What is the strongest correlation 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. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

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What is the strength of the relationship between two variables?

A correlation coefficient measures the degree (strength) of the relationship between two variables. The Pearson Correlation Coefficient measures the strength of the linear relationship between two variables.

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What is the relationship between two or more variables?

Correlation is the relationship between two or more variables. It is the linear relationship of how one variable changes in respect to the other.

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What is the relationship between two variables in research?

A hypothesis states a presumed relationship between two variables in a way that can be tested with empirical data. It may take the form of a cause-effect statement, or an "if x,...then y" statement. The cause is called the independent variable; and the effect is called the dependent variable.

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What are variables relationship?

What do we mean by variables being related to each other? Fundamentally, it means that the values of variable correspond to the values of another variable, for each case in the dataset. In other words, knowing the value of one variable, for a given case, helps you to predict the value of the other one.

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TEAS Math Tutorial - The Relationship Between Two Variables - Chapter 32

What's a strong positive correlation?

Strong positive correlation: When the value of one variable increases, the value of the other variable increases in a similar fashion. For example, the more hours that a student studies, the higher their exam score tends to be.

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What is high correlation?

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.

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What is the strongest correlation in psychology?

Correlation coefficients range from -1 to 1, with the strongest correlations being closer to -1 or 1. A correlation of 0 indicates no relationship between two variables. Negative correlations can be as strong or stronger than positive correlations; the most important factor is the magnitude of the correlation.

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Which of the following indicates the strongest relationships?

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

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Which correlation is the strongest quizlet?

When you are thinking about correlation, just remember this handy rule: The closer the correlation is to 0, the weaker it is, while the close it is to +/-1, the stronger it is.

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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.

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Is 0.9 A strong correlation?

The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.

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Is 0.4 A strong correlation?

For this kind of data, we generally consider correlations above 0.4 to be relatively strong; correlations between 0.2 and 0.4 are moderate, and those below 0.2 are considered weak. When we are studying things that are more easily countable, we expect higher correlations.

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What is a strong and weak correlation?

A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.

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Is a negative correlation strong?

A negative correlation can indicate a strong relationship or a weak relationship. Many people think that a correlation of –1 indicates no relationship. But the opposite is true. A correlation of -1 indicates a near-perfect relationship along a straight line, which is the strongest relationship possible.

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What's a weak correlation?

The correlation between two variables is considered to be weak if the absolute value of r is between 0.25 and 0.5.

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Is 0.46 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.

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Is 0.80 A strong correlation?

A coefficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables.

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Is R 0.6 a strong correlation?

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.

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What is a strong R value?

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.

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What does a correlation of 0.7 mean?

This is interpreted as follows: a correlation value of 0.7 between two variables would indicate that a significant and positive relationship exists between the two.

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What does a correlation coefficient of 0.70 infer?

It describes the relationship between two variables. What does a correlation coefficient of 0.70 infer? Multiple Choice. There is almost no correlation because 0.70 is close to 1.0. 70% of the variation in one variable is explained by the other variable.

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Is 0.06 A strong correlation?

Correlation Coefficient = 0.8: A fairly strong positive relationship. Correlation Coefficient = 0.6: A moderate positive relationship.

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Is .5 a strong correlation?

Correlation coefficients whose magnitude are between 0.5 and 0.7 indicate variables which can be considered moderately correlated. Correlation coefficients whose magnitude are between 0.3 and 0.5 indicate variables which have a low correlation.

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Is a correlation of 50 good?

A correlation coefficient of . 10 is thought to represent a weak or small association; a correlation coefficient of . 30 is considered a moderate correlation; and a correlation coefficient of . 50 or larger is thought to represent a strong or large correlation.

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Correlation coefficients are indicators of the strength of the linear relationship between two different variables, x and y. A linear correlation coefficient that is greater than zero indicates a positive relationship. A value that is less than zero signifies a negative relationship. Finally, a value of zero indicates no relationship between the two variables x and y.

This article explains the significance of linear correlation coefficients for investors, how to calculate covariance for stocks, and how investors can use correlation to predict the market.

  • Correlation coefficients are used to measure the strength of the linear relationship between two variables.
  • A correlation coefficient greater than zero indicates a positive relationship while a value less than zero signifies a negative relationship.
  • A value of zero indicates no relationship between the two variables being compared.
  • A negative correlation, or inverse correlation, is a key concept in the creation of diversified portfolios that can better withstand portfolio volatility.
  • Calculating the correlation coefficient is time-consuming, so data are often plugged into a calculator, computer, or statistics program to find the coefficient.

