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Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of Height of son, father, x y (in (in centimeters) centimeters) 186.7 174.9 190.1 185.7 173.9 178.6 193.2 189.8 181.7 189.0 171.6 182.3 188.0 187.9 157.4 175.1 201.8 190.3 160.1 173.3 181.2 175.9 161.3 166.5 190.0 195.7 174.7 174.7 170.8 170.1 Send data to calculator V xy 32,653.83 35,301.57 31,058.54 36,669.36 34,341.3 31,282.68 35,325.2 27,560.74 38,402.54 27,745.33 31,873.08 26,856.45 37,183 30,520.09 29,053.08 Height of son (in centimeters) 210+ 200- 190- 180- 170+ 160- 150- Figure 1 150 160 170 180 190 200 210 Height of father (in centimeters) What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)

Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of Height of son, father, x y (in (in centimeters) centimeters) 186.7 174.9 190.1 185.7 173.9 178.6 193.2 189.8 181.7 189.0 171.6 182.3 188.0 187.9 157.4 175.1 201.8 190.3 160.1 173.3 181.2 175.9 161.3 166.5 190.0 195.7 174.7 174.7 170.8 170.1 Send data to calculator V xy 32,653.83 35,301.57 31,058.54 36,669.36 34,341.3 31,282.68 35,325.2 27,560.74 38,402.54 27,745.33 31,873.08 26,856.45 37,183 30,520.09 29,053.08 Height of son (in centimeters) 210+ 200- 190- 180- 170+ 160- 150- Figure 1 150 160 170 180 190 200 210 Height of father (in centimeters) What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of father, x Height of son, y (in centimeters) 174.9 185.7 178.6 189.8 189.0 182.3 187.9 175.1 190.3 173.3 175.9 166.5 195.7 174.7 170.1 (in centimeters) 186.7 190.1 173.9 193.2 181.7 171.6 188.0 157.4 201.8 160.1 181.2 161.3 190.0 174.7 170.8 Send data to calculator ху 32,653.83 35,301.57 31,058.54 36,669.36 34,341.3 31,282.68 35,325.2 27,560.74 38,402.54 27,745.33 31,873.08 26,856.45 37,183 30,520.09 29,053.08 Height of son (in centimeters) 210+ 200+ 190+ 180- 170+ 160- 150- Figure 1 150 160 170 180 190 200 210 Height of father (in centimeters) What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)
Transcribed Image Text:Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of father, x Height of son, y (in centimeters) 174.9 185.7 178.6 189.8 189.0 182.3 187.9 175.1 190.3 173.3 175.9 166.5 195.7 174.7 170.1 (in centimeters) 186.7 190.1 173.9 193.2 181.7 171.6 188.0 157.4 201.8 160.1 181.2 161.3 190.0 174.7 170.8 Send data to calculator ху 32,653.83 35,301.57 31,058.54 36,669.36 34,341.3 31,282.68 35,325.2 27,560.74 38,402.54 27,745.33 31,873.08 26,856.45 37,183 30,520.09 29,053.08 Height of son (in centimeters) 210+ 200+ 190+ 180- 170+ 160- 150- Figure 1 150 160 170 180 190 200 210 Height of father (in centimeters) What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)
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