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What can you say about the relationship between a correlation r and the slope b of the least squares line form of data?
Wiki User
∙ 14y ago
You can say that the correlation is positive if and only if the slope is positive. The correlation is zero if and only if the slope is zero. And the correlation is negative if and only if the slope is negative. On the other hand, slope does change when your measurement units change, while correlation does not change. (For example, the correlation between height in inches and weight in pounds will be the same as the correlation between height in centimeters and weight in kilograms, as long as both sets of measurements were taken on the same observations.)
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∙ 14y ago
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What negative correlation indicate?
the negative sign on correlation just means that the slope of the Least Squares Regression Line is negative.
If two variables have a negative linear correlation is the slope of the least squares negative?
Negative
What is correlation What are the different types of correlation Why is it important to determine correlation What does it mean when it is said that two variables have no correlation?
A correlation is the relationship between two or more variables. Correlations are described as either weak or strong, and positive or negative. There can be a perfect correlation between variables, or no correlation between variables. It is important to determine the correlation between variables in order to know if and how closely changes in one variable are reflected by changes in another variable. This is done by determining the coefficient of correlation (r), which describes the strength of the relationship between variables and the direction. -1 ≤ r ≤ +1 if r= +1 or -1, there is a perfect correlation if r= 0 there is no correlation between the variables. a value closer to + or - 1 demonstrates a strong correlation, while a value closer to 0 demonstrates a weak correlation. a + value demonstrates that when one variable increases the other variable increases, while a - value demonstrates that when one variable increases the other variable decreases. However, it is very important to understand that correlation is not the same as relationship. Consider the two variables, x and y such that y = x2 where x lies between -a and +a. There is a clear and well-defined relationship between x and y, but the correlation coefficient r is 0. This is true of any pair of variables whose graph is symmetric about one axis. Conversely, a high correlation coefficient does not mean a strong relationship - at least, not a strong causal relationship. There is pretty strong correlation between my age and [the log of] the number of television sets in the world. That is not because TV makes me grow old nor that my ageing produces TVs. The reason is that both variables are related to the passage of time.
How will you interpret the coefficient of correlation?
Correlation is a measure of the strength of a linear relationship between two variables. In theory it ranges between -1 and +1, although in practice, random and observation error make this value smaller.Near -1, the correlation is very strongly negative, which means that an increase in one variable is accompanied by a decrease in the other.Near +1, the correlation is very strongly positive, which means that an increase in one variable is accompanied by an increase in the other.Near 0, the correlation is weak and there is no linear pattern in which the two variables change.There are two very critical points to remember:Correlation does not measure causation. For example, the number of cars on the road is correlated to my age but my getting older does not cause more cars to be made and cars do not cause me to grow old (at least, not with most drivers!)Correlation will only measure a linear relationship. If you examine a relationship like y = x2, over a symmetric interval, the correlation coefficient will be close to 0. But there is, clearly, a very strong relationship - just that it is not linear.Finally, the importance of any correlation coefficient is subjective and depends on the context. A correlation coefficient that is high for a sociological study may be considered moderate for a high school physics experiment.
What is Multiple Correlation?
Let me assume that you are familiar with the (Pearson) correlation coefficient. If you estimate how one variable might be a linear function of another (using least-squares) then the measure of how strong the association is is known as that with which you are correlation coefficient. If you generalise by estimating what linear function one variable is of two or more other variables then the measure of how strong the relationship is is the multiple correlation.For mathematical reasons which may or may not interest you, and which I won't go into here, if we now go backwards we find that the multiple correlation for the situation where one variable is regressed against one other variable is just the square of the Pearson correlation coefficient.As you probably know, the Pearson ranges from -1 to +1. Because the multiple correlation is the squared value it ranges only from 0 to 1 and can indicate only degree of association, not the sense of direction.
What negative correlation indicate?
the negative sign on correlation just means that the slope of the Least Squares Regression Line is negative.
If two variables have a negative linear correlation is the slope of the least squares negative?
Negative
What makes the term used to describe the relationship between variables whose graph is a straight line?
There are many terms used for the purpose: slope, gradient, relationship, regression, correlation, error, scatter; as well as phrases: line of best fit, least squares, maximum likelihood. The question needs to be more specific.
What is correlation What are the different types of correlation Why is it important to determine correlation What does it mean when it is said that two variables have no correlation?
A correlation is the relationship between two or more variables. Correlations are described as either weak or strong, and positive or negative. There can be a perfect correlation between variables, or no correlation between variables. It is important to determine the correlation between variables in order to know if and how closely changes in one variable are reflected by changes in another variable. This is done by determining the coefficient of correlation (r), which describes the strength of the relationship between variables and the direction. -1 ≤ r ≤ +1 if r= +1 or -1, there is a perfect correlation if r= 0 there is no correlation between the variables. a value closer to + or - 1 demonstrates a strong correlation, while a value closer to 0 demonstrates a weak correlation. a + value demonstrates that when one variable increases the other variable increases, while a - value demonstrates that when one variable increases the other variable decreases. However, it is very important to understand that correlation is not the same as relationship. Consider the two variables, x and y such that y = x2 where x lies between -a and +a. There is a clear and well-defined relationship between x and y, but the correlation coefficient r is 0. This is true of any pair of variables whose graph is symmetric about one axis. Conversely, a high correlation coefficient does not mean a strong relationship - at least, not a strong causal relationship. There is pretty strong correlation between my age and [the log of] the number of television sets in the world. That is not because TV makes me grow old nor that my ageing produces TVs. The reason is that both variables are related to the passage of time.
