Midterm_test_Mat_3375

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University of Ottawa *

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3375

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Mathematics

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Jan 9, 2024

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MAT 3375 Midterm test October 19 2023 Professor M. Alvo Time: 70 minutes Student number : Given name : Family name : This is an open book exam. Calculators are permitted. Answer all questions in the spaces provided. The test is out of 20. Each question is worth 2 points. 1
We are interested in studying the relationship between the degree of brand liking Y and moisture content ( X 1 ) and sweetness ( X 2 ) of a certain product. The data is given below Liking Moisture Sweetness 1 64 4 2 2 73 4 4 3 61 4 2 4 76 4 4 5 72 6 2 6 80 6 4 7 71 6 2 8 83 6 4 9 83 8 2 10 89 8 4 11 86 8 2 12 93 8 4 13 88 10 2 14 95 10 4 15 94 10 2 16 100 10 4 Mean 81.75 7 3 Variance 131.1333 5.333 1.0667 2
a. What can you deduce from the scatter and Box plots below? 3
b. Indicate the usual assumptions made in fitting the following simple linear model Y i = β 0 + β 1 X i 1 + ε i , i = 1 , ..., 16 c. Complete the analysis of variance table below whereby the degree of brand liking Y is regressed against moisture content ( X 1 ) . Response: Liking Sum of Squares df Mean Square F p-value Moisture 1566.45 Residuals 400.55 Total 15 4
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