Skip to main content
Ch. 2 - Exploring Data with Tables and Graphs
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 2 - Exploring Data with Tables and GraphsProblem 2.4.4a
Chapter 2, Problem 2.4.4a

Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults.


a. Their heights are measured in inches and those same heights are recorded in centimeters .

Verified step by step guidance
1
Understand the problem: The goal is to estimate the linear correlation coefficient (r) for the paired data. The data consists of heights measured in inches and the same heights recorded in centimeters. Since these two variables are directly proportional, we expect a strong positive linear relationship.
Recall the formula for the linear correlation coefficient (r): r measures the strength and direction of the linear relationship between two variables. It is calculated as: r = ∑(x-x¯)(y-y¯)∑(x-x¯)2∑(y-y¯)2, where x and y are the paired data points, and x̄ and ȳ are their respective means.
Analyze the relationship: Since the heights in inches and centimeters are directly proportional (1 inch = 2.54 cm), the scatterplot of the data would form a perfect straight line with a positive slope. This indicates a very strong positive correlation.
Estimate the value of r: Based on the direct proportionality and the perfect linear relationship, the value of r is expected to be very close to 1. This is because r = 1 represents a perfect positive linear correlation.
Conclude: Without performing calculations, we can confidently estimate that the linear correlation coefficient r for this data is approximately 1, given the direct proportionality between the two variables.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Correlation Coefficient (r)

The linear correlation coefficient, denoted as r, quantifies the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation. Understanding r is crucial for interpreting how closely two sets of data are related.
Recommended video:
Guided course
05:43
Correlation Coefficient

Units of Measurement

Units of measurement refer to the standard quantities used to express physical quantities, such as inches and centimeters for height. When analyzing data, it is important to recognize that while the numerical values may differ due to unit conversion, the underlying relationship between the variables remains unchanged. This concept is essential for correctly interpreting correlation in datasets measured in different units.
Recommended video:
Guided course
05:53
Parameters vs. Statistics

Paired Data

Paired data consists of two related sets of observations, where each pair corresponds to a single entity or subject. In this context, the heights of individuals measured in inches and centimeters represent paired data. Analyzing paired data allows for the assessment of relationships between two variables, making it fundamental for calculating correlation coefficients like r.
Recommended video:
Guided course
04:39
Visualizing Qualitative vs. Quantitative Data
Related Practice
Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

[Image]

Frequency Distribution For the frequency distribution from Exercise 1, find the following.


a. Class limits of the first class

b. Class boundaries of the first class

c. Class midpoint of the first class

162
views
Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

Frequency Distribution Construct a frequency distribution of the magnitudes. Use a class width of 0.50 and use a starting value of 1.00.

107
views
Textbook Question

Interpreting Normal Quantile Plots Which of the following normal quantile plots appear to represent data from a population having a normal distribution? Explain.


a. " style="" width="380">

236
views
1
rank
Textbook Question

Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults.


c. Their pulse rates are measured and their IQ scores are measured .

128
views
Textbook Question

Environment


a. After collecting the average (mean) global temperatures for each of the most recent 100 years, we want to construct the graph that is most appropriate for these data. Which graph is best?

89
views
Textbook Question

Body Temperatures Listed below are the temperatures from nine males measured at 8 AM and again at 12 AM (from Data Set 5 “Body Temperatures” in Appendix B). Construct a scatterplot. Based on the graph, does there appear to be a relationship between 8 AM temperatures and 12 AM temperatures?

122
views