Suppose we fit a multiple regression model of the median housing value versus po

Question

Suppose we fit a multiple regression model of the median housing value versus population, education, income and poverty of the towns.

The fitted multiple regression model is: Value= ?126 + 0.642Population ? 23.9Education + 10.2Income + 3.1Poverty

a) Interpret the coefficient of 1 ˆ ? = 0.642 in the context of this problem.

b) Interpret the coefficient of 2 ˆ ? = ?23.9 in the context of this problem.

The residual plots from fitting the model in part (a) are given below. Discuss, in detail, each of the residual plots and assess which (if any) assumptions are violated. Be sure to mention all of the assumptions.

E.) Suggest how to include the GROUP variable of the towns into a multiple regression model that already includes the population (POPULATION) and the per capita income (INCOME).

Variable Description VALUE This is the response variable of interest. It is the median housing value of each town (in thousands). POPULATION The total population in each town (in thousands). EDUCATION A variable indicating: - 1 if more than 40% of a town’s population had earned a bachelor’s degree or higher, and - 0 otherwise INCOME The per capita income for each town (in thousands) POVERTY A variable indicating: - 1 if more that 10% of a town’s family live in poverty, and - 0 otherwise GROUP A 5-level variable indicating membership in one of the five town groupings designated by the Connecticut State Data Center here at UCONN. - Rural - Urban Periphery - Urban Core - Suburban - Wealthy

Explanation / Answer

In multiple regression the values of the slopes are interpreted as to how much of a unit change in Y will occur for a unit increase in a particular X predictor variable, given that the other variables are held constant.

Thus, with other factors are held constant with one unit change in population the value increases by 0.642.

And, with other factors are held constant with one unit change in education the value increases by -23.9.

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