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Problem 5. Infestation of crops by insects has long been of great concern to farmers and agri- cultural scientists. The article " Cotton Square Damage by the Plant Bug, Lygus hesperus, and Abscission Rates" (J. Econ. Entomology, 1988:1328-1337) reports data on X = age of a cotton plant (days) and Y =% damaged square. Consider the n = 11 observations studied in the ar- ticle. The summary statistics are listed in the following table. Suppose one used simple linear regression to analyze the data. Σ Σ Σ Σ Σ 479 213 4,653 26,985 10,953 (1). What is the sample correlation coefficient between X and Y? (2). What are the least squares estimates of Bo and B1? (3). Let ŷ, = Bo+B¡I, where Bg and ß¡ are the least squares estimates of Bo and B, respectively. Show that i=1 i=1

Problem 5. Infestation of crops by insects has long been of great concern to farmers and agri- cultural scientists. The article " Cotton Square Damage by the Plant Bug, Lygus hesperus, and Abscission Rates" (J. Econ. Entomology, 1988:1328-1337) reports data on X = age of a cotton plant (days) and Y =% damaged square. Consider the n = 11 observations studied in the ar- ticle. The summary statistics are listed in the following table. Suppose one used simple linear regression to analyze the data. Σ Σ Σ Σ Σ 479 213 4,653 26,985 10,953 (1). What is the sample correlation coefficient between X and Y? (2). What are the least squares estimates of Bo and B1? (3). Let ŷ, = Bo+B¡I, where Bg and ß¡ are the least squares estimates of Bo and B, respectively. Show that i=1 i=1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Problem 5. Infestation of crops by insects has long been of great concern to farmers and agri- cultural scientists. The article " Cotton Square Damage by the Plant Bug, Lygus hesperus, and Abscission Rates" (J. Econ. Entomology, 1988:1328-1337) reports data on X = age of a cotton plant (days) and Y =% damaged square. Consider the n ticle. The summary statistics are listed in the following table. Suppose one used simple linear regression to analyze the data. 11 observations studied in the ar- %3D 213 4,653 479 26,985 10,953 (1). What is the sample correlation coefficient between X and Y? (2). What are the least squares estimates of Bo and B1? Let ŷ, = Bo+B1#1, where B, and B, are the least squares estimates of Bo and B1, respectively. Show that i=1 (4). Suppose (4: – în)² = 800.65. Is there a significant linear relationship between the two variables at a significance level a= 0.01?
Transcribed Image Text:Problem 5. Infestation of crops by insects has long been of great concern to farmers and agri- cultural scientists. The article " Cotton Square Damage by the Plant Bug, Lygus hesperus, and Abscission Rates" (J. Econ. Entomology, 1988:1328-1337) reports data on X = age of a cotton plant (days) and Y =% damaged square. Consider the n ticle. The summary statistics are listed in the following table. Suppose one used simple linear regression to analyze the data. 11 observations studied in the ar- %3D 213 4,653 479 26,985 10,953 (1). What is the sample correlation coefficient between X and Y? (2). What are the least squares estimates of Bo and B1? Let ŷ, = Bo+B1#1, where B, and B, are the least squares estimates of Bo and B1, respectively. Show that i=1 (4). Suppose (4: – în)² = 800.65. Is there a significant linear relationship between the two variables at a significance level a= 0.01?
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