The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated. The most common correlation coefficient, generated by the Pearson product-moment correlation, is used to measure the linear relationship between two variables. However, in a non-linear relationship, this correlation coefficient may not always be a suitable measure of dependence.

The possible range of values for the correlation coefficient is -1.0 to 1.0. In other words, the values cannot exceed 1.0 or be less than -1.0. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation. If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship. A value of zero indicates that there is no relationship between the two variables.

When interpreting correlation, it's important to remember that just because two variables are correlated, it does not mean that one causes the other.

In the financial markets, the correlation coefficient is used to measure the correlation between two securities. For example, when two stocks move in the same direction, the correlation coefficient is positive. Conversely, when two stocks move in opposite directions, the correlation coefficient is negative.

If the correlation coefficient of two variables is zero, there is no linear relationship between the variables. However, this is only for a linear relationship. It is possible that the variables have a strong curvilinear relationship. When the value of ρ is close to zero, generally between -0.1 and +0.1, the variables are said to have no linear relationship (or a very weak linear relationship).

For example, suppose that the prices of coffee and computers are observed and found to have a correlation of +.0008. This means that there is no correlation, or relationship, between the two variables.

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The covariance of the two variables in question must be calculated before the correlation can be determined. Next, each variable's standard deviation is required. The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.

Standard deviation is a measure of the dispersion of data from its average. Covariance is a measure of how two variables change together. However, its magnitude is unbounded, so it is difficult to interpret. The normalized version of the statistic is calculated by dividing covariance by the product of the two standard deviations. This is the correlation coefficient.

 Correlation = ρ = cov ( X , Y ) σ X σ Y \text{Correlation}=\rho=\frac{\text{cov}(X,Y)}{\sigma_X\sigma_Y} Correlation=ρ=σXσYcov(X,Y)

A positive correlation—when the correlation coefficient is greater than 0—signifies that both variables move in the same direction. When ρ is +1, it signifies that the two variables being compared have a perfect positive relationship; when one variable moves higher or lower, the other variable moves in the same direction with the same magnitude.

The closer the value of ρ is to +1, the stronger the linear relationship. For example, suppose the value of oil prices is directly related to the prices of airplane tickets, with a correlation coefficient of +0.95. The relationship between oil prices and airfares has a very strong positive correlation since the value is close to +1. So, if the price of oil decreases, airfares also decrease, and if the price of oil increases, so do the prices of airplane tickets.

In the chart below, we compare one of the largest U.S. banks, JPMorgan Chase & Co. (JPM), with the Financial Select SPDR Exchange Traded Fund (ETF) (XLF). As you can imagine, JPMorgan Chase & Co. should have a positive correlation to the banking industry as a whole. 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.

Understanding the correlation between two stocks (or a single stock) and its industry can help investors gauge how the stock is trading relative to its peers. All types of securities, including bonds, sectors, and ETFs, can be compared with the correlation coefficient.

A negative (inverse) correlation occurs when the correlation coefficient is less than 0. This is an indication that both variables move in the opposite direction. In short, any reading between 0 and -1 means that the two securities move in opposite directions. When ρ is -1, the relationship is said to be perfectly negatively correlated.

In short, if one variable increases, the other variable decreases with the same magnitude (and vice versa). However, the degree to which two securities are negatively correlated might vary over time (and they are almost never exactly correlated all the time). 

For example, suppose a study is conducted to assess the relationship between outside temperature and heating bills. The study concludes that there is a negative correlation between the prices of heating bills and the outdoor temperature. The correlation coefficient is calculated to be -0.96. This strong negative correlation signifies that as the temperature decreases outside, the prices of heating bills increase (and vice versa).

When it comes to investing, a negative correlation does not necessarily mean that the securities should be avoided. The correlation coefficient can help investors diversify their portfolio by including a mix of investments that have a negative, or low, correlation to the stock market. In short, when reducing volatility risk in a portfolio, sometimes opposites do attract.  

For example, assume you have a $100,000 balanced portfolio that is invested 60% in stocks and 40% in bonds. In a year of strong economic performance, the stock component of your portfolio might generate a return of 12% while the bond component may return -2% because interest rates are rising (which means that bond prices are falling).

Thus, the overall return on your portfolio would be 6.4% ((12% x 0.6) + (-2% x 0.4). The following year, as the economy slows markedly and interest rates are lowered, your stock portfolio might generate -5% while your bond portfolio may return 8%, giving you an overall portfolio return of 0.2%.

