Math Problem Statement

Suppose a doctor measures the​ height, x, and head​ circumference, y, of 8 children and obtains the data below. The correlation coefficient is

0.9690.969

and the least squares regression line is

ModifyingAbove y with caret equals 0.200 x plus 11.950y=0.200x+11.950.

Complete parts ​(a) and​ (b)**** below.

​Height, x

27.2527.25

25.2525.25

26.2526.25

25.2525.25

27.527.5

26.7526.75

25.7525.75

26.7526.75

2727

26.7526.75

26.7526.75   Head​ Circumference, y

17.317.3

17.017.0

17.217.2

17.017.0

17.517.5

17.317.3

17.117.1

17.317.3

17.417.4

17.317.3

17.317.3

Question content area bottom

Part 1

​(a)**** Compute the coefficient of​ determination,

Upper R squaredR2.

Upper R squaredR2equals=enter your response here​%

​(Round to one decimal place as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Correlation
Regression Analysis
Coefficient of Determination

Formulas

Coefficient of determination: R² = r²
Linear regression equation: y = mx + b

Theorems

Least Squares Method
Properties of Correlation Coefficient

Suitable Grade Level

Grades 10-12