Which of the following correlation coefficients may represent a strong correlation?

Home>AP statistics>This page

Nội dung chính Show

  • How to Interpret a Correlation Coefficient
  • Scatterplots and Correlation Coefficients
  • How to Calculate a Correlation Coefficient
  • Test Your Understanding
  • Is 0.43 A strong correlation?
  • What is a weak correlation coefficient?
  • Which correlation coefficient represents the weakest relationship between two variables?
  • What is the relationship between correlation coefficient and regression coefficient?
  • What is the range of correlation coefficient explain strong moderate and weak relationship?
  • Is 0.7 A strong correlation?
  • Is 0.23 A strong correlation?
  • What is a high correlation between two variables?
  • Is 0.1 A strong correlation?
  • Which of the following correlation coefficients is strongest?
  • Which correlation coefficient indicates the strongest relationship between two variables quizlet?
  • Is 0.46 A strong correlation?
  • Is 0.22 A strong correlation?
  • Is .40 a strong correlation?
  • What is Karl Pearson coefficient of correlation?
  • Which correlation coefficient represents the strongest relationship between two variables? Video Answer
  • Scatterplots, Correlation Coefficient, and Line of Best Fit
  • What is a strong positive correlation coefficient?
  • Is 1.2 A strong positive correlation?
  • Which of the following correlation coefficients may represent a strong correlation?
  • Is 0.8 A strong positive correlation?

Índice

  • How to Interpret a Correlation Coefficient
  • Scatterplots and Correlation Coefficients
  • How to Calculate a Correlation Coefficient
  • Test Your Understanding
  • Is 0.43 A strong correlation?
  • What is a weak correlation coefficient?
  • Which correlation coefficient represents the weakest relationship between two variables?
  • What is the relationship between correlation coefficient and regression coefficient?
  • What is the range of correlation coefficient explain strong moderate and weak relationship?
  • Is 0.7 A strong correlation?
  • Is 0.23 A strong correlation?
  • What is a high correlation between two variables?
  • Is 0.1 A strong correlation?
  • Which of the following correlation coefficients is strongest?
  • Which correlation coefficient indicates the strongest relationship between two variables quizlet?
  • Is 0.46 A strong correlation?
  • Is 0.22 A strong correlation?
  • Is .40 a strong correlation?
  • What is Karl Pearson coefficient of correlation?
  • Which correlation coefficient represents the strongest relationship between two variables? Video Answer
  • Scatterplots, Correlation Coefficient, and Line of Best Fit

Correlation coefficients measure the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient, measures the strength of the linear association between variables measured on an interval or ratio scale.

Note: Your browser does not support HTML5 video. If you view this web page on a different browser (e.g., a recent version of Edge, Chrome, Firefox, or Opera), you can watch a video treatment of this lesson.

In this tutorial, when we speak simply of a correlation coefficient, we are referring to the Pearson product-moment correlation. Generally, the correlation coefficient of a sample is denoted by r, and the correlation coefficient of a population is denoted by ρ or R.

How to Interpret a Correlation Coefficient

The sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables.

  • A negative correlation means that if one variable gets bigger, the other variable tends to get smaller.

Keep in mind that the Pearson product-moment correlation coefficient only measures linear relationships. Therefore, a correlation of 0 does not mean zero relationship between two variables; rather, it means zero linear relationship. (It is possible for two variables to have zero linear relationship and a strong curvilinear relationship at the same time.)

Scatterplots and Correlation Coefficients

The scatterplots below show how different patterns of data produce different degrees of correlation.

Which of the following correlation coefficients may represent a strong correlation?

Maximum positive correlation
(r = 1.0)

Strong positive correlation
(r = 0.80)

Zero correlation
(r = 0)

Maximum negative correlation
(r = -1.0)

Moderate negative correlation
(r = -0.43)

Strong correlation & outlier
(r = 0.71)

Several points are evident from the scatterplots.

Advertisement

How to Calculate a Correlation Coefficient

If you look in different statistics textbooks, you are likely to find different-looking (but equivalent) formulas for computing a correlation coefficient. In this section, we present several formulas that you may encounter.

The most common formula for computing a product-moment correlation coefficient (r) is given below.

Product-moment correlation coefficient. The correlation r between two variables is:

r = Σ (xy) / sqrt [ ( Σ x2 ) * ( Σ y2 ) ]

where Σ is the summation symbol, x = xi - x, xi is the x value for observation i, x is the mean x value, y = yi - y, yi is the y value for observation i, and y is the mean y value.

