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What do you know about a linear model from the correlation coefficient?
Wiki User
∙ 10y ago
It's a measure of how well a simple linear model accounts for observed variation.
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∙ 10y ago
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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.
Why is it necessary to know the coefficient of linear expansion of solids?
By knowing the coefficient of linear expansion of solids, you can determine how a solid reacts to temperature. Everything reacts to thermal expansion. For instance, a concrete bridge expands when hot, and with the formula for expansion and the coefficient for it, you know just how much that concrete expands and you can plan and build accordingly. That saves lives.
When you have a scatter plot and you have to choose a correlation I know Positive Negative and no correlation are options Is moderate correlation an option?
Yes. * A positive correlation is when the dependant variable increases as the independent one does. * A negative correlation is when the dependant variable decreases as the independent one increases. * Perfect correlation is when all the points lie along a straight line; no correlation is when the points lie all over the place. In calculating the correlation coefficient it can have a value between -1 and 1, with 0 indication no correlation and values between 0 and ±1 showing a greater correlation until ±1 which is perfect correlation. Moderate correlation would be one of these intermediate values, eg ±0.5, which shows the points are moderately related.
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 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.
Describe linear model in your own words?
The words "in your own words" means the teacher wants YOU to describe it, not some anonymous person on the internet. Read your textbook so you know what the linear model is, then just say it the way you would tell a friend about it.
What is a bivariate fit?
A bivariate fit is a correlation analysis in statistics. Basically you have 2 sets of paired data and want to know if they statistically correlated. You graph the pairs, as X,Y and make a linear regression line between the points. The slope of the line is the correlation coeffiencint, the closer the line is to a 45 degree angle the more likely your data is dependent on one another. if the line is flat then there is no correlation.
Is autocorrelation function a copy of original function?
No. You probably know what a sample correlation is. This statistic is often used to measure how well a linear function of one variable predicts the value of another variable. The statistic can assume any value from -1 to 1, and the extreme values show the strongest (linear) relationship. Calculating the autocorrelation function for a time series involves doing a series of calculations that are the same as those done to obtain a sample correlation coefficient. Since these values must always be between -1 and 1 they cannot in general form a copy of the original function. Here is where the idea of copying appears. Suppose you want to calculate the 1st autocorrelation coefficient from the series v0, v1, v2, v3, v4, ... . Then calculate the sample correlation for the pairs (v1, v0), (v2, v1), (v3, v2), (v4, v3), ... Notice that it is as if you were to write down the original time series on one line and then copy it on a second line shifting it one item to the right so that the pairs needed to compute the sample correlation could be read from the columns of the two lines. The 2nd autocorrelation would be computed as if by copying the second line shifting it two places to the right and so on.
What is the coefficient of friction of linoleum rubber?
You need two different materials to determine the coefficient of friction. Without another material you cannot know what the coefficient of friction is.
Difference between linear and transactional model of communication?
linear model involves only one way communication that is messages are sent and the receiver only recieves.it is one dimensional. interactional model involves not only mesages sent but also the feedback from the receiver where as in transactional model besides sending messages and giving a feedback we also have non verbal messages.
How do you estimate the best fit of curve?
You always use some model (i.e. function) to fit experimental curve. If you do not know the kind of curve (linear, parabola, Gauss, etc.) you can try to fit with different functions and then compare the residual sum of squares and coefficient of determination of those fit functions. I use MagicPlot for curve fitting, you can try to find something in MagicPlot on-line help.
How do we know if a correlation is significant or not?
There are several statistical measures of correlation: some require only a nominal scale, that is, data classified according to two criteria; others require an ordinal scale, which is the ability to determine whether one measurement is bigger or smaller than another; others require an interval scale, which allows you to determine the difference in values but not the ratio between them. [A good example of the latter is temperature measured in any scale other than Kelvin: the difference between 10 degrees C and 15 degrees C is 5 C degrees, but 15 C is not 1.5 times as warm as 10 C.]The contingency coefficient, which is suitable for nominal data, has a chi-squared distribution.The Spearman rank correlation, requiring ordinal data, has its own distribution for small data sets but as the number of units increases to n, the distribution approaches Student's t-distribution with n-2 degrees of freedom.The Kendall rank correlation coefficient can be used in identical situations and gives the same measure of significance. However, the Kendall coefficient can also be used to test partial correlation - whether the correlation between two variables is "genuine" or whether it arises because both variables are actually correlated to a third variable.The Pearson's product moment correlation coefficient (PMCC) is the most powerful but requires measurement on an interval scale as well as an underlying bivariate Normal distribution.The significance levels of these correlation measures are tabulated for testing.A simple "rule of thumb" for testing the significance of PMCC is that values below -0.7 or above 0.7 are highly significant. Values in the ranges (-0.7, -0.3) and (0.3, 0.7) are moderate, and values between -0.3 and +0.3 are not significant.
