- #1

- 1,252

- 84

- Summary:
- Understand the possible limitations of multivariate linear regression

Hello,

With multivariate linear regression, there is a single dependent variable ##y## and multiple independent variables ##x_1##, ##x_2##, ##x_3##, etc.

There is a linear, weighted relationship between ##y## and the various ##x## variables:

$$ y = c_1 x_1 + c_2 x_2 + c_3 x_3 $$

The independent variables are ideally totally independent from each other. Otherwise we run into the problem of collinearity. However, multivariate linear regression can still be used if pairs of independent variables are linearly related...

What happens if we discover that one or two of the independent variables ##x## has a curvilinear correlation with the dependent variable ##y## while the other have a linear correlation? Or if there is curvilinear correlation between the independent variables themselves?

Should multivariate linear regression still be used?

Thank you!

With multivariate linear regression, there is a single dependent variable ##y## and multiple independent variables ##x_1##, ##x_2##, ##x_3##, etc.

There is a linear, weighted relationship between ##y## and the various ##x## variables:

$$ y = c_1 x_1 + c_2 x_2 + c_3 x_3 $$

The independent variables are ideally totally independent from each other. Otherwise we run into the problem of collinearity. However, multivariate linear regression can still be used if pairs of independent variables are linearly related...

What happens if we discover that one or two of the independent variables ##x## has a curvilinear correlation with the dependent variable ##y## while the other have a linear correlation? Or if there is curvilinear correlation between the independent variables themselves?

Should multivariate linear regression still be used?

Thank you!