A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the?
Least Squares method
What is correlation. What are the different types of correlation. Why is it important to determine correlation. What does it mean when it is said that two variables have no correlation?
A correlation is the relationship between two variables.Correlations are described as either weak or strong, and positive or negative, however there can be a perfect correlation between variables, or no correlation between variables.It is important to determine the correlation between variables in order to know if and how strongly one variable affects another variable (if one variable changes, how will the other variable react). This is done by determining the coefficient of correlation (r), which describes the strength of the relationship between variables and the direction.-1 is less than or equal to r, r is less than or equal to +1if r= +1 or -1, there is a perfect relationshipif r= 0 there is no relationship between the variables, meaning that one variable does not affect the other variable and one variable could change without any change to the other variable.a value closer to + or - 1 demonstrates a strong relationship, while a value closer to 0 demonstrates a weak relationship.a + value demonstrates that when one variable increases the other variable increases, while a - value demonstrates that when one variable increases the other variable decreases.* * * * *Mostly a very good answer but ...It is very important to understand that correlation is not the same as relationship. Consider the two variables, x and y such that y = x2 where x lies between -a and +a. There is a clear and well-defined relationship between x and y, but the correlation coefficient r is 0. This is true of any pair of variables whose graph is symmetric about one axis.Conversely, a high correlation coefficient does not mean a strong relationship - at least, not a strong causal relationship. There is pretty strong correlation between my age and [the log of] the number of television sets in the world. That is not because TV makes me grow old nor that my ageing produces TVs. The reason is that both variables are related to the passage of time.
What has the author Haojian Feng written?
Haojian. Feng has written: 'Xiang guan ping cha gai lun' -- subject(s): Correlation (Statistics), Least squares
What is the relationship between ethics?
What is the relationship between ethics and WHAT? You need at least two things to have a relationship.
What is the meaning of correlation coefficient?
The correlation coefficient takes on values ranging between +1 and -1. The following points are the accepted guidelines for interpreting the correlation coefficient:0 indicates no linear relationship.+1 indicates a perfect positive linear relationship: as one variable increases in its values, the other variable also increases in its values via an exact linear rule.-1 indicates a perfect negative linear relationship: as one variable increases in its values, the other variable decreases in its values via an exact linear rule.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.Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship via a firm linear rule.The value of r squared is typically taken as "the percent of variation in one variable explained by the other variable," or "the percent of variation shared between the two variables."Linearity Assumption. The correlation coefficient requires that the underlying relationship between the two variables under consideration is linear. If the relationship is known to be linear, or the observed pattern between the two variables appears to be linear, then the correlation coefficient provides a reliable measure of the strength of the linear relationship. If the relationship is known to be nonlinear, or the observed pattern appears to be nonlinear, then the correlation coefficient is not useful, or at least questionable.
How will you interpret the coefficient of correlation?
Correlation is a measure of the strength of a linear relationship between two variables. In theory it ranges between -1 and +1, although in practice, random and observation error make this value smaller.Near -1, the correlation is very strongly negative, which means that an increase in one variable is accompanied by a decrease in the other.Near +1, the correlation is very strongly positive, which means that an increase in one variable is accompanied by an increase in the other.Near 0, the correlation is weak and there is no linear pattern in which the two variables change.There are two very critical points to remember:Correlation does not measure causation. For example, the number of cars on the road is correlated to my age but my getting older does not cause more cars to be made and cars do not cause me to grow old (at least, not with most drivers!)Correlation will only measure a linear relationship. If you examine a relationship like y = x2, over a symmetric interval, the correlation coefficient will be close to 0. But there is, clearly, a very strong relationship - just that it is not linear.Finally, the importance of any correlation coefficient is subjective and depends on the context. A correlation coefficient that is high for a sociological study may be considered moderate for a high school physics experiment.
Is there a correlation between birth control and weight gain?
i think there is a connection... i cant say exactly what... but yes there is.... at least that's what i have seen...
What is Multiple Correlation?
Let me assume that you are familiar with the (Pearson) correlation coefficient. If you estimate how one variable might be a linear function of another (using least-squares) then the measure of how strong the association is is known as that with which you are correlation coefficient. If you generalise by estimating what linear function one variable is of two or more other variables then the measure of how strong the relationship is is the multiple correlation.For mathematical reasons which may or may not interest you, and which I won't go into here, if we now go backwards we find that the multiple correlation for the situation where one variable is regressed against one other variable is just the square of the Pearson correlation coefficient.As you probably know, the Pearson ranges from -1 to +1. Because the multiple correlation is the squared value it ranges only from 0 to 1 and can indicate only degree of association, not the sense of direction.
