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Which statistic estimates the error in a regression solution?
The mean sum of squares due to error: this is the sum of the squares of the differences between the observed values and the predicted values divided by the number of observations.
What is the difference between the stochastic error term and the residual?
Ah, the stochastic error term and the residual are like happy little clouds in our painting. The stochastic error term represents the random variability in our data that we can't explain, while the residual is the difference between the observed value and the predicted value by our model. Both are important in understanding and improving our models, just like adding details to our beautiful landscape.
What is the difference between a bias and a random error?
Bias is systematic error. Random error is not.
What is the difference between corelation and regression?
I've included links to both these terms. Definitions from these links are given below. Correlation and regression are frequently misunderstood terms. Correlation suggests or indicates that a linear relationship may exist between two random variables, but does not indicate whether X causes Yor Y causes X. In regression, we make the assumption that X as the independent variable can be related to Y, the dependent variable and that an equation of this relationship is useful. Definitions from Wikipedia: In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. In statistics, regression analysis refers to techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called a response variable) and of one or more independent variables (also known as explanatory variables or predictors). The dependent variable in the regression equation is modeled as a function of the independent variables, corresponding parameters ("constants"), and an error term. The error term is treated as a random variable. It represents unexplained variation in the dependent variable. The parameters are estimated so as to give a "best fit" of the data. Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used.
Linear regression model?
y(i) = a + b1.x1(i) + b2.x2(i) + b3.x3(i) + ... + bk.xk(i) + e(i)where i = 1, 2, ... n are n observations ofthe independent variables x1, x2, ... xk,y is the dependent variablea and the b are regression parameters.The e are independent, identically distributed random variables (representing the error).
The random error in a regression equation?
includes both positive and negative terms.
The regression equation is determined by minimizing?
The total squared error between the predicted y values and the actual y values
What are the sources of error in regression model?
Random error, measurement error, mis-specification of model (overspecification or underspecification), non-normality, plus many more.
What is the role of the stochastic error term in regression analysis?
Regression analysis is based on the assumption that the dependent variable is distributed according some function of the independent variables together with independent identically distributed random errors. If the error terms were not stochastic then some of the properties of the regression analysis are not valid.
Which statistic estimates the error in a regression solution?
The mean sum of squares due to error: this is the sum of the squares of the differences between the observed values and the predicted values divided by the number of observations.
What is the difference between the stochastic error term and the residual?
Ah, the stochastic error term and the residual are like happy little clouds in our painting. The stochastic error term represents the random variability in our data that we can't explain, while the residual is the difference between the observed value and the predicted value by our model. Both are important in understanding and improving our models, just like adding details to our beautiful landscape.
What is the difference between a bias and a random error?
Bias is systematic error. Random error is not.
What is the significance of smaller Root mean square error?
When we use linear regression to predict values, we input a given x value and we use the equation of the correlation line to predict the y values. Sometimes we want to know how spread out the y values are. We look at the difference between the predicted and the actual y values. These differences are called residual and they are either positive if the y value is more than the estimated y value or negative if it is less. So for example if the observed value is 10 and the predicted one is 15, the residual is 15-10=5. Now we can find the residual for each y value in our data set and square it. Then we can take the average of those squares. Last, we take the square root of the average of the squared residuals and this is the RMS or root mean square error. The units are the same as the y values. If the RMS error is big, then the y values are not too close to the predicted ones on the y value and the our line does not provide as good of a model to predict values. If it is small, the y values are well predicted by the regression line. For a horizontal line, the RMS error is the same as the standard deviation. r is the regression coefficient and it measures how closely clustered the points are relative to the standard deviaton. The RMS error measures the spread in the original y units.
What is the difference between corelation and regression?
I've included links to both these terms. Definitions from these links are given below. Correlation and regression are frequently misunderstood terms. Correlation suggests or indicates that a linear relationship may exist between two random variables, but does not indicate whether X causes Yor Y causes X. In regression, we make the assumption that X as the independent variable can be related to Y, the dependent variable and that an equation of this relationship is useful. Definitions from Wikipedia: In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. In statistics, regression analysis refers to techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called a response variable) and of one or more independent variables (also known as explanatory variables or predictors). The dependent variable in the regression equation is modeled as a function of the independent variables, corresponding parameters ("constants"), and an error term. The error term is treated as a random variable. It represents unexplained variation in the dependent variable. The parameters are estimated so as to give a "best fit" of the data. Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used.
What is stochastic error term?
A Stochastic error term is a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the econometrician's ignorance or inability to model all the movements of the dependent variable.
If amount of error along regression line is similar is this homoscedasticity?
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If the regression sum of squares is large relative to the error sum of squares is the regression equation useful for making predictions?
If the regression sum of squares is the explained sum of squares. That is, the sum of squares generated by the regression line. Then you would want the regression sum of squares to be as big as possible since, then the regression line would explain the dispersion of the data well. Alternatively, use the R^2 ratio, which is the ratio of the explained sum of squares to the total sum of squares. (which ranges from 0 to 1) and hence a large number (0.9) would be preferred to (0.2).
