I have a couple questions about Quant that dont make sense? What is the difference between the slope coefficent and the correlation coefficient? (don’t hey both describe the relationship between the 2 variables) But in a regression, they say there is the correlation between the indep and dependent variable and there is a slope coefficent ? I dont understand the difference in the definitions of the two? Second of all, what is the difference between a time series and cross sectional data (regression) ?
1 definition -> Correlation coefficient = sqrt(R^2) 2. Defines the extent of linear relation between the two variables. In a single variable regression R^2 = Amount of variance in the Dependent variable explained by the Independent variable. Slope coefficient is the “b1” portion - what is associated with the Independent variable. They are two completely different things, as far as I know.
thanks CP But I am looking for the definition of the slope coefficent and how it differs from the definition of the correlation coefficient. Because the both describe the relationship between 2 variables, the last time I checked.
then please check again. they are both NOT the same. Y=b0+b1*x b1 is the slope. it is the amount by which Y the dependent variable will change for each unit change in X.
The way I see this is: the slope coefficient is the slope of the line and the coerrelation coefficient is the goodness of fit the observations are to that line. the b1 coefficient is a relation b/w x and y and the correlation coefficient is a relation b/w observed y and actual y.
The material doesnt teach the theory very well here. The slope coef you are referring to is in the 1 dimensional case. In theory, it is a vector of estimates of the unknown true effect of the X variable’s linear predictive influence on the independant Y. The true relationship is unknown and the ordinary least squares model is used to best estimate (minimize errors) based on the underlying assumptions and data we are given. Thats why as N increases and approaches the true population, the errors —> 0. So these are found from the OLS method. The t value estimates if B is significantly different than 0. The R^2 is the predicted Y values using the B estimates derived from the X values and plugging the X values back in. A new set of Y values are created based on the model. Then the mean of the new values is subracted from the new Y estimates and squared, then summed. From this, you can guess that since we are trying to create a line (in the 1 dimensional case) these estimates will be streamlined given their X values. The observations, say a scatter plot with the true Y values go through the same process. That is the denominator. The true Y values will have a greater variation from their mean, therefore a larger denominator. The estimates in the numerator will be more “streamlined” think a line through a scatter plot. So the R^2 is that measurement ratio. If you see a scatter plot that is all over the place, you can see that no line can be very predictive, therefore lower R^2 and higher error. If there is a tendency around a line, R^2 is higher. If they are all points on a line, R^2 is 1. Im sure someone can explain better, I am trying to recall from Stats. Hopefully it helps.
a7m002 Wrote: ------------------------------------------------------- > I have a couple questions about Quant that dont > make sense? > > What is the difference between the slope > coefficent and the correlation coefficient? (don’t > hey both describe the relationship between the 2 > variables) But in a regression, they say there > is the correlation between the indep and dependent > variable and there is a slope coefficent ? I dont > understand the difference in the definitions of > the two? > > Second of all, what is the difference between a > time series and cross sectional data (regression) > ? I hate quant 
1. Slope coefficient measures the change that will occur in dependent variable when the independent variable changes by a particular keeping all other independent variables constant Correlation coefficient measures how well will a set of independent variables explain the change in dependent variable. So you can think of slope coefficient being a quantitative measure while correlation being a qualitative measure. 2. Time series regression measures relationships between variables over a period of time. Eg: Return of two stocks for 5 years. Cross series regression measures relationships between variables at a given time. Eg: an analyst may regress stock returns for different companies measured over the same period against differences in the companies’ yields for the period.
> 1. Slope coefficient measures the change that will > occur in dependent variable when the independent > variable changes by a particular keeping all other > independent variables constant When we talk about the slope of the line it’s only one independent variable, so we don’t need to keep other variables constant because there are no other variables. That definition above is more related to multiple variables regression. But in this case we use coefficient, not slope of the line. > Correlation coefficient measures how well will a > set of independent variables explain the change in > dependent variable. Correlation measure degree of dependency! Not how well independent will explain dependent - that is done by R squared - coefficient of determination. > So you can think of slope coefficient being a > quantitative measure while correlation being a > qualitative measure. correlation is also qualitive! Ranges from -1 to 1 > 2. Time series regression measures relationships > between variables over a period of time. Eg: > Return of two stocks for 5 years. > > Cross series regression measures relationships > between variables at a given time. > Eg: an analyst may regress stock returns for > different companies measured over the same period > against differences in the companies’ yields for > the period.
Thanks for your help, I think I got it
Re: 2. Time series regression measures relationships between variables over a period of time. Eg: Return of two stocks for 5 years. Cross series regression measures relationships between variables at a given time. Eg: an analyst may regress stock returns for different companies measured over the same period against differences in the companies’ yields for the period. from your explanation, they are the same. Return of two stocks for 5 years from 2002-2007, is stock returns for different companies measured over the same period (2002-2007)
francisgy Wrote: ------------------------------------------------------- > Re: > 2. Time series regression measures relationships > between variables over a period of time. Eg: > Return of two stocks for 5 years. > > Cross series regression measures relationships > between variables at a given time. > Eg: an analyst may regress stock returns for > different companies measured over the same period > against differences in the companies’ yields for > the period. > > from your explanation, they are the same. Return > of two stocks for 5 years from 2002-2007, is stock > returns for different companies measured over the > same period (2002-2007) Sorry for the confusion but I meant: Time Series: Returns between two stocks over five years. So you have five observations in each year (if making annual observations) Cross Section: Returns and earnings yield measured between two (or three, fifty, hundred) companies over the same year (2007) or same decade (2002-2012)[which is also termed as the same time period]. So in 2007: Company A: Reutrns 5% Earnings yield 6% Company B: Reutrns 4% Earnings yield 5% Company C: Reutrns 9% Earnings yield 14% Company D: Reutrns 3% Earnings yield 8%
Time Series: Returns between two stocks over five years??? suppose your X axis is year from 2002 to 2007, Y axis is return of IBM, and you analyze IBM return and S&P return so how can you draft a chart with two Y axis, one is IBM and the other is S&P? your time series is wrong
just a thought . if you knew so much - do not ask questions. your first response seems to be “you are wrong”, “oh no no”. haven’t you ever seen two lines drawn as stock returns. y axis is return %. x axis is time. use excel plot what idreesz has shown - as two sets of data points… most of the graphs in the text too draw such plots…
> your first response seems to be “you are wrong”, “oh no no”. haha CP, you pinned it correctly Anyways, francisgy, good thing is mostly your questions are intelligent. But you also might want to spend a few more seconds on responses you get for those questions.
No. I’m not intelligent, and most case, I’m not correct, I just find different concepts mixed together