MULTIPLE LINEAR REGRESSION What is the model for the multiple linear regression when weight gain is a dependent variable and the explanatory variables are hemoglobin change, tap water consumption, and age. Be sure to define all symbols and model assumptions.

Multiple linear regression can be said to be a statistical technique that uses several explanatory variables to predict the outcome of a response variable.

The Formula for Multiple Linear Regression Is

yi= β0+β1xi1+β2xi2+...+βpxip+ϵ

where, for i=n observations

yi= Dependent variable

xi= Expanatory variable

β0= y - intercept (constant term)

βp= Slope coefficients for each explanatory variable

ϵ= The model’s error term (also known as the residuals)

From the question written above,

yi= weight gain which is dependent on the explanatory variables which are hemoglobin change, tap water consumption, and age. i.e. xi

Model assumptions

1. There is a linear relationship between the dependent variables and the independent variables.

2. The independent variables are not too highly correlated with each other.

3. yi observations are selected independently and randomly from the population.

4. Residuals should be normally distributed with a mean of 0 and variance σ.

(Investopedia, 2019)

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