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I am studying linear regression. I want to ask is the linear word in multiple linear regression refers to the linear relationship between the target variable and each of the regression coefficients b_0, b_1,b_2, ..., b_n? Also in multiple linear regression there is a linearity assumption does this assumption refers to the linear relationship between the dependent variable and each independent variables which we confirm using scatter plot?

MLR equation that I am using:

$\hat y = b_0 + b_1x_1 + b_2x_2 + \dots + b_n x_n$

Also if this linearity assumption is not satisfied should I then try polynomial regression? And is this polynomial regression also a kind of linear regression where the independent variable is non-linearly related to dependent variable but the regression coefficients are linearly related to target variable?

I know I have asked too many doubts so please bear with me and be kind to clear my doubts.

Sycorax
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shri
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  • Welcome to Cross Validated! Does this answer your question? If not, why not? What questions remain? – Dave Jul 12 '23 at 17:23
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    The thread at https://stats.stackexchange.com/questions/148638 provides some information for disambiguating the various senses of "linear" you refer to. – whuber Jul 12 '23 at 20:05

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