# Hw7 - Homework 7(due Apr 2 1 Consider the following 4...

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Homework 7 (due Apr. 2) 1. Consider the following 4 sample points (given in the format ( x, y )): (1, 2), (2, 4.2), (3, 5.9), (4, 8.3). We want to fit a simple regression model using the matrix method for multiple regression. Note: DO NOT use Minitab for this problem. a) Write down the matrix X and the vector y . b) Calculate the matrix C = ( X 0 X ) - 1 . For inverting, you can use the formula for 2 × 2 matrices from the lecture notes. c) Find the vector of estimated regression coefficients ˆ β . What are the estimated slope and intercept? d) Using the results in (c), find the residuals, and use them to estimate σ 2 . e) Using the estimated value of σ 2 , find 95% confidence interval on the mean response and 95% prediction interval for x 0 = 2 . 5. Note that for the vector x 0 0 you would have to use (1, 2.5). 2. The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x 1 ), the num- ber of days in the month ( x 2 ), the average product purity ( x 3 ), and the tons of product produced ( x 4 ). The past year’s historical data are available and

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