Assignment 1

# Assignment 1 - STAT 331/361/SYDE 334 Assignment 1 Due...

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STAT 331/361/SYDE 334 Assignment 1 Due: Thursday, January 31 st in class Notes : Questions 2, 3, and 4 require some computation with R. Please include your R commands and output in the body of your assignment. For plots, please give them a title and label the axes. These questions are based on ones from the textbook, with a few of the numbers and actual question requirements changed. 1. Sometimes we may deal with a model where we know the intercept must be zero. In that case, the model takes the form y i = β 1 x i + ε i , i =1, 2, …, n , where ε i ~ N(0, σ 2 ) are independent errors. a) Find the Least Squares Estimates of β 1 and σ 2 b) Let 1 ˆ ii ey x i β =− be the residuals from the fitted model. Is it true that = 0? Why or why not? 1 n i i e = c) Prove that Var( 1 ˆ ) = 2 2 1 n i i x σ = 2. Calibration of measurement equipment is very important in reducing measurement error. To calibrate, we measure known x ’s and obtain the observed y ’s, and then fit a model to convert future measured y ’s back into x ’s.

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Assignment 1 - STAT 331/361/SYDE 334 Assignment 1 Due...

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