What if, instead of a balanced portfolio, your portfolio were 100% equities? Using the same return assumptions, your all-equity portfolio would have a return of 12% in the first year and -5% in the second year. These figures are clearly more volatile than the balanced portfolio's returns of 6.4% and 0.2%.

The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables: x and y. The sign of the linear correlation coefficient indicates the direction of the linear relationship between x and y. When r (the correlation coefficient) is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.

Even for small datasets, the computations for the linear correlation coefficient can be too long to do manually. Thus, data are often plugged into a calculator or, more likely, a computer or statistics program to find the coefficient.

Both the Pearson coefficient calculation and basic linear regression are ways to determine how statistical variables are linearly related. However, the two methods do differ. The Pearson coefficient is a measure of the strength and direction of the linear association between two variables with no assumption of causality. The Pearson coefficient shows correlation, not causation. Pearson coefficients range from +1 to -1, with +1 representing a positive correlation, -1 representing a negative correlation, and 0 representing no relationship.

Simple linear regression describes the linear relationship between a response variable (denoted by y) and an explanatory variable (denoted by x) using a statistical model. Statistical models are used to make predictions.

Simplify linear regression by calculating correlation with software such as Excel.

In finance, for example, correlation is used in several analyses including the calculation of portfolio standard deviation. Because it is so time-consuming, correlation is best calculated using software like Excel. Correlation combines statistical concepts, namely, variance and standard deviation. Variance is the dispersion of a variable around the mean, and standard deviation is the square root of variance.

There are several methods to calculate correlation in Excel. The simplest is to get two data sets side-by-side and use the built-in correlation formula:

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If you want to create a correlation matrix across a range of data sets, Excel has a Data Analysis plugin that is found on the Data tab, under Analyze. 

Select the table of returns. In this case, our columns are titled, so we want to check the box "Labels in first row," so Excel knows to treat these as titles. Then you can choose to output on the same sheet or on a new sheet.

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Once you hit enter, the data is automatically created. You can add some text and conditional formatting to clean up the result.

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The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables, x and y.

Correlation combines several important and related statistical concepts, namely, variance and standard deviation. Variance is the dispersion of a variable around the mean, and standard deviation is the square root of variance. 

The formula is: 

 r = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) [ n ∑ x 2 − ( ∑ x ) 2 ] [ n ∑ y 2 − ( ∑ y ) 2 ) ] \bold{r}=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2)]}} r=[nx2(x)2][ny2(y)2)]n(xy)(x)(y)

The computing is too long to do manually, and sofware, such as Excel, or a statistics program, are tools used to calculate the coefficient.

The correlation coefficient is a value between -1 and +1. A correlation coefficient of +1 indicates a perfect positive correlation. As variable x increases, variable y increases. As variable x decreases, variable y decreases. A correlation coefficient of -1 indicates a perfect negative correlation. As variable x increases, variable z decreases. As variable x decreases, variable z increases.

A graphing calculator is required to calculate the correlation coefficient. The following instructions are provided by Statology.

Step 1: Turn on Diagnostics

You will only need to do this step once on your calculator. After that, you can always start at step 2 below. If you don’t do this, r (the correlation coefficient) will not show up when you run the linear regression function.

  • Press [2nd] and then [0] to enter your calculator’s catalog. Scroll until you see “diagnosticsOn”.
  • Press enter until the calculator screen says “Done”.

This is important to repeat: You never have to do this again unless you reset your calculator.

Step 2: Enter Data

Enter your data into the calculator by pressing [STAT] and then selecting 1:Edit. To make things easier, you should enter all of your “x data” into L1 and all of your “y data” into L2.

Step 3: Calculate!

Once you have your data in, you will now go to [STAT] and then the CALC menu up top. Finally, select 4:LinReg and press enter.

That’s it! You’re are done! Now you can simply read off the correlation coefficient right from the screen (its r). Remember, if r doesn’t show on your calculator, then diagnostics need to be turned on. This is also the same place on the calculator where you will find the linear regression equation and the coefficient of determination.

The linear correlation coefficient can be helpful in determining the relationship between an investment and the overall market or other securities. It is often used to predict stock market returns. This statistical measurement is useful in many ways, particularly in the finance industry.

For example, it can be helpful in determining how well a mutual fund is behaving compared to its benchmark index, or it can be used to determine how a mutual fund behaves in relation to another fund or asset class. By adding a low, or negatively correlated, mutual fund to an existing portfolio, diversification benefits are gained.

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