yi 's are indicator variable for the experiment that is if a particular medicine is effective on some individual. Here, xi1 and ri.2 are age and blood pressure of i th individual, respectively. Our assumption is that the log odds ratio follows a linear model. That is p-P(i-1) and 10i b) What should be a good estimator for ?,A, e) Suppose. On, A,n...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
1. Ten steel rods of nominally the same composition and diameter were subjected to various tensile forces (x, in thousands of pounds), and elongation (y, in thousands of an inch) of the steel rods was observed. The following data was observed: Σ!! Xi-458, Σ i X- 260.46, 201y630, 1 48735.1, 21 ry 3558.42. (a) Fit the least squares line that will enable us to predict elongation in terms of tensile force. For (b) and (c), assume independent normally distributed errors...
(i) Show that 15 (ii) Show that (X) 5/12 and E(Y) 5/8 3(1 - 2X2 +X4) 4(2- 3X +X3) (iii) Show that 3(y|X) (iv) Verify thatE(Y)E(Y) 14] 7. (a) State Chebyshev's inequality and prove it using Markov's inequality 15] (b) Let (2, P) be a probability space representing a random experiment that can be repeated many times under the same conditions, and let A C S2 be a random event. Suppose the experiment is repeated n times (i) Write down...
Section 12.3 Multiple Linear Regression:
Number ONE:
Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a through h EEB Click the icon to see the software output. Data Table The regression equation is Y-1738.93 - 384.54x1 517.39x2 Predictor Constant X1 X2 Coef 1738.93 - 384.54 -517.39 SE Coef 369.06 101.65 - 3.78 0.002 353.04 - 1.47 0.162 4.71 0.000 s-172.003 R-sq-55.0% R-sq(adj):49.0% Analysis of Variance MS Source Regression Residual Error 17...
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