/*! 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 4 In a鈥揹, each set of bivariate ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 4

In a鈥揹, each set of bivariate data has a causal relationship. Determine the explanatory and response variables for each set of data. a. height and weight of a student b. grade on a math test and number of hours the student studied c. number of hours worked and paycheck amount d. number of gallons of gas consumed and weight of a car

Short Answer

Expert verified
a. Explanatory variable: 'height', Response variable: 'weight'\n b. Explanatory variable: 'number of hours the student studied', Response variable: 'grade on a math test'\n c. Explanatory variable: 'number of hours worked', Response variable: 'paycheck amount'\n d. Explanatory variable: 'weight of a car', Response variable: 'number of gallons of gas consumed'.

Step by step solution

01

Identify explanatory and response variables for the first set of data

For 'height and weight of a student', the explanatory variable is the 'height' as it does not depend on the weight but instead, it could influence it. The response variable is the 'weight' because it could be affected by the height of a student.
02

Identify explanatory and response variables for the second set of data

In 'grade on a math test and number of hours the student studied', the number of 'hours the student studied' could influence the 'grade on a math test', which makes it the explanatory variable. Therefore, the 'grade on a math test' would be the response variable.
03

Identify explanatory and response variables for the third set of data

Regarding 'number of hours worked and paycheck amount', the 'number of hours worked' is the explanatory variable as it influences the 'paycheck amount'. Thus, the 'paycheck amount' is the response variable.
04

Identify explanatory and response variables for the fourth set of data

For 'number of gallons of gas consumed and the weight of a car', the 'weight of a car' could influence the 'number of gallons of gas consumed', therefore, it is the explanatory variable. The response variable would be the 'number of gallons of gas consumed'.

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.

Causal Relationships
Understanding causal relationships is crucial in analyzing bivariate data. A causal relationship implies that changes in one variable lead to changes in another.
This type of relationship differs from simply observing that two variables move together in a pattern. For example, if we consider the relationship between studying hours and test grades, there's a cause-and-effect link: more study time often leads to better grades.
Sometimes, identifying causal relationships involves controlled experiments where changes to one variable are observed and their effects measured on another.
  • Causality means one variable, the cause, directly affects another, the effect.
  • Not all correlated variables have a causal link; some may exhibit correlation without causation.
  • Clear causal relationships help us make predictions using explanatory and response variables.
Explanatory Variables
Explanatory variables, also known as independent variables, are key components in understanding causal relationships. These are the variables that we manipulate or consider as the cause to measure their effect on another variable.
In the context of bivariate data from the original exercise, let's identify the explanatory variables:
  • Height (in the relationship to weight) is an explanatory variable, as it can influence a person's weight.
  • The amount of time a student spends studying is explanatory because it can affect the test grades.
  • The hours worked can determine the paycheck, making hours a clear explanatory variable.
  • The car's weight is considered explanatory concerning gas consumption; heavier cars may use more gas.

Recognizing the right explanatory variables is crucial for data analysis as it sets the foundation for building models and understanding impacts.
Response Variables
Response variables, also known as dependent variables, are those that are affected by the explanatory variable. They represent the outcome or effect in the context of a study.
Understanding which are the response variables allows us to predict the outcomes based on changes in the explanatory variables.
The original exercise provides clear examples:
  • Weight is a response variable influenced by the student's height.
  • Test grades respond to the number of hours studied.
  • The amount of the paycheck is the response to the hours worked.
  • Gas consumption responds to how heavy the car is.

Choosing the correct response variable is essential for experiments and studies since it helps to measure the effect accurately of the explanatory variables.
Educational Problems
Educational problems often examine causality to enhance learning outcomes. By analyzing explanatory and response variables, educators and researchers can understand factors that contribute to student success or failure.
Take the example of studying hours affecting math test grades. This reflects a common educational inquiry: how instructional time impacts achievement.
Such analyses help in:
  • Designing effective study programs by focusing on impactful variables.
  • Improving teaching strategies based on causative factors.
  • Identifying barriers to learning that can be addressed for better performance.

Understanding and solving educational problems requires identifying the causal relationships and using explanatory and response variables effectively to craft improvement strategies.

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

Use the following situation to answer Exercises 4鈥�20. A company produces a security device known as Toejack. Toejack is a computer chip that parents attach between the toes of a child, so parents can track the child鈥檚 location at any time using an online system. The company has entered into an agreement with an Internet service provider, so the price of the chip will be low. Set up a demand function鈥攁 schedule of how many Toejacks would be demanded by the public at different prices. Fixed costs are \(\$ 24,500,\) and variable costs are \(\$ 6.12\) per Toejack. Express expenses, \(E\) , as a function of \(q,\) the quantity produced.

A supplier of school kits has determined that the combined fixed and variable expenses to market and sell G kits is W. a. What expression models the price of a school kit at the breakeven point? b. Suppose a new marketing manager joined the company and determined that the combined fixed and variable expenses would only be 80% of the cost if the supplier sold twice as many kits. Write an expression for the price of a kit at the breakeven point using the new marketing manager鈥檚 business model.

Determine the maximum profit and the price that would yield the maximum profit for each. a. \(P=-400 p^{2}+12,400 p-50,000\) b. \(P=-370 p^{2}+8,800 p-25,000\) c. \(P=-170 p^{2}+88,800 p-55,000\)

An automobile GPS system is sold to stores at a wholesale price of \(\$ 97 .\) A popular store sells them for \(\$ 179.99 .\) What is the store's markup?

The expense function for the Wonder Widget is \(E=4.14 q+55,789 .\) a. What is the fi xed cost in the expense function? b. What is the cost of producing 500 Wonder Widgets? c. What is the average cost per widget of producing 500 Wonder Widgets? Round to the nearest cent. d. What is the total cost of producing 600 Wonder Widgets? e. What is the average cost per widget of producing 600 Wonder Widgets? Round to the nearest cent. f. As the number of widgets increased from 500 to 600, did the average expense per widget increase or decrease? g. What is the average cost per widget of producing 10,000 Wonder Widgets? Round to the nearest cent.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.