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Can A regression equation have a negative coefficient of correlation and a negative coefficient of determination?
It's not quite possible for the coefficient of determination to be negative at all, because of its definition as r2 (coefficient of correlation squared). The coefficient of determination is useful since tells us how accurate the regression line's predictions will be but it cannot tell us which direction the line is going since it will always be a positive quantity even if the correlation is negative. On the other hand, r (the coefficient of correlation) gives the strength and direction of the correlation but says nothing about the regression line equation. Both r and r2 are found similarly but they are typically used to tell us different things.
What does correlation tell us?
Correlation is a statistical technique that is used to measure and describe the strength and direction of the relationship between two variables.
How do you know if a scatter plot has a strong correlation?
You can look at the r value and tell from there. Also you can try to see if there is a linear assocation and if its tightly centered or loosely centered.
What should be the value of R squared for a good correlation?
1 is the best, 0 is the worst. So the closer you are to 1, the better. Beyond that, I can't tell you a specific cutoff. It depends on what you're trying to prove. Sometimes, you won't settle for anything less than 0.99. Other times, you'll be tickled pink to get a 0.3. But the whole point of an R-squared is to give a numerical representation of how close the correlation is without resorting to vague terms like "good correlation". Publish the value of R-squared and let the readers make their own decisions about whether it's "good" or "bad".
What kind of research is needed to establish a cause-and-effect relationship between two variables?
You need to set up an experimental study. The variable which is the cause should be randomly assigned and the effect variable is then observed. Other study designs can only tell you that there is a link or correlation, but not necessarily a causal relation.
What is the range of correlation coefficient and what does its value tell?
The product-moment correlation coefficient or PMCC should have a value between -1 and 1. A positive value shows a positive linear correlation, and a negative value shows a negative linear correlation. At zero, there is no linear correlation, and the correlation becomes stronger as the value moves further from 0.
Can A regression equation have a negative coefficient of correlation and a negative coefficient of determination?
It's not quite possible for the coefficient of determination to be negative at all, because of its definition as r2 (coefficient of correlation squared). The coefficient of determination is useful since tells us how accurate the regression line's predictions will be but it cannot tell us which direction the line is going since it will always be a positive quantity even if the correlation is negative. On the other hand, r (the coefficient of correlation) gives the strength and direction of the correlation but says nothing about the regression line equation. Both r and r2 are found similarly but they are typically used to tell us different things.
What is the connection between slope in a linear function and the a coefficient in a quadratic?
The slope of a linear function is the coefficient of the x term. The sign of this number will determine if the line increases as x increases, or decreases as x increases (slopes up or down). The magnitude of the slope determines how steep the line is (how fast it increases).The coefficient of the x2 term in a quadratic function will tell you similar characteristics of the parabola. The sign will tell you if the parabola opens up or down. The magnitude of the coefficient tells you how steeply the graph changes.
How can you tell from a scatter plot wheather two variables have a positive correlation a negative correlation or no correlation?
Positive correlation = the slope of the scattered dots will rise from left to right (positive slope) Negative correlation = the slope of the scattered dots will fall from left to right (negative slope) No correlation = no real visible slope, the dots are too scattered to tell.
What does coefficient tell you?
Nothing. It depends what you're talking about specifically. Coefficient is just a number in an equation.
When coefficient of correlation is not perfect you should use an appropriate regression line for projection?
When the correlation coefficient isn't equal to 1 you have any number of choices. Contrary to what a maths syllabus might tell you, there is no right or wrong answer here. Do whatever you think best! Maths does have a creative element to it (this isn't it though...) If its close to zero though, a regression line is probably a poor choice. There aren't many ways to draw a nice fitting curve in this case, but you might be able to model it with a random (e.g. bivariate normal) distribution.
What does correlation tell us?
Correlation is a statistical technique that is used to measure and describe the strength and direction of the relationship between two variables.
What does coefficent tell you?
the degree of correlation between two sets of data
What does a coefficent tell you?
the degree of correlation between two sets of data
What is the difference between a subscript and a coefficient in a chemical formula?
The subscripts tell you how the atoms are bound together. The coefficient tells you how many atoms there are.
What does the coefficient of -13644 tell us?
It tells you that something has a value of -13644.
How can you tell if it appears to have a good r-square?
r^2 , the square of the correlation coefficient represents the percentage of variation explained by the independent variable of the dependent variable. It varies between 0 and 100 percent. The user has to make his/her own judgment as to whether the obtained value of r^2 is good enough for him/her.
