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Chapter 4: Problem 41

Indicate which variable you think should be the predictor \((x)\) and which variable should be the response \((y) .\) Explain your choices. a. You collect data on the number of gallons of gas it takes to fill up the tank after driving a certain number of miles. You wish to know how many miles you've driven based on the number of gallons it took to fill. up the tank. b. Data on salaries and years of experience at a two-year college are used in a lawsuit to determine whether a faculty member is being paid the correct amount for her years of experience. c. You wish to buy a belt for a friend and know only his weight. You have data on the weight and waist sizes for a large sample of adult men.

Short Answer

Expert verified
a) Predictor (x): Number of miles driven. Response (y): Number of gallons to fill up the tank.\nb) Predictor (x): Years of experience. Response (y): Faculty salary.\nc) Predictor (x): Weight of men. Response (y): Waist size for belts.

Step by step solution

01

Response to question a

In this case, the number of gallons it takes to fill up the tank is the dependent variable (y), because it depends on the number of miles driven. On the other hand, the number of miles driven is the independent variable (x), as it can be manipulated freely.
02

Response to question b

For this scenario, the faculty member's salary is the dependent variable (y) as it could change with the different amounts of experience. On the contrary, years of experience is the independent variable (x) since it is what is being used as a measure to see if it influences the salary they receive.
03

Response to question c

In this situation, the belt size is the dependent variable (y) because it might be directly affected by the friend's weight. The weight of the adult men is taken as an independent variable (x) as it can be controlled and used to predict the belt size.

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Key Concepts

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

Dependent Variable
A dependent variable is one that changes in response to another variable, usually called the independent variable. It's a central concept in any statistical analysis because it represents the outcome we are interested in predicting or understanding. In the context of our exercises:
  • In question (a), the amount of fuel required to fill the gas tank is our dependent variable. This is because the gallons depend on the number of miles driven.
  • For question (b), the faculty member's salary is dependent. It is influenced by their years of experience.
  • In question (c), waist size is affected by an individual's weight, making it the dependent variable.
The dependent variable is also known as the "response variable", which signifies its role in reacting or responding to changes in other variables.
Independent Variable
An independent variable is something that you can change or control in a model or experiment, and it causes an effect on the dependent variable. Think of it as the input side鈥攊t's what you change to see the effect on your subject. The exercises provide excellent examples:
  • In the first scenario (a), miles driven is the independent variable because it is the factor being manipulated to see its effect on fuel consumption.
  • For scenario (b), the years of experience are the independent variable as they are used to determine how much they affect salary.
  • In scenario (c), weight is an independent variable as it is being used to predict the belt size.
By identifying the independent variable, we set the stage for our investigations and analyses, helping us to structure our statistical models.
Statistical Analysis
Statistical analysis is the method of collecting, exploring, and presenting large amounts of data to discover patterns and trends. In our scenarios, statistical analysis is used to understand relationships between variables:
  • In question (a), we would analyze how the number of miles influences the fuel needed, typically using regression analysis techniques.
  • In question (b), analysis is required to see how years of experience affect salaries, which might involve calculating averages, variances, and possibly testing hypotheses regarding fairness in pay.
  • For question (c), statistical analysis might explore the correlation between weight and waist size, aiming to predict suitable belt sizes based on weight data.
Such a statistical approach allows for informed decision-making based on numerical data rather than gut feelings. Through thorough analysis, these questions can provide real-world insights into how these variables are interconnected.

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Most popular questions from this chapter

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