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You have a set of data points (x1,y1), (x2,y2), ..., (xn,yn), and you have assumed a line model, y = mx + b + e, where e is random error.
You have fit the regression model to obtain estimates of the slope, m, and the intercept, b. Let me call them m and b.
Now you can calculate yi - mxi - b for i = 1, 2, ... n. Notice that, for each i, this is an estimate of the error in yi. It's called the residual because it's what's 'left over' in yi after removing the part 'explained' by the regression.
Another way of understanding this is to take a set of linearly related (x,y) pairs, graph them, calculate the regression line, plot it on the same graph and then measure the verticaldistances between the regression line and the each of the pairs. Those vertical distances are the residuals.
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What is the purpose of a residual analysis in simple linear regression?
One of the main reasons for doing so is to check that the assumptions of the errors being independent and identically distributed is true. If that is not the case then the simple linear regression is not an appropriate model.
In a good regression model the residual plot shows?
a random pattern
How is linear regression used?
Linear regression can be used in statistics in order to create a model out a dependable scalar value and an explanatory variable. Linear regression has applications in finance, economics and environmental science.
What is the difference between simple and multiple linear regression?
I want to develop a regression model for predicting YardsAllowed as a function of Takeaways, and I need to explain the statistical signifance of the model.
What is true about the y-intercept in the linear regression model?
The value depends on the slope of the line.
What is the purpose of a residual analysis in simple linear regression?
One of the main reasons for doing so is to check that the assumptions of the errors being independent and identically distributed is true. If that is not the case then the simple linear regression is not an appropriate model.
In a good regression model the residual plot shows?
a random pattern
How is linear regression used?
Linear regression can be used in statistics in order to create a model out a dependable scalar value and an explanatory variable. Linear regression has applications in finance, economics and environmental science.
What are some of the advantages and disadvantages of making forecasts using regression methods?
+ 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.
What is the difference between simple and multiple linear regression?
I want to develop a regression model for predicting YardsAllowed as a function of Takeaways, and I need to explain the statistical signifance of the model.
Where ridge regression is used?
Ridge regression is used in linear regression to deal with multicollinearity. It reduces the MSE of the model in exchange for introducing some bias.
What is true about the y-intercept in the linear regression model?
The value depends on the slope of the line.
What is the difference between the logistic regression and regular regression?
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.
What is Full Regression?
Regression :The average Linear or Non linear relationship between Variables.
Is it true that the y-intercept in the linear regression model is always 0?
It could be any value
Why are your predictions inaccurate using a linear regression model?
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.
which characteristics of a data set makes a linear regression model unreasonable?
A correlation coefficient close to 0 makes a linear regression model unreasonable. Because If the correlation between the two variable is close to zero, we can not expect one variable explaining the variation in other variable.
