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A professional body wishes to analyse the performance of its students on a particular two-part examination. It records the scores obtained by a sample of 12 students on the first part of the exam, and the scores obtained by the same students on the second part of the exam. The results are as follows: Student 1 2 3 4 5 6 7 8 9 10 11 12 First-partexamscorex(%) 82 49 73 60 61 77 65 85 91 53 59 73 Second-partexamscorey(%) 76 58 75 66 70 71 76 92 87 59 63 71 ?x=828, ?y=864, ?x2 =59,054, ?y2 =63,362, (a) Calculate the fitted linear regression equation of y on x. (b) Calculate an estimate for the error variance σ2. (c) Write down the ANOVA table.

A professional body wishes to analyse the performance of its students on a particular two-part examination. It records the scores obtained by a sample of 12 students on the first part of the exam, and the scores obtained by the same students on the second part of the exam. The results are as follows: Student 1 2 3 4 5 6 7 8 9 10 11 12 First-partexamscorex(%) 82 49 73 60 61 77 65 85 91 53 59 73 Second-partexamscorey(%) 76 58 75 66 70 71 76 92 87 59 63 71 ?x=828, ?y=864, ?x2 =59,054, ?y2 =63,362, (a) Calculate the fitted linear regression equation of y on x. (b) Calculate an estimate for the error variance σ2. (c) Write down the ANOVA table.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
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A professional body wishes to analyse the performance of its students on a particular two-part examination. It records the scores obtained by a sample of 12 students on the first part of the exam, and the scores obtained by the same students on the second part of the exam. The results are as follows: Student 1 2 3 4 5 6 7 8 9 10 11 12 First-partexamscorex(%) 82 49 73 60 61 77 65 85 91 53 59 73 Second-partexamscorey(%) 76 58 75 66 70 71 76 92 87 59 63 71 ?x=828, ?y=864, ?x2 =59,054, ?y2 =63,362, (a) Calculate the fitted linear regression equation of y on x. (b) Calculate an estimate for the error variance σ2. (c) Write down the ANOVA table. (d) Perform an F-test to test the null hypothesis that there is no linear relationship (3) (2) (5) between x and y, based on the above table. (4) (e) Calculate the proportion of variation explained by the model and comment.
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