If Q has orthonormal columns, what is the least squares solution x to Qx = b?

Please answer 1 and 2

A statistics student is studying if there is a relationship between the price of a used car and the number of miles Using the computer output, what is the equation of the least-squares regression line? it has been driven. She collects data for 20 cars of the ý = -0.181 + 24157.2x same model with different mileage, and determines each car's price using a used car website. The analysis is ý = 24157.2 -0.181x given in the computer output. ý = 2164.1 + 0.024x Predictor Coef SE Coef t-ratio Oŷ = 0.024 + 2164.1x Constant 24157.2 2164.1 2.965 0.046 Mileage -0.181 0.024 5.377 0.000 S 3860.7 R-Sq = 68.0% R-Sq(Adj) = 67.5%

A certain experiment produces the data (1, 1.8), (2,2.7), (3, 3.4), (4, 3.8), (5, 3.9) Describe the model that produces a least-squares fit of these points bya function of the form у %3D Вух + Вx? Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price to be set for the product. a. Give the design matrix, the observation vector, and the unknown parameter vector. b. [M] Find the associated least-squares curve for the data.

Each month for several months, the average temperature in °C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.11x.  a) Predict the number of pounds of steam consumed in a month where the average temperature is 65°C. Round the answer to two decimal places. b) If two months differ in their average temperatures by 5°C, by how much do you predict the number of pounds of steam consumed to differ? Round the answer to two decimal places.