# What is residual in linear regression model?

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 **vertical**
distances between the regression line and the each of the pairs.
Those vertical distances are the residuals.

### 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 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.

### 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.

### What is multiple and partial correlation?

multiple correlation: Suppose you calculate the linear regression of a single dependent variable on more than one independent variable and that you include a mean in the linear model. The multiple correlation is analogous to the statistic that is obtainable from a linear model that includes just one independent variable. It measures the degree to which the linear model given by the linear regression is valuable as a predictor of the independent variable. For calculation…

### What can you conclude if the global test of regression does not reject the null hypothesis?

You can conclude that there is not enough evidence to reject the null hypothesis. Or that your model was incorrectly specified. Consider the exact equation y = x2. A regression of y against x (for -a < x < a) will give a regression coefficient of 0. Not because there is no relationship between y and x but because the relationship is not linear: the model is wrong! Do a regression of y against x2…

### What is the normal probability plot of residuals?

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…

### What is F variate?

The F-variate, named after the statistician Ronald Fisher, crops up in statistics in the analysis of variance (amongst other things). Suppose you have a bivariate normal distribution. You calculate the sums of squares of the dependent variable that can be explained by regression and a residual sum of squares. Under the null hypothesis that there is no linear regression between the two variables (of the bivariate distribution), the ratio of the regression sum of squares…

### What is weighted residual method?

In estimating a linear relationship using ordinary least squares (OLS), the regression estimates are such that the sums of squares of the residuals are minimised. This method treats all residuals as being as important as others. There may be reasons why the treatment of all residuals in the same way may not be appropriate. One possibility is that there is reason to believe that there is a systematic trend in the size of the error…

### When you use your regression line to predict values that are not in the sample and discovered large residual values in each prediction what can you say about your regression line?

There are several possible explanations: Leaving aside the two most obvious reasons: calculation error and attempted extrapolation, there are the following possibilities: The true relationship is non-linear. A relevant variable has been missed omitted. The observations are very variable: leading to a very large residual error. There is not enough variation in the independent (or predictive) variable so that Sxx is very small.

### What is the difference between the stochastic error term and the residual?

the residual is the difference between the observed Y and the estimated regression line(Y), while the error term is the difference between the observed Y and the true regression equation (the expected value of Y). Error term is theoretical concept that can never be observed, but the residual is a real-world value that is calculated for each observation every time a regression is run. The reidual can be thought of as an estimate of the…

### How does a linear regression allow us to better estimate trends costs and other factors in complex situations?

You question is how linear regression improves estimates of trends. Generally trends are used to estimate future costs, but they may also be used to compare one product to another. I think first you must define what linear regression is, and what the alternative forecast methods exists. Linear regression does not necessary lead to improved estimates, but it has advantages over other estimation procesures. Linear regression is a mathematical procedure that calculates a "best fit"…

### Is it true if you log the all values and make regression linear?

Your question is a bit hard to understand, but I'll do my best. Sometimes taking the log of your independent variable will improve a linear fit. If you have two sets of data, X and Y, and they don't seem to fit a linear relationship, you may take the log of X, and the log of X may fit a linear relationship. Example: Suppose your data correctly fits the model y = a Xm. So…

### Difference between regression coefficient and correlation coefficient?

difference between correlation and regression? (1) The correlation answers the STRENGTH of linear association between paired variables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X. (2a) Correlation is calculated whenever: * both X and Y is measured in each subject and quantify how much they are linearly associated. * in particular the Pearson's product moment correlation coefficient…

### What does the term residual mean?

Let's say that you fit a simple regression line y = mx + b to a set of (x,y) data points. In a typical research situation the regression line will not touch all of the points; it might not touch any of them. The vertical difference between the y-co-ordinate of one of the data points and the y value of the regression line for the x-co-ordinate of that data point is called a residual. There…

### When are OLS estimators BLUE?

For Classical Regression Model the OLS or Ordinary Least Squares - estimators (or the betas) are BLUE (Best, Linear, Unbiased, Estimator) when : The regression is linear in the coefficients, it is correctly specified and has an additive error term. Mean of the error term is zero. (Include a constant term in the regression (B0 which will force the mean to be zero) The independent variables are not correlated with the error term. (If they…

### What is the Gauss-Markov theory?

In statistics, the Gauss-Markov theorem states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.

### 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 of the independent variables x1, x2, ... xk, y is the dependent variable a and the b are regression parameters. The e are independent, identically distributed random variables (representing the error).

### Why is it important to look at a scatter plot prior to starting a simple linear regression?

To see if there is a linear relationship between the dependent and independent variables. The relationship may not be linear but of a higher degree polynomial, exponential, logarithmic etc. In that case the variable(s) may need to be transformed before carrying out a regression. It is also important to check that the data are homoscedastic, that is to say, the error (variance) remains the same across the values that the independent variable takes. If not…

### When you introduce more than one independent variable into a linear regression analysis?

Generally, when the dependent variable appears to be the result of more than one independent variables, a multiple regression model may be suitable. It is difficult to justify adding an additional variable, that does not significantly reduce the residual error of the fit. The setting of thresholds to justify addition of variables is in the area of "stepwise regression." The data must be adequate and consistent with the assumption of independent variables. I note from…