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Finding a least-squares regression line is a very useful tool in statistics. Usually this is done using several messy formulas, but we can use what we learned about projections to find the answer much more elegantly. A group of students took a quiz, and we want to use a sample of the results to predict other scores. Before the quiz, a sample of five students had missed 0,1,2, 3, and 6 classes. They scored, respectively, 9, 8, 5, 6, and 2 points. Assume that there is an approximately linear relationship between the variables. 1. Let x be the number of classes a student misses (the explanatory variable) and y be the quiz Score (the response variable.) Suppose all of these points lay on the same line, y = C + Dx. Write a system of (five) equations in the variables C and D. Then rewrite the system as a matrix equation. 2. This system (clearly) has no solution. Find the least-squares solution by left-multiplying by the matrix A". Use the solution to write the line of best fit ŷ = C + Dx. (Notation note: in statistics, ŷ is used for this line that approximates the points.) 3. Suppose another student with 3 absences takes the quiz. What score does your model predict they will get?

Finding a least-squares regression line is a very useful tool in statistics. Usually this is done using several messy formulas, but we can use what we learned about projections to find the answer much more elegantly. A group of students took a quiz, and we want to use a sample of the results to predict other scores. Before the quiz, a sample of five students had missed 0,1,2, 3, and 6 classes. They scored, respectively, 9, 8, 5, 6, and 2 points. Assume that there is an approximately linear relationship between the variables. 1. Let x be the number of classes a student misses (the explanatory variable) and y be the quiz Score (the response variable.) Suppose all of these points lay on the same line, y = C + Dx. Write a system of (five) equations in the variables C and D. Then rewrite the system as a matrix equation. 2. This system (clearly) has no solution. Find the least-squares solution by left-multiplying by the matrix A". Use the solution to write the line of best fit ŷ = C + Dx. (Notation note: in statistics, ŷ is used for this line that approximates the points.) 3. Suppose another student with 3 absences takes the quiz. What score does your model predict they will get?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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Finding a least-squares regression line is a very useful tool in statistics. Usually this is done using several messy formulas, but we can use what we learned about projections to find the answer much more elegantly. A group of students took a quiz, and we want to use a sample of the results to predict other scores. Before the quiz, a sample of five students had missed 0,1,2, 3, and 6 classes. They scored, respectively, 9, 8, 5, 6, and 2 points. Assume that there is an approximately linear relationship between the variables. 1. Let x be the number of classes a student misses (the explanatory variable) and y be the quiz Score (the response variable.) Suppose all of these points lay on the same line, y = C + Dx. Write a system of (five) equations in the variables C and D. Then rewrite the system as a matrix equation. 2. This system (clearly) has no solution. Find the least-squares solution by left-multiplying by the matrix A". Use the solution to write the line of best fit ŷ = C + Dx. (Notation note: in statistics, ŷ is used for this line that approximates the points.) 3. Suppose another student with 3 absences takes the quiz. What score does your model predict they will get?
Transcribed Image Text:Finding a least-squares regression line is a very useful tool in statistics. Usually this is done using several messy formulas, but we can use what we learned about projections to find the answer much more elegantly. A group of students took a quiz, and we want to use a sample of the results to predict other scores. Before the quiz, a sample of five students had missed 0,1,2, 3, and 6 classes. They scored, respectively, 9, 8, 5, 6, and 2 points. Assume that there is an approximately linear relationship between the variables. 1. Let x be the number of classes a student misses (the explanatory variable) and y be the quiz Score (the response variable.) Suppose all of these points lay on the same line, y = C + Dx. Write a system of (five) equations in the variables C and D. Then rewrite the system as a matrix equation. 2. This system (clearly) has no solution. Find the least-squares solution by left-multiplying by the matrix A". Use the solution to write the line of best fit ŷ = C + Dx. (Notation note: in statistics, ŷ is used for this line that approximates the points.) 3. Suppose another student with 3 absences takes the quiz. What score does your model predict they will get?
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