An example of multivariate regression could be to predict the price of a house based on several independent variables such as the size of the house, the number of bedrooms, the location, and the age of the house.
The dependent variable in this case is the price of the house, and the independent variables are size, number of bedrooms, location, and age. The multivariate regression equation would look like:
Price = β0 + β1(Size) + β2(Number of bedrooms) + β3(Location) + β4(Age) + ε
where β0 is the intercept, β1, β2, β3, and β4 are the regression coefficients, and ε is the error term.
By analyzing the data and estimating the regression coefficients, we can determine which independent variables have the most significant impact on the price of the house. For example, the regression analysis might show that the size of the house and the location have a stronger impact on the price than the number of bedrooms and the age of the house. Based on this information, we can make more informed decisions about buying or selling houses, or about pricing houses in different locations based on their characteristics.