STAT 393 Linear Models

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STAT 393 Linear Models

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STAT 393 Linear Models

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Course Code: STAT393
University: Victoria University Of Wellington

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Country: New Zealand

Question:
Describe the Linear Models For Independent Variables or Regressors.

Answer:
Introduction 
Secondary data used in analysis were obtained from Massey University website. The data was collected from Canberra, Australia in February 1987. It consist information of twenty houses that were on sale. The variables are cost of house in dollars which is the dependent variable, floor area in square metres, area land in square metres, number of main rooms, age of house in years and whether the house is centrally heated or not.  The data is used to forecast or predict the price of house In Canberra. This will help the potential buyer in decision making.
Methodology 
The statistical tool used in analysis is linear regression analysis where price is the dependent variable and floor, land, rooms, age and centrally heat are independent variables or regressors.  Regression analysis is a statistical process for estimating the relationships among variables. It involves techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. Running multiple linear regression
Where x1 is floor, x2 is land, x3 is rooms, x4 is age of house, x5 is whether room is centrally heated or not and y is price of the house.
R statistical software is used for analysis and the results were discussed below.
Results and discussion 
From figure 1, a scatter plot which check association between dependent variable and independent variable graphically, there is positive correlation between price and floor of the house and price with land area. Thus when floor and land size increases the price of house also increases and vice versa. There exist negative exist negative correlation between price of house and age of the house, this means when age of house increases price of a house decreases and vice versa. The older the house the lower the price of the house, there is no correlation between price of the house and number of rooms and whether the room is centrally heated or not.
Adjusted R-squared is 0.8905 which means 89.05% of the price changes are explained by dependent variables and the model is a good fit.
The level of significance is 0.05, probability of t-value of land is 0.8 which is greater than p-value of 0.05 thus the size of land is insignificant in predicting price of house and can be dropped from the model. Floor size, number of rooms, age of house and whether the houses is centrally heated or not are significance and can be used in predicting the price of the house.
The model is given by y .
Suppose that the potential house buyer found a property with the following
Characteristics: floor area 141.0 square metres, land area 710 square metres, 7 rooms, 3.5
Years old, central heating installed. If the asking price was $89,000 this is bargain as the predicted price is $84 708 
Reference 

Whitley E, Ball J. (2002). Statistics review 1: Presenting and summarizing data.Crit Care. 
Venkat N., Vijav V., Venu G. and Rao R. (2016). Handbook of Statistics.

      Retrieved from: https://www.sciencedirect.com/science/handbooks/01697161.

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