Although there have been lot of studies undertaken in the past on factors affecting the weight of the brain and whether it corresponds to the size of the head or not. Also, some of the past research was done considering multiple linear regression based on data set of one year for some of the age groups. Hence, this gives motivation to resolve both the factors stated previously by formulating a regression model based on mixed effects model and linear regression while considering data from male and female with an age range from 1 to 2.
The dataset used is the Head size and brain weight analyzer (https://www.kaggle.com/saarthaksangam/headbrain). The dataset comprises of:
- Gender
- Age Range
- Head size in cm^3
- Brain Weight in grams
Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.