1. (10pt) The RTTO model is given by Y =B1Xii, i = 1,...,n, N(0, a2). The...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Given are five observations for two variables, and y. 1 2 3 5 Yi 3 7 5 11 14 The estimated regression equation for these data is ý = 0.2 +2.6z. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE = Sy.- SST = = (y - SSR = = (y - SSE SST SSR b. Compute the coefficient of determination (to 3 decimals). Does this least squares line provide a good fit? Yes, the...
Given are five observations for two variables, x and y. xi Yi 1 4 2 7 3 8 4 5 11 15 The estimated regression equation for these data is y = 1.2 + 2.6x. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSD = 2(y - ý) SST = 2(y; - 5)2 SSR = 2() - 12 SSE SST SSR b. Compute the coefficient of determination 2 (to 3 decimals). Does this least squares...
Check My Work (2 remaining) eBook Video Given are five observations for two variables, and y 4 7813 15 The estimated regression equation for these data is-1+2.8z. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). (y,-y? SST SSE SST SSR b. Compute the coefficient of determination 2 (to 3 decimals) Does this least squares line provide a good fit? Select your answer C. Compute the sample correlation coefficient (to 4 decimals) Check My Work (2...
9 (y - y)(y - )? (9 - 7) 100 100 100 100 200 200 200 200 500 500 500 500 16.7 12.2 8.4 6.6 15.3 10.71 10.3 21.1 45.6 43.9 47.7 43.2 SSE SST SSR 3. Complete all remaining columns of the table above using the regression equation you found and then find the sum of squared values (SSE, SST and SSR). Complete the given ANOVA table and comment whether the regression coefficient related to the factor's main effect...
Given are five observations for two variables, z and y. 12 3 4 5 37 7 13 14 The estimated regression equation for these data is 0.4 +2.8. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SST E(,- SSE SST SSR b. Compute the coefficient of determination 2 (to 3 decimals). Does this least squares line provide a good fit? No, the least squares line does not produce much of a fit c. Compute the...
Makeup for an Active Learning Activity with an excused absence E I MINDTAP Video eBook Given are five observations for two variables, z and y. 1 2 3 4 5 v 4 7 6 12 14 The estimated regression equation for these data is y 1.1+2.5x. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE SST SSR b. Compute the coefficient of determination r2 (to 3 decimals). Does this least squares line provide a good...
(17 points) Occasionally, a mean function in which the intercept is known to be 0 may be fit. Equivalently, our simple linear regression model is Y; = B1X: + € Assume in a fixed model (z values are fixed), this mean function is given by E[Y] =B120. (a) Assuming € are i.i.d following N(0,02), the residual sum of squares for this model, is SSE = +1(Y; – B12:) Show B1, the least squares estimate of B1. Show that ſi is...
Consider the following set of ordered pairs. 5 4 1 n 5 5 3 2 4 3 у 3 a) Calculate the slope and y-intercept for these data. b) Calculate the total sum of squares (SST). c) Partition the sum of squares into the SSR and SSE. a) Calculate the slope and y-intercept for these data. X у (Round to four decimal places as needed.) b) Calculate the total sum of squares (SST). SST = (Round to one decimal place...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...