Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation co squares regression line is y = 0.208x+ 11.736. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.3 16.9 17.2 17.0 17.6 17.3 17.2 17.3 17.3 17.4 17.4 27 25.75 26 25 28 26.75 26 27 27 27.25 26.75 (a) Compute the coefficient of determination, R2. R2 : % (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model.

Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation co squares regression line is y = 0.208x+ 11.736. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.3 16.9 17.2 17.0 17.6 17.3 17.2 17.3 17.3 17.4 17.4 27 25.75 26 25 28 26.75 26 27 27 27.25 26.75 (a) Compute the coefficient of determination, R2. R2 : % (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 11PPS

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Question

Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.904 and the least squares regression line is y=0.208x+11.736. Complete parts (a) and (b) below.

Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.

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