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# a term used to describe the case when the independent variables in a multiple regression model are correlated is _____.

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## Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

Multicollinearity is when independent variables in a regression model are correlated. I explore its problems, testing your model for it, and solutions.

## Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results.

I use regression to model the bone mineral density of the femoral neck in order to, pardon the pun, flesh out the effects of multicollinearity. Image By Henry Vandyke Carter – Henry Gray (1918)

In this blog post, I’ll highlight the problems that multicollinearity can cause, show you how to test your model for it, and highlight some ways to resolve it. In some cases, multicollinearity isn’t necessarily a problem, and I’ll show you how to make this determination. I’ll work through an example dataset which contains multicollinearity to bring it all to life!

## Why is Multicollinearity a Potential Problem?

A key goal of regression analysis is to isolate the relationship between each independent variable and the dependent variable. The interpretation of a regression coefficient is that it represents the mean change in the dependent variable for each 1 unit change in an independent variable when you hold all of the other independent variables constant. That last portion is crucial for our discussion about multicollinearity.

The idea is that you can change the value of one independent variable and not the others. However, when independent variables are correlated, it indicates that changes in one variable are associated with shifts in another variable. The stronger the correlation, the more difficult it is to change one variable without changing another. It becomes difficult for the model to estimate the relationship between each independent variable and the dependent variable independently because the independent variables tend to change in unison.

There are two basic kinds of multicollinearity:

Structural multicollinearity: This type occurs when we create a model term using other terms. In other words, it’s a byproduct of the model that we specify rather than being present in the data itself. For example, if you square term X to model curvature, clearly there is a correlation between X and X2.Data multicollinearity: This type of multicollinearity is present in the data itself rather than being an artifact of our model. Observational experiments are more likely to exhibit this kind of multicollinearity.Related post: What are Independent and Dependent Variables?

## What Problems Do Multicollinearity Cause?

Multicollinearity causes the following two basic types of problems:

The coefficient estimates can swing wildly based on which other independent variables are in the model. The coefficients become very sensitive to small changes in the model.

Multicollinearity reduces the precision of the estimated coefficients, which weakens the statistical power of your regression model. You might not be able to trust the p-values to identify independent variables that are statistically significant.

Imagine you fit a regression model and the coefficient values, and even the signs, change dramatically depending on the specific variables that you include in the model. It’s a disconcerting feeling when slightly different models lead to very different conclusions. You don’t feel like you know the actual effect of each variable!

Now, throw in the fact that you can’t necessarily trust the p-values to select the independent variables to include in the model. This problem makes it difficult both to specify the correct model and to justify the model if many of your p-values are not statistically significant.

As the severity of the multicollinearity increases so do these problematic effects. However, these issues affect only those independent variables that are correlated. You can have a model with severe multicollinearity and yet some variables in the model can be completely unaffected.

The regression example with multicollinearity that I work through later on illustrates these problems in action.

## Do I Have to Fix Multicollinearity?

Multicollinearity makes it hard to interpret your coefficients, and it reduces the power of your model to identify independent variables that are statistically significant. These are definitely serious problems. However, the good news is that you don’t always have to find a way to fix multicollinearity.

The need to reduce multicollinearity depends on its severity and your primary goal for your regression model. Keep the following three points in mind:

The severity of the problems increases with the degree of the multicollinearity. Therefore, if you have only moderate multicollinearity, you may not need to resolve it.

Multicollinearity affects only the specific independent variables that are correlated. Therefore, if multicollinearity is not present for the independent variables that you are particularly interested in, you may not need to resolve it. Suppose your model contains the experimental variables of interest and some control variables. If high multicollinearity exists for the control variables but not the experimental variables, then you can interpret the experimental variables without problems.

Source : statisticsbyjim.com

## [Solved] A term used to describe the case when the independent variables in a multiple regression modelare correlated is

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A term used to describe the c...

Q.

## A term used to describe the case when the independent variables in a multiple regression modelare correlated is

A. regression B. correlation

C. multicollinearity

D. none of the above

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### Related questions

What is/are true about ridge regression?1. When lambda is 0, model works like linear regression model2. When lambda is 0, model doesn�t work like linear regression model3. When lambda goes to infinity, we get very, very small coefficients approaching 04. When lambda goes to infinity, we get very, very large coefficients approaching infinity

What is/are true about ridge regression?1. When lambda is 0, model works like linear regression model2. When lambda is 0, model doesn’t work like linear regression model3. When lambda goes to infinity, we get very, very small coefficients approaching 04. When lambda goes to infinity, we get very, very large coefficients approachinginfinity

What is/are true about ridge regression?1. When lambda is 0, model works like linear regression model2. When lambda is 0, model doesn’t work like linear regression model3. When lambda goes to infinity, we get very, very small coefficients approaching 04. When lambda goes to infinity, we get very, very large coefficients approaching infinity

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient ofdetermination is

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Suppose that we have N independent variables (X1,X2… Xn) and dependent variable is Y. Now Imagine that you are applying linear regression by fitting the best fit line using least square error on this data. You found that correlation coefficient for one of it’s variable(Say X1) with Y is 0.95.

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## QMB Module 7 Flashcards

Study with Quizlet and memorize flashcards terms like The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the: response variable, . leading coefficient, . correlation coefficient, r. error term, ., Since the multiple regression equation generates a plane or surface, its graph is called a: response surface. response plane. dependent variable graph. dependent variable plane., Dummy variables must always have: positive values. a value of 1. values of either 0 or 1. a value of 0. and more.

## QMB Module 7

The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the:

response variable, .

correlation coefficient, r.

error term, .

Click card to see definition 👆

error term

Click again to see term 👆

Since the multiple regression equation generates a plane or surface, its graph is called a:

response surface. response plane.

dependent variable graph.

dependent variable plane.

Click card to see definition 👆

response service

Click again to see term 👆

1/21 Created by soccercutie4114

### Terms in this set (21)

The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the:

response variable, .

correlation coefficient, r.

error term, . error term

Since the multiple regression equation generates a plane or surface, its graph is called a:

response surface. response plane.

dependent variable graph.

dependent variable plane.

response service

Dummy variables must always have:

positive values. a value of 1.

values of either 0 or 1.

a value of 0.

values either 0 or 1

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is called the:

slope of the least squares regression line.

error term.

multiple coefficient of determination.

correlation.

multiple coefficient of determination

In a multiple regression model, the values of the error term, ε, are assumed to be:

skewed to the left.

normally distributed.

skewed to the right.

uniformly distributed.

normally distributed

In general, R2 always _____ as independent variables are added to the regression model.

increases or decreases depending on how the variables relate to the response variable.

increases stays the same decreases increases

A variable used to model the effect of categorical independent variables is called a(n):

quantitative variable.

categorical variable.

dummy variable.

explanatory variable.

dummy variable

In a multiple regression model, the error term ε is assumed to have a mean of:

μ 0. 1. -1. 0

When we use the estimated regression equation to develop an interval that can be used to predict the mean for a specific unit that meets a particular set of given criteria, that interval is called a(n):

population interval.

prediction interval.

estimation interval.

confidence interval.

prediction interval

In a multiple regression model, the variance of the error term, ε, is assumed to be:

larger as the values of x increase.

1.

the same for all values of x1, x2,..., xp.

0. the same values

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