Do the given vectors form an orthogonal basis for ℝ3? v1 = 1 0 −1 , v2 = 2 4 2 , v3 = 3 −3 3 Yes, the given set does form an orthogonal basis for ℝ3. No, the given set does not form an orthogonal basis for ℝ3. You are given the theorem below. Let {v1, v2, , vk} be an orthogonal basis for a subspace W of ℝn and let w be any vector in W. Then the unique scalars c1, , ck such that w = c1v1 + + ckvk are given by ci = w · vi vi · vi for i = 1, , k. Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w]basis B of w with respect to the basis basis B = {v1, v2, v3} of ℝ3. w = 1 1 1 [w]basis B =

1. the manager of collins import autos believes the number of cars sold in a day (q) depends on two factors: (1) the number of hours the dealership is open (h) and (2) the number of salespersons working that day (s). after collecting data for two months (53 days), the manager estimates the following log-linear model: q 4 equation 1 a. explain, how to transform the log-linear model into linear form that can be estimated using multiple regression analysis. the computer output for the multiple regression analysis is shown below: q4 table b. how do you interpret coefficients b and c? if the dealership increases the number of salespersons by 20%, what will be the percentage increase in daily sales? c. test the overall model for statistical significance at the 5% significance level. d. what percent of the total variation in daily auto sales is explained by this equation? what could you suggest to increase this percentage? e. test the intercept for statistical significance at the 5% level of significance. if h and s both equal 0, are sales expected to be 0? explain why or why not? f. test the estimated coefficient b for statistical significance. if the dealership decreases its hours of operation by 10%, what is the expected impact on daily sales?