sta108samplefinal

sta108samplefinal - Statistics 108 Instructor: Prabir...

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Statistics 108 Sample Final Examination Instructor: Prabir Burman Show all Work 1. An experiment was conducted to study the relationship between the amount of a certain chemical additive (X, in grams) and the drying time (Y) of a varnish. Two models were fitted with x=X- X =X-4.5, on the basis of 8 samples. Y ˆ =5.2625-0.2202x, SSE=8.1815, Y ˆ =4.2154-0.2203x+0.1994x 2 , SSE=1.5015. a) Is a linear fit appropriate? Carry out a test at a 0.01 level of significance to decide this. Find the p- value of your test. b) Using the quadratic regression model, estimate the mean drying time when the amount of additive is equal to 5.0. c) Obtain the regression Y ˆ = 0 b + 1 b X+ 11 b X 2 in the original variable by finding 0 b , 1 b and 11 b . 2. A land developer was interested in creating a model to use for estimating the selling price of beach lots on the Oregon coast. To do so, he recorded the following items for each of 20 beach lots recently sold: Y=sale price of beach lot (in thousands of dollars), X 1 = area of lot (in hundreds of square feet), X 2 =elevation of lot, X 3 =slope of lot The fitted regression line is given below Y ˆ =-2.491+0.099X 1 +0.029X 2 +0.086X 3 , s(b 1 )=0.068, s(b 2 )=0.006, s(b 3 )=0.031, SSTO=27.313, SSE=5.903.
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sta108samplefinal - Statistics 108 Instructor: Prabir...

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