The formula below uses population means and population standard deviations to compute a population correlation coefficient (ρ) from population data.

Population correlation coefficient. The correlation ρ between two variables is:

ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ]
* [ (Yi - μY) / σy ] }

where N is the number of observations in the population, Σ is the summation symbol, Xi is the X value for observation i, μX is the population mean for variable X, Yi is the Y value for observation i, μY is the population mean for variable Y, σx is the population standard deviation of X, and σy is the population standard deviation of Y.

The formula below uses sample means and sample standard deviations to compute a sample correlation coefficient (r) from sample data.

Sample correlation coefficient. The correlation r between two variables is:

r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ]
* [ (yi - y) / sy ] }

where n is the number of observations in the sample, Σ is the summation symbol, xi is the x value for observation i, x is the sample mean of x, yi is the y value for observation i, y is the sample mean of y, sx is the sample standard deviation of x, and sy is the sample standard deviation of y.

The interpretation of the sample correlation coefficient depends on how the sample data are collected. With a large simple random sample, the sample correlation coefficient is an unbiased estimate of the population correlation coefficient.

Each of the latter two formulas can be derived from the first formula. Use the first or second formula when you have data from the entire population. Use the third formula when you only have sample data, but want to estimate the correlation in the population. When in doubt, use the first formula.

Fortunately, you will rarely have to compute a correlation coefficient by hand. Many software packages (e.g., Excel) and most graphing calculators have a correlation function that will do the job for you.

Test Your Understanding

Problem 1

A national consumer magazine reported the following correlations.

  • The correlation between car weight and car reliability is -0.30.
  • The correlation between car weight and annual maintenance cost is 0.20.

Which of the following statements are true?

I. Heavier cars tend to be less reliable.II. Heavier cars tend to cost more to maintain.

III. Car weight is related more strongly to reliability than to maintenance cost.

(A) I only(B) II only(C) III only(D) I and II only

(E) I, II, and III

Solution

The correct answer is (E). The correlation between car weight and reliability is negative. This means that reliability tends to decrease as car weight increases. The correlation between car weight and maintenance cost is positive. This means that maintenance costs tend to increase as car weight increases.

The strength of a relationship between two variables is indicated by the absolute value of the correlation coefficient. The correlation between car weight and reliability has an absolute value of 0.30. The correlation between car weight and maintenance cost has an absolute value of 0.20. Therefore, the relationship between car weight and reliability is stronger than the relationship between car weight and maintenance cost.

If you would like to cite this web page, you can use the following text:

Berman H.B., "Correlation Coefficient", [online] Available at: https://stattrek.com/statistics/correlation URL [Accessed Date: 9/12/2022].

Try Numerade Free for 30 Days

Try Numerade Free for 30 Days


Continue

Try Numerade Free for 30 Days

Try Numerade Free for 30 Days


Continue

Try Numerade Free for 30 Days

Try Numerade Free for 30 Days


Continue

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

Looking for an answer to the question: Which correlation coefficient represents the strongest relationship between two variables? On this page, we have gathered for you the most accurate and comprehensive information that will fully answer the question: Which correlation coefficient represents the strongest relationship between two variables?

The greater the absolute value of the Pearson product-moment correlation coefficient, the stronger the linear relationship. The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. In this regard, what number is a strong correlation?

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables. Secondly, is 0.4 A strong correlation?

The weakest linear relationship is indicated by a correlation coefficient equal to 0. Hereof, what number is a strong correlation? The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.

Correlation is significant at the 0.01 level (2-tailed). (This means the value will be considered significant if is between 0.001 to 0,010, See 2nd example below). ... (This means the value will be considered significant if is between 0.010 to 0,050).


Is 0.43 A strong correlation?

Generally, a value of r greater than 0.7 is considered a strong correlation. Anything between 0.5 and 0.7 is a moderate correlation, and anything less than 0.4 is considered a weak or no correlation.


What is a weak correlation coefficient?

As a rule of thumb, a correlation coefficient between 0.25 and 0.5 is considered to be a “weak” correlation between two variables.


Which correlation coefficient represents the weakest relationship between two variables?

Strength - The weakest linear relationship is indicated by a correlation coefficient equal to 0 (actually this represents no correlation!).


What is the relationship between correlation coefficient and regression coefficient?

