/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 For each of the following pairs ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 10

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Weight of a car and gas mileage b. Size and selling price of a house c. Height and weight d. Height and number of siblings

Short Answer

Expert verified
a. Negative correlation, as heavier cars consume more fuel, leading to lower gas mileage. b. Positive correlation, as larger houses generally tend to have higher prices. c. Positive correlation, since taller individuals usually have greater weights. d. Correlation close to 0, because there is no direct relationship between height and the number of siblings.

Step by step solution

01

a. Weight of a car and gas mileage

We would expect a negative correlation between the weight of a car and its gas mileage. This is due to the fact that heavier cars generally tend to consume more fuel for the same distance driven, thus having a lower gas mileage. Increased weight typically requires more energy to move and overcome friction, which means that cars with higher weights will in most cases burn more fuel to cover the same distance. Therefore, as the weight of a car increases, its gas mileage tends to decrease, implying a negative correlation.
02

b. Size and selling price of a house

We would expect a positive correlation between the size of a house and its selling price. This is because larger houses generally tend to have higher prices than smaller ones. Size often correlates with the number of rooms, the quality of the construction and the overall living space provided, which are factors that influence the value of a property. Therefore, as the size of a house increases, its selling price is also likely to increase, implying a positive correlation.
03

c. Height and weight

We would expect a positive correlation between height and weight. This is due to the fact that taller individuals generally tend to have greater weights than shorter individuals. Height contributes to the overall mass a person carries. There is more room for the body to store fat, and bigger mass raises the weight of bones, blood and other organs, resulting in an overall increase in body weight. Therefore, as someone's height increases, their weight tends to increase as well, implying a positive correlation.
04

d. Height and number of siblings

We would expect a correlation close to 0 between height and the number of siblings. This is because a person's height is primarily influenced by genetics, nutrition, and health, while the number of siblings is determined by their family's decisions about children and other external factors. There is no direct relationship between these two variables and any correlation observed may be purely coincidental. Thus, the correlation between height and the number of siblings is not expected to be significant, and most likely would be close to 0.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Positive Correlation
A positive correlation is when two variables move in the same direction, meaning as one increases, the other also tends to increase.
This relationship can help predict how one variable changes in response to another. For example, think of the size and selling price of a house.
Generally, larger homes cost more. Why? Because more space often means more rooms and amenities, boosting the price. So, as the size of a house goes up, so does its price.
This is a classic example of positive correlation:
  • More space 鈫� Higher price
  • More amenities 鈫� Higher price
Knowing these relationships can make things like market predictions and personal budgeting much easier.
Negative Correlation
A negative correlation describes a situation where one variable increases as the other decreases. They move in opposite directions, which can be intriguing and insightful.
For instance, consider the weight of a car and its gas mileage. In general, heavier cars often get fewer miles per gallon. Why does this happen?
It's because it takes more energy and thus more fuel to move heavier cars.
Here's how it looks:
  • Heavier car 鈫� Lower gas mileage
  • More weight 鈫� More fuel consumption
By understanding negative correlations, we can make more informed choices, like selecting a more fuel-efficient vehicle.
Zero Correlation
Zero correlation occurs when there is no observable relationship between two variables. This means changes in one variable don't predict any changes in the other.
An example is the height of a person and the number of siblings they have.
These two factors are usually unrelated; your height is influenced by genetics and diet, while sibling count is determined by family decisions.
So, we expect zero correlation here:
  • Height doesn't affect number of siblings
  • Number of siblings doesn't affect height
Recognizing zero correlations helps us understand when variables are independent, which can refine data analysis.
Variables and Relationships
Whenever we look at variables, we're essentially looking for patterns or relationships that can help us understand the real world better.
Variables are characteristics or properties that can vary. In data studies, they are essential as they allow us to measure and predict outcomes.
Let's break it down:
  • Variables: These are the elements we study. They could be anything from the size of a car to the number of siblings.
  • Relationships: These showcase how variables are connected. Are they affected by one another, or are they independent?
By analyzing these relationships, we can identify correlations鈥攑ositive, negative, or zero. Knowing these can help in predicting trends, making decisions, and understanding complexities in fields from science to economics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The paper "Noncognitive Predictors of Student Athletes' Academic Performance" (Journal of College Reading and Learning [2000]: e167) summarizes a study of 200 Division I athletes. It was reported that the correlation coefficient for college grade point average (GPA) and a measure of academic self-worth was \(r=0.48\). Also reported were the correlation coefficient for college GPA and high school GPA \((r=0.46)\) and the correlation coefficient for college GPA and a measure of tendency to procrastinate \((r=-0.36) .\) Write a few sentences summarizing what these correlation coefficients tell you about GPA for the 200 athletes in the sample.

The article "That's Rich: More You Drink, More You Earn" (Calgary Herald, April 16,2002 ) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will increase income? Explain why or why not.

Explain why it can be misleading to use the least squares regression line to obtain predictions for \(x\) values that are substantially larger or smaller than the \(x\) values in the data set.

Is the following statement correct? Explain why or why not. A correlation coefficient of 0 implies that there is no relationship between two variables.

Medical researchers have noted that adoles- - Medical researchers have noted that adolles cent females are much more likely to deliver lowbirth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother's age. One such study is described in the article "Body Size and Intelligence in 6 -Year-Olds: Are Offspring of Teenage Mothers at Risk?" (Maternal and Child Health Journal [2009]: 847-856). The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article and also with data published by the National Center for Health Statistics. $$\begin{array}{lcccccc} \text { Mother's age } & 15 & 17 & 18 & 15 & 16 & 19 \\ \text { Birth weight } & 2289 & 3393 & 3271 & 2648 & 2897 & 3327 \end{array}$$ $$\begin{array}{lcccc} \text { Mother's age } & 17 & 16 & 18 & 19 \\ \text { Birth weight } & 2970 & 2535 & 3138 & 3573 \end{array}$$ a. If the goal is to learn about how birth weight is related to mother's age, which of these two variables is the response variable and which is the predictor variable? b. Construct a scatterplot of these data. Would it be reasonable to use a line to summarize the relationship between birth weight and mother's age? c. Find the equation of the least squares regression line. d. Interpret the slope of the least squares regression line in the context of this study. e. Does it make sense to interpret the intercept of the least squares regression line? If so, give an interpretation. If not, explain why it is not appropriate for this data set. (Hint: Think about the range of the \(x\) values in the data set.) f. What would you predict for birth weight of a baby born to an 18 -year-old mother? g. What would you predict for birth weight of a baby born to a 15 -year-old mother? h. Would you use the least squares regression equation to predict birth weight for a baby born to a 23 -year-old mother? If so, what is the predicted birth weight? If not, explain why.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.