Assignment_3_Solutions

# Assignment_3_Solutions - Assignment 3 Statistics 371...

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Assignment 3 Statistics 371 Solutions 1. In this question, we look at the use of the t and F distributions in testing hypotheses involving the coefficients of a regression model. a) Find (interpolate when necessary) , a constant c so that , and a constant d so that 20 (| | 1.90) Pt 10 (| | ) 0.90 c ≤= 6,30 ( 1.80) PF 10,10 (| | ) 0.90 d [Draw pictures if you have trouble with these calculations] From the tables, we have and so . Hence . Using R, we get 20 ( 1.725) 0.05 >= 20 ( 2.086) 0.025 20 ( 1.90) 0.04 >≈ 20 (| | 1.90) 0.08 ≥≈ 20 (| | 1.90) 0.072 ≥= From the tables, we have so 10 ( 1.812) 0.95 10 (| | 1.812) 0.90 = From tables, we have so . From R, we get 6,30 ( 1.98) 0.10 6,30 ( 1.80) 0.10 ≥> 6,30 ( 1.80) 0.133 Since , we have and from the tables 0 F 10,10 ( ) 0.90 d 2.32 d = In a packaging trial, a market research firm decided to investigate three different colours and two different styles of packaging leading to 6 different treatments, coded as below. The overall purpose of the investigation was to better understand how colour and style of packaging affected customer opinion of the product. colour style treatment x1 x2 x3 x4 x5 x6 Red 1 1 1 0 0 0 0 0 Red 2 2 0 1 0 0 0 0 Blue 1 3 0 0 1 0 0 0 Blue 2 4 0 0 0 1 0 0 Green 1 5 0 0 0 0 1 0 Green 2 6 0 0 0 0 0 1 Using a panel of 42 volunteers, they presented each of the six versions of the packaging to 7 of the volunteers. After explaining the goal, the volunteers were each given a questionnaire about the packaging. The response variate is the score on the questionnaire, a number out of 100. The data are in the file ass2q2.txt. b) A simple model to describe the data is 01 Y treatment R β = ++ . Explain why this simple model is a bad idea.

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The treatment number is an index, not a quantitative explanatory variate. For example this model implies that the effect of changing from treatment 2 to treatment 3 is the same as the effect of changing from treatment 4 to treatment 5. Alternately, consider the model . 2 12 3 4 5 6 123456 , ~ ( 0 , Yx x x x x x R R M V N I ββ β σ =+ + + + + + ) c) Check the fit of the model using the four basic plots. Are any remedies required?
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Assignment_3_Solutions - Assignment 3 Statistics 371...

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