Correlation coefficient indicates the extent to which two variables move together. Regression indicates the impact of a change of unit on the estimated variable ( y) in the known variable (x). To find a numerical value expressing the relationship between variables.


What is the range of correlation coefficient explain strong moderate and weak relationship?

If we wish to label the strength of the association, for absolute values of r, 0-0.19 is regarded as very weak, 0.2-0.39 as weak, 0.40-0.59 as moderate, 0.6-0.79 as strong and 0.8-1 as very strong correlation, but these are rather arbitrary limits, and the context of the results should be considered.


Is 0.7 A strong correlation?

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.


Is 0.23 A strong correlation?

If the correlation coefficient between two variables is found to be 0.23 based on a sample of 200 cases it comes as statistically significant.


What is a high correlation between two variables?

Correlation is a term that refers to the strength of a relationship between two variables where a strong, or high, correlation means that two or more variables have a strong relationship with each other while a weak or low correlation means that the variables are hardly related.


Is 0.1 A strong correlation?

Positive correlation is measured on a 0.1 to 1.0 scale. Weak positive correlation would be in the range of 0.1 to 0.3, moderate positive correlation from 0.3 to 0.5, and strong positive correlation from 0.5 to 1.0. The stronger the positive correlation, the more likely the stocks are to move in the same direction.


Which of the following correlation coefficients is strongest?

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0.


Which correlation coefficient indicates the strongest relationship between two variables quizlet?

When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation of -0.97 is a strong negative correlation, while a correlation of 0.10 would be a weak positive correlation.


Is 0.46 A strong correlation?

Values between 0.3 and 0.7 (0.3 and −0.7) indicate a moderate positive (negative) linear relationship through a fuzzy-firm linear rule. Values between 0.7 and 1.0 (−0.7 and −1.0) indicate a strong positive (negative) linear relationship through a firm linear rule.


Is 0.22 A strong correlation?

Values between 0 and 0.3 (0 and -0.3) indicate a weak positive (negative) linear relationship via a shaky linear rule. Values between 0.3 and 0.7 (-0.3 and -0.7) indicate a moderate positive (negative) linear relationship via a fuzzy-firm linear rule.


Is .40 a strong correlation?

40, which is certainly larger than the . 08 from the U.S. study, but it's far from the near-perfect correlation conventional wisdom and warning labels would imply.


What is Karl Pearson coefficient of correlation?

Karl Pearson's coefficient of correlation is defined as a linear correlation coefficient that falls in the value range of -1 to +1. Value of -1 signifies strong negative correlation while +1 indicates strong positive correlation.

Which correlation coefficient represents the strongest relationship between two variables? Video Answer

Scatterplots, Correlation Coefficient, and Line of Best Fit

What is a strong positive correlation coefficient?

We can see the correlation coefficient is currently at 0.98, which is signaling a strong positive correlation. A reading above 0.50 typically signals a positive correlation.

Is 1.2 A strong positive correlation?

Positive correlation is measured on a 0.1 to 1.0 scale. Weak positive correlation would be in the range of 0.1 to 0.3, moderate positive correlation from 0.3 to 0.5, and strong positive correlation from 0.5 to 1.0. The stronger the positive correlation, the more likely the stocks are to move in the same direction.

Which of the following correlation coefficients may represent a strong correlation?

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0.

Is 0.8 A strong positive correlation?

Correlation Coefficient = 0.8: A fairly strong positive relationship. Correlation Coefficient = 0.6: A moderate positive relationship. Correlation Coefficient = 0: No relationship. As one value increases, there is no tendency for the other value to change in a specific direction.

What correlation coefficients are strong?

Calculating a Pearson correlation coefficient requires the assumption that the relationship between the two variables is linear. The relationship between two variables is generally considered strong when their r value is larger than 0.7.

Is or 0.85 A strong correlation coefficient?

If is between 0.85 and 1, there is a strong correlation. If is between 0.5 and 0.85, there is a moderate correlation. If is between 0.1 and 0.5, there is a weak correlation.

Is 0.92 A strong correlation?

As the numbers approach 1 or -1, the values demonstrate the strength of a relationship; for example, 0.92 or -0.97 would show, respectively, a strong positive and negative correlation.

Is 0.5 A strong correlation?

Positive correlation is measured on a 0.1 to 1.0 scale. Weak positive correlation would be in the range of 0.1 to 0.3, moderate positive correlation from 0.3 to 0.5, and strong positive correlation from 0.5 to 1.0.