G Sometimes, people consider a simple linear regression model without the intercept term. Given data (x1, y1),(x2, y2), . . . ,(xn, yn), consider the following model yi = βxi + ?i , i = 1, . . . , n where we assume ?i ∼ N(0, σ2 ) and they are independent. (a) (10 pts) What is the distribution of yi? Write down the distribution and parameters. (by) (10 pts) Express the total square error as a function of β and find βˆ that minimizes the tot

Jace wrote a sentence as an equation. 56 is 14 more than a number. 14+ = 56 which statement best describes jace's work? jace is not correct. the phrase more than suggests using the symbol > and jace did not use that symbol. jace is not correct. he was correct to use addition, but the equation should be 56+ p = 14 jace is not correct. the first number in the sentence is 56, so the equation should start with 56. jace is correct. the phrase more than suggests addition, so jace showed that 14 plus a variable equals 56. o

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Abox holds 500 paperclips. after a week on the teacher's desk 239 paperclips remained. how many paperclips were used?