Chapter 3: Q. 36 (page 191)

An eccentric professor believes that a child with an IQ $100$ should have a reading test score $50$ and that the reading score should increase by $1$ a point for every additional point of IQ. What is the equation of the professor’s regression line for predicting reading scores from IQ?

Short Answer

Expert verified

The equation is $\hat{y} = x - 50$ .

Step by step solution

Given Information

We have,

$x =$ IQ score starting from $100$

Reading test scorelocalid="1649920422526" $= 50$

$y =$ reading test score

The reading test score $y$ increases by $1$ a point per every additional point of $IQ x$ :

$\hat{y} = a + 1 x = a + x$

with $a$ some constant.

Explanation

The reading test score for a child with an IQ of $100$ may be $50$ , depending on the IQ of the child.

We need $y = 50$ when $x = 100$ .

Analyze the equation at $x = 100$ :

localid="1650004532020" $\hat{y} = a + x = a + 100$

We need $y = 50$ when $x = 100$ so,

$a + 100 = 50$

Subtract the equation with $100,$

localid="1650004514276" $a = 50 - 100 = - 50$

Accordingly, the equation for predicting reading scores from IQ using the professor's regression line is:

localid="1650004499566" $\hat{y} = a + x = - 50 + x = x - 50$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

An eccentric professor believes that a child with an IQ $100$ should have a reading test score $50$ and that the reading score should increase by $1$ a point for every additional point of IQ. What is the equation of the professor’s regression line for predicting reading scores from IQ?

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

An eccentric professor believes that a child with an IQ 100should have a reading test score 50and that the reading score should increase by 1 a point for every additional point of IQ. What is the equation of the professor’s regression line for predicting reading scores from IQ?

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

An eccentric professor believes that a child with an IQ $100$ should have a reading test score $50$ and that the reading score should increase by $1$ a point for every additional point of IQ. What is the equation of the professor’s regression line for predicting reading scores from IQ?