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.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The
Transcribed Image Text: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.
Height, x
Head Circumference, y 17.3 16.9 17.2 17.0 17.6 17.3 17.2 17.3
27 25.75
26
25
28
26.75
26
27
27
27.25 26.75
17.3 17.4 17.4
(a) Compute the coefficient of determination, R2.
R = % (Round to one decimal place as needed.)
(b) Interpret the coefficient of determination.
Approximately % of the variation in
is explained by the least-squares regression model.
(Round to one decimal place as needed.)
Expert Solution
Step 1
The correlation coefficient (r)=0.904
we know that,
coefficient of determination measure variability in Y( Dependent variable) explained by x ( independent variables)
a) coefficient of determination= r^2
=( 0.904)^2
= 0.817×100
R^2 =81.7%
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