/*! 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 89 Let \(y=\) death rate and \(x=\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 89

Let \(y=\) death rate and \(x=\) average age of residents, measured for each county in Louisiana and in Florida. Draw a hypothetical scatterplot, identifying points for each state, such that the mean death rate is higher in Florida than in Louisiana when \(x\) is ignored, but lower when it is controlled.

Short Answer

Expert verified
Draw Florida points higher on y-axis without age control; lower when age is controlled.

Step by step solution

01

Understand the exercise

We are given that the mean death rate (y) is compared between counties in Louisiana and Florida, based on average age (x). Initially, we need to draw a scatterplot where the mean death rate in Florida appears higher than in Louisiana without considering age. However, when age is considered, Florida's death rate should appear lower than Louisiana's.
02

Represent the data without controlling x

Begin by drawing a scatterplot with "Death Rate" on the y-axis and "Average Age of Residents" on the x-axis. Plot two sets of points, one representing each state. To depict Florida having a higher mean death rate without controlling for age, ensure that the overall cluster of Florida points is positioned higher on the y-axis compared to Louisiana's cluster.
03

Add an age-controlled perspective

Now, add another layer to the scatterplot where differences in the average age (x-axis) are visible. Plot the data so that Florida points show lower death rates among older populations compared to Louisiana. This can be done by ensuring that, for similar age values, Florida's points tend to lie lower on the y-axis than Louisiana's.

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.

Death Rate Comparison
When analyzing data, comparing death rates between different regions can reveal important health insights. In our scenario, we begin by comparing mean death rates between Florida and Louisiana counties. Without controlling any variables, Florida appears to have a higher death rate. This initial observation might suggest poorer health conditions in Florida. Death rate comparison is critical, especially in health studies, as it helps identify regions requiring more health interventions.
However, just comparing averages can be misleading.
  • Death rates can be influenced by various factors not immediately apparent.
  • Factors like age, lifestyle, and socio-economic status can distort comparisons.
Thus, a deeper analysis is necessary to understand true health dynamics.
Average Age Analysis
The average age of residents in a region can significantly affect health outcomes and, consequently, death rates. Older populations often have higher death rates due to natural aging processes. In our exercise, the average age acts as a confounding variable.
At first glance, Florida seems to have worse health conditions due to higher death rates. Upon investigation, it's apparent that Florida's population is, on average, older.
  • The high average age skews the death rate upward.
  • This doesn't necessarily indicate poorer health, but rather reflects age distribution.
Age analysis helps clarify misconceptions and refine conclusions, ensuring that policies and health interventions are appropriately targeted.
Controlled Variables in Statistics
In statistical analysis, controlling variables is essential to draw accurate conclusions. When a variable like average age influences both the independent and dependent variables, it's termed a confounder. By ignoring such variables, we risk forming inaccurate conclusions.
In our exercise, by controlling the average age, we gain a clearer perspective.
  • Florida initially seems to have a higher death rate.
  • Once age is controlled, the mortality rate comparison reveals Florida fares better than Louisiana among older populations.
Controlled analysis sharpens focus and highlights the underlying factors affecting observed outcomes.
This approach is instrumental in fields such as epidemiology and public health.
Data Representation in Scatterplots
A scatterplot is a powerful tool for visualizing relationships between two variables, such as death rate and average age. In the exercise, drawing a scatterplot helps us intuitively understand the interactions between these entities for different regions.
Scatterplots allow for easy visual comparison.
  • They show how two variables relate across different groups, here being states.
  • Visual patterns like clusters and trends become apparent, guiding interpretation.
Incorporating age control into our scatterplot reveals refined trends.
Data representation through scatterplots is not just about drawing dots, but about uncovering deeper meanings and patterns hidden in the datasets.

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

For a study of University of Georgia female athletes, the prediction equation relating \(y=\) total body weight (in pounds) to \(x_{1}=\) height (in inches) and \(x_{2}=\) percent body fat is \(\hat{y}=-121+3.50 x_{1}+1.35 x_{2}\). a. Find the predicted total body weight for a female athlete at the mean values of 66 and 18 for \(x_{1}\) and \(x_{2}\). b. An athlete with \(x_{1}=66\) and \(x_{2}=18\) has actual weight \(y=115\) pounds. Find the residual, and interpret it.

When \(\alpha+\beta x=0,\) so that \(x=-\alpha / \beta,\) show that the logistic regression equation \(p=e^{\alpha+\beta x} /\left(1+e^{\alpha+\beta x}\right)\) gives \(p=0.50\)

When a model has a very large number of predictors, even when none of them truly have an effect in the population, one or two may look significant in \(t\) tests merely by random variation. Explain why performing the \(F\) test first can safeguard against getting such false information from \(t\) tests.

Consider the relationship between \(\hat{y}=\) annual income (in thousands of dollars) and \(x_{1}=\) number of years of education, by \(x_{2}=\) gender. Many studies in the United States have found that the slope for a regression equation relating \(y\) to \(x_{1}\) is larger for men than for women. Suppose that in the population, the regression equations are \(\mu_{y}=-10+4 x_{1}\) for men and \(\mu_{y}=-5+2 x_{1}\) for women. Explain why these equations imply that there is interaction between education and gender in their effects on income.

In the previous exercise, \(r^{2}=0.88\) when \(x_{1}\) is the predictor and \(R^{2}=0.914\) when both \(x_{1}\) and \(x_{2}\) are predictors. Why do you think that the predictions of \(y\) don't improve much when \(x_{2}\) is added to the model? (The association of \(x_{2}\) with \(y\) is \(r=0.5692 .)\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

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.