/*! 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 55 If there is a positive correlati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 55

If there is a positive correlation between number of years studying math and shoe size (for children), does that prove that larger shoes cause more studying of math or vice versa? Can you think of a confounding variable that might be influencing both of the other variables?

Short Answer

Expert verified
No, the correlation between shoe size and years of studying math in children does not imply causation. A possible confounding variable affecting both could be the age of the children.

Step by step solution

01

Understanding Correlation and Causation

First, it's important to understand the difference between correlation and causation. Correlation is when two factors appear to be related to each other, but it does not indicate that one causes the other. Causation means that one variable actually leads to a change in the other. Here, the example given states that there is a positive correlation between the number of years studying math and shoe size in children. However, this doesn't necessarily mean that larger shoes cause more studying of math or vice versa.
02

Identifying a Confounding Variable

A confounding variable is an extra variable that you haven't accounted for. It's some third element that's affecting both of the factors you're looking at. In the given example, the confounding variable could very likely be age. As a child goes older, they are likely to study math for more years and naturally, their shoe size increases as well.
03

Final Analysis and Conclusion

Although there is a correlation between shoe size and years of studying math, there is no evidence to suggest causation. The observed correlation is likely due to the influence of a third factor, age, which affects both shoe size and years of study. Thus, it would be incorrect to say that larger shoes cause more studying of math or vice versa.

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!

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

a. The first scatterplot shows the college tuition and percentage acceptance at some colleges in Massachusetts. Would it make sense to find the correlation using this data set? Why or why not? b. The second scatterplot shows the composite grade on the ACT (American College Testing) exam and the English grade on the same exam. Would it make sense to find the correlation using this data set? Why or why not?

Construct a set of numbers (with at least three points) with a strong negative correlation. Then add one point (an influential point) that changes the correlation to positive. Report the data and give the correlation of each set.

The table shows the Earned Run Average (ERA) and WHIP rating (walks plus hits per inning) for the top 40 Major League Baseball pitchers in the 2017 season. Top pitchers will tend to have low ERA and WHIP ratings. (Source: ESPN.com) a. Make a scatterplot of the data and state the sign of the slope from the scatterplot. Use WHIP to predict ERA. b. Use linear regression to find the equation of the best-fit line. Show the line on the scatterplot using technology or by hand. c. Interpret the slope. d. Interpret the \(y\) -intercept or explain why it would be inappropriate to do so. $$\begin{array}{|ll|} \hline \text { WHIP } & \text { ERA } \\ \hline 0.87 & 2.25 \\ \hline 0.95 & 2.31 \\ \hline 0.9 & 2.51 \\ \hline 1.02 & 2.52 \\ \hline 1.15 & 2.89 \\ \hline 0.97 & 2.9 \\ \hline 1.18 & 2.96 \\ \hline 1.04 & 2.98 \\ \hline1.31 & 3.09 \\ \hline 1.07 & 3.2 \\ \hline 1.13 & 3.28 \\ \hline 1.1 & 3.29 \\ \hline 1.35 & 3.32 \\ \hline 1.17 & 3.36 \\ \hline 1.32 & 3.4 \\ \hline 1.23 & 3.43 \\ \hline 1.25 & 3.49 \\ \hline 1.22 & 3.53 \\ \hline 1.19 & 3.53 \\ \hline 1.21 & 3.54 \\ \hline \end{array}$$ $$\begin{array}{|ll|} \hline \text { WHIP } & \text { ERA } \\ \hline 1.21 & 3.55 \\ \hline 1.22 & 3.64 \\ \hline 1.22 & 3.66 \\ \hline 1.27 & 3.82 \\ \hline 1.15 & 3.83 \\ \hline 1.16 & 3.86 \\ \hline 1.27 & 3.89 \\ \hline 1.35 & 3.9 \\ \hline1.28 & 3.92 \\ \hline 1.42 & 4.03 \\ \hline 1.26 & 4.07 \\ \hline 1.36 & 4.13 \\ \hline 1.28 & 4.14 \\ \hline 1.22 & 4.15 \\ \hline 1.33 & 4.16 \\ \hline 1.37 & 4.19 \\ \hline 1.2 & 4.24 \\ \hline 1.25 & 4.26 \\ \hline 1.3 & 4.26 \\ \hline 1.37 & 4.26 \\ \hline \end{array}$$

Data on the 3-point percentage, field-goal percentage, and free-throw percentage for a sample of 50 professional basketball players were obtained. Regression analyses were conducted on the relationships between 3 -point percentage and field-goal percentage and between 3 -point percentage and freethrow percentage. The StatCrunch results are shown below. (Source: nba.com) Simple linear regression results: Dependent Variable: 3 Point \(\%\) Independent Variable: Field Goal \% 3 Point \(\%=40.090108-0.091032596\) Field Goal \% Sample size: 50 \(\mathrm{R}\) (correlation coefficient) \(=-0.048875984\) \(\mathrm{R}-\mathrm{sq}=0.0023888618\) Estimate of error standard deviation: \(7.7329785\) Simple linear regression results: Dependent Variable: 3 Point \(\%\) Independent Variable: Free Throw \% 3 Point \(\%=-8.2347225+0.54224127\) Free Throw \(\%\) Sample size: 50 \(\mathrm{R}\) (correlation coefficient) \(=0.57040364\) \(\mathrm{R}-\mathrm{sq}=0.32536031\) Estimate of error standard deviation: \(6.3591944\) Based on this sample, is there a stronger association between 3 -point percentage and field-goal percentage or 3 -point percentage and freethrow percentage? Provide a reason for your choice based on the StatCrunch results provided.

Coefficient of Determination Does a correlation of \(-0.70\) or \(+0.50\) give a larger coefficient of determination? We say that the linear relationship that has the larger coefficient of determination is more strongly correlated. Which of the values shows a stronger correlation?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

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.