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The F-statistic is a test on ratio of the sum of squares regression and the sum of squares error (divided by their degrees of freedom). If this ratio is large, then the regression dominates and the model fits well. If it is small, the regression model is poorly fitting.
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).
+ Linear regression is a simple statistical process and so is easy to carry out. + Some non-linear relationships can be converted to linear relationships using simple transformations. - The error structure may not be suitable for regression (independent, identically distributed). - The regression model used may not be appropriate or an important variable may have been omitted. - The residual error may be too large.
in general regression model the dependent variable is continuous and independent variable is discrete type. in genral regression model the variables are linearly related. in logistic regression model the response varaible must be categorical type. the relation ship between the response and explonatory variables is non-linear.
how can regression model approach be useful in lean construction concept in the mass production of houses
Random error, measurement error, mis-specification of model (overspecification or underspecification), non-normality, plus many more.
a random pattern
The F-statistic is a test on ratio of the sum of squares regression and the sum of squares error (divided by their degrees of freedom). If this ratio is large, then the regression dominates and the model fits well. If it is small, the regression model is poorly fitting.
The F-statistic is a test on ratio of the sum of squares regression and the sum of squares error (divided by their degrees of freedom). If this ratio is large, then the regression dominates and the model fits well. If it is small, the regression model is poorly fitting.
When you use linear regression to model the data, there will typically be some amount of error between the predicted value as calculated from your model, and each data point. These differences are called "residuals". If those residuals appear to be essentially random noise (i.e. they resemble a normal (a.k.a. "Gaussian") distribution), then that offers support that your linear model is a good one for the data. However, if your errors are not normally distributed, then they are likely correlated in some way which indicates that your model is not adequately taking into consideration some factor in your data. It could mean that your data is non-linear and that linear regression is not the appropriate modeling technique.
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).
There are many possible reasons. Here are some of the more common ones: The underlying relationship is not be linear. The regression has very poor predictive power (coefficient of regression close to zero). The errors are not independent, identical, normally distributed. Outliers distorting regression. Calculation error.
+ Linear regression is a simple statistical process and so is easy to carry out. + Some non-linear relationships can be converted to linear relationships using simple transformations. - The error structure may not be suitable for regression (independent, identically distributed). - The regression model used may not be appropriate or an important variable may have been omitted. - The residual error may be too large.
In a statistical model, variations in the dependent variable can be attributed to independent variables. However, there is a random element that is not accounted for and this is the stochastic error.
in general regression model the dependent variable is continuous and independent variable is discrete type. in genral regression model the variables are linearly related. in logistic regression model the response varaible must be categorical type. the relation ship between the response and explonatory variables is non-linear.
Regression analysis describes the relationship between two or more variables. The measure of the explanatory power of the regression model is R2 (i.e. coefficient of determination).
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.