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Chapter 13: Problem 46

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Data that are modeled by \(y=-0.238 x+25\) have a negative correlation.

Short Answer

Expert verified
True. The data modeled by \(y = -0.238x + 25\) have a negative correlation, as suggested by the negative value of the slope.

Step by step solution

01

Understand the Concept of Correlation

The correlation between two variables measures the direction and strength of the relationship between them. If one variable increases and the other also increases, it's a positive correlation. If one variable increases while the other decreases, it's a negative correlation.
02

Interpret the Slope of the Given Model

In the equation provided, \(y = -0.238x + 25\), the slope is -0.238. This negative value suggests a negative relationship between x and y. As x increases, y decreases, which is characteristic of a negative correlation.
03

Confirm or Refute the Statement

Based on the interpretation of the slope of the model, it can be confirmed that the statement is true. Data that are modeled by \(y = -0.238x + 25\) indeed have a negative correlation.

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Most popular questions from this chapter

Evaluate the double integral. $$ \int_{1}^{2} \int_{0}^{4}\left(3 x^{2}-2 y^{2}+1\right) d x d y $$

Sketch the region of integration and evaluate the double integral. $$ \int_{0}^{1} \int_{y}^{\sqrt{y}} x^{2} y^{2} d x d y $$

Sketch the region \(R\) whose area is given by the double integral. Then change the order of integration and show that both orders yield the same area. $$ \int_{0}^{2} \int_{x / 2}^{1} d y d x $$

Plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of \(r\) and confirm your result. The number \(r\) is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between \(-1\) and 1, and the closer \(|r|\) is to 1, the better the model. $$ (1,4),(2,6),(3,8),(4,11),(5,13),(6,15) $$

Sketch the region \(R\) whose area is given by the double integral. Then change the order of integration and show that both orders yield the same area. $$ \int_{0}^{1} \int_{2 y}^{2} d x d y $$
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