Which of the following co-efficients of correlation indicates the strongest relationship between two sets of variables?
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Answer (Detailed Solution Below)Option 1 : -0.98 Free General Science Mock Test 10 Questions 10 Marks 12 Mins Correlational Research in psychology:
The correlation r measures the strength of the linear relationship between two quantitative variables. Pearson r: \(r = {1 \over {n-1}} \sum ({x_{i} - {\bar x} \over S_{x}}) ({y_{i} - {\bar y} \over S_{y}})\)
Since -0.98 is close to -1 as compared between 0.90 and 1 therefore, -0.98 coefficients of correlation indicate the strongest relationship between two sets of variables. Latest AWES Army Public School Updates Last updated on Sep 22, 2022 The Army Welfare Education Society, known as AWES, has released AWES Army Public School Recruitment Notification 2022. Through this recruitment process, teachers will be recruited for 136 Army Public Schools situated in various military and cantonment areas across India. The candidates can apply for the post online from 25th August 2022 to 5th October 2022. The exam is scheduled for 5th and 6th November 2022. The willing candidates should go through the AWES Army Public School Preparation Tips to have an edge over others in the exam. Video TranscriptWhich of the following Pearson′s correlation coefficients indicates the strongest correlation? Is it (A) negative 0.14, (B) negative 0.87, (C) negative 0.88, or (D) negative 0.33? We begin by recalling that Pearson′s correlation coefficient describes the measure of linear agreement between two variables. In effect, it tells us how close a set of points sit to a straight line. We know that points with a positive correlation will sit near to a straight line with positive slope or gradient, whereas points with a negative correlation will sit near to a straight line with negative slope, that is, sloping downwards from left to right. Points with a perfect positive linear correlation will sit exactly on a straight line with positive slope or gradient, and the Pearson′s correlation coefficients will be equal to one, whereas points with a perfect negative linear correlation will sit entirely on a straight line with a negative slope, and the correlation coefficient will be equal to negative one. It is important to note that this does not mean that the gradient or slope of the line will be equal to negative one. Likewise, a correlation coefficient of one does not mean that the slope of the positive correlation line is one. It just means that the points do lie on a straight line with negative gradient and their correlation coefficient is equal to negative one. We can therefore see that Pearson′s correlation coefficients vary from negative one to one, with a value of negative one indicating the strongest possible negative correlation and a value of positive one indicating the strongest positive correlation. All of the options in this question are negative. So, to find the value that indicates the strongest correlation, we′re looking for the value which is closest to negative one. The correct answer is therefore option (C). Out of the four options, negative 0.88 indicates the strongest correlation. Home>AP statistics>This page Índice
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 CoefficientThe sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables.
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 CoefficientsThe scatterplots below show how different patterns of data produce different degrees of correlation. Maximum positive correlation Strong positive correlation Zero correlation Maximum negative
correlation Moderate negative correlation Strong correlation & outlier Several points are evident from the scatterplots. Advertisement How to Calculate a Correlation CoefficientIf 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 ] 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 ] 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 UnderstandingProblem 1 A national consumer magazine reported the following correlations.
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 AnswerScatterplots, Correlation Coefficient, and Line of Best FitWhich correlation coefficient represents the strongest correlation compared to others?Answer: -0.85 (Option d) is the strongest correlation coefficient which represents the strongest correlation as compared to others. Let us understand how did we arrive at the answer. What does the correlation coefficient of this graph show?The correlation coefficient shows how strong the relationship between two variables is and goes from 0 to 1. if it is negative, the relationship is an inverse one. The strongest relationship here is therefore -0.80 as it is the closest to 1 out of all the options. It shows that the relationship between the two variables is strongly inverse. What is a positive and negative correlation coefficient?A positive correlation coefficient indicates that the value of one variable depends on the other variable directly. A zero-correlation coefficient indicates that there is no correlation between both variables. A negative correlation coefficient indicates that the value of one variable depends on the other variable inversely. How do you find the strongest correlation?According to the rule of correlation coefficients, the strongest correlation is considered when the value is closest to +1 (positive correlation) or -1 (negative correlation). A positive correlation coefficient indicates that the value of one variable depends on the other variable directly. Which correlation indicates the strongest relationship between two variables?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. What is the strongest negative correlation?The strength of a correlation relationship is quantified by its correlation coefficient, the strongest possible being "perfectly" correlated. A perfect negative correlation has a value of -1.0 and indicates that when X increases by z units, Y decreases by exactly z; and vice-versa. Is 0.2 A strong negative 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. Is negative 0.5 a strong correlation?Negative correlation is measured from -0.1 to -1.0. Weak negative correlation being -0.1 to -0.3, moderate -0.3 to -0.5, and strong negative correlation from -0.5 to -1.0. Which correlation coefficient represents the strongest relationship between two variables quizlet?A correlation coefficient is a number between 0 and 1. The closer to 1, the stronger the relationship is (the more predictive it is).
Which of the following correlation coefficient represents the strongest relationship between two variables psychology?Correct answer:
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.
Is 0.74 A strong correlation?In summary: As a rule of thumb, a correlation greater than 0.75 is considered to be a “strong” correlation between two variables.
Which of the following have the strongest correlation?Correlation (r):
The coefficient of correlation (r) is always between -1 and 1, with the strongest correlation being closest to -1 or 1.
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