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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 cases of high multicollinearity it is not possible to assess the individual significance of one or more partial regression coefficient true or false or uncertain?
The given statement is true. Reason: High multicollinearity can make it difficult to determine the individual significance of predictors in a model.
A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables True or false?
True , it would have been false only if it was mentioned no relationship . But as it mentions linear it is true.
If the coefficient of determination for a data set containing 12 points is 0.5 6 of the data points must lie on the regression line for the data set.?
That is not true. It is possible for a data set to have a coefficient of determination to be 0.5 and none of the points to lies on the regression line.
What is sample regression function?
To take a simple case, let's suppose you have a set of pairs (x1, y1), (x2, y2), ... (xn, yn). You have obtained these by choosing the x values and then observing the corresponding y values experimentally. This set of pairs would be called a sample.For whatever reason, you assume that the y's and related to the x's by some function f(.), whose parameters are, say, a1, a2, ... . In far the most frequent case, the y's will be assumed to be a simple linear function of the x's: y = f(x) = a + bx.Since you have observed the y's experimentally they will almost always be subject to some error. Therefore, you apply some statistical method for obtaining an estimate of f(.) using the sample of pairs that you have.This estimate can be called the sample regression function. (The theoretical or 'true' function f(.) would simply be called the regression function, because it does not depend on the sample.)
