Math Problem Statement

Researchers wondered if brain size has an effect on a​ person's IQ. From a sample of 20​ individuals, the equation of the​ least-squares regression line is

ModifyingAbove y with caretyequals=71.8plus+​0.0286x,

where x represents the size of a brain in cubic centimeters and y represents IQ. What is the interpretation of the​ slope?

Question content area bottom

Part 1

Choose the correct answer below.

A.

IQ is predicted to increase by 71.8 for every 1 cubic centimeter increase in brain size.

B.

IQ is predicted to be 71.8 for a brain size of 0 cubic centimeters.

C.

IQ is predicted to increase by 0.0286 for every 1 cubic centimeter increase in brain size.

D.

A​ person's brain size is predicted to be 0.0286 cubic centimeters if their IQ is 0.

E.

A​ person's brain size is predicted to increase by 71.8 cubic centimeters for every​ one-unit increase in their IQ.

F.

A​ person's brain size is predicted to increase by 0.0286 cubic centimeters for every​ one-unit increase in their IQ.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Regression Analysis
Slope Interpretation

Formulas

Least-squares regression line: y = mx + b

Theorems

Least-Squares Regression Theorem
Slope-Intercept Form

Suitable Grade Level

Grades 10-12