420Hw09 - ) 1 = & & & ---- 28 168 42 84 168 84...

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STAT 420 Fall 2008 Homework #9 (due Friday, October 31, by 3:00 p.m.) From the textbook: 1. 5.12 (d) x y y ˆ = 5 x e = y y ˆ 1.0 3.4 5 1.6 1.2 7.0 6 1.0 1.4 6.0 7 1.0 1.6 9.0 8 1.0 1.8 8.0 9 1.0 Recall Homework 4: ˆ = = = n i i n i i i x y x 1 2 1 = 5. 2.0 11.0 10 1.0 Without β 0 in the model, SSTotal = Y T Y = Σ y 2 , dfTotal = n . SSE = Σ e 2 . Without β 0 in the model, RegrSS = Y Y ˆ ˆ T = 2 y ˆ = Σ 2 ˆ x 2 . 2. 6.12 ________________________________________________________________________ x 1 x 2 y 3 5 13 3 7 18 2 5 10 2 6 10 2 7 14 1 5 8 3. Do NOT use a computer for this problem. Consider the model of the form: Y i = β 0 + β 1 X i 1 + β 2 X i 2 + e i , i = 1, 2, … , 7, where e i ’s are independent N ( 0 , σ 2 ) random variables. 1 7 11
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X T X = ± ² ³ ³ ³ ³ ´ µ 2 2 2 1 2 2 1 2 1 1 2 1 i i i i i i i i i i x x x x x x x x x x n = ± ² ³ ³ ³ ´ µ 258 84 42 84 32 14 42 14 7 , ( X T X
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Unformatted text preview: ) 1 = & & & ---- 28 168 42 84 168 84 1200 168 1 , X T Y = & & & 2 1 i i i i i y x y x y = & & & 516 180 84 . a) Fill in the blanks (you can give a range for p-value): Call: lm(formula = Y ~ X1 + X2) Residuals: 1 2 3 4 5 6 7 0 1 0 -2 0 1 0 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) X1 X2 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: on degrees of freedom Multiple R-Squared: , Adjusted R-squared: F-statistic: on and DF, p-value: b) Construct a 95% prediction interval for the value of Y at x 1 = 3 and x 2 = 6....
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This note was uploaded on 05/09/2010 for the course MATH 420 taught by Professor Stepanov during the Spring '10 term at University of Illinois, Urbana Champaign.

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420Hw09 - ) 1 = & & & ---- 28 168 42 84 168 84...

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