OLS Regression Model for Estimating Unknown Coefficients

1) The OLS regression model of the form;
Y=β0+β1X1+β2X2+β3X3+β4X4+ε
The model above is used for estimating the unknown scalars that isβ0, β1, β2, β3, and β4
which are the coefficients of the independent variables. The sample size is part of the
population and therefore we only consider a sample size with five variables. In the
model above Y is the dependent variable and moreover, the independent variables are
variables that stand alone and don’t change by other variables. From the model above
the independent variables include X1, X2, X3 and X4. The unit of measurement of
these variables should always be considered as they help in understanding the model
better. The population is always very big hence analyzing all the data is always
expensive and time consuming and therefore we always consider the sample size
(Stock, James, Mark and Watson, 2015).
2)
60 80 100 120 140 160 180 200
0
200
400
600
800
1000
1200
Scatter plot of Market Price ($000)
by Sydney price index
Sydney price index
Market Price ($000)
Figure 1

The figure 1 above shows the relationship between market price ($000) and Sydney price index
and therefore the two variables are related. The two variables are directly proportional but this
doesn’t happen in all instances and therefore we can conclude that the Sydney price index is not
the only factor to consider.
a) Making a scatter plot with market price ($000) and annual % change
0 2 4 6 8 10 12 14 16 18
0
200
400
600
800
1000
1200
Scatter plot of Market Price ($000)
by annual %change
Annual % change
Market Price ($000)
FFigure-2
From figure-2 above we notice that most values lies within 0 to 5 and 11 to 16 annual % change,
between 5 to 10 we only have one point which is 6.6 annual % changes and it corresponds to
$651 of the market price. It shows relationship between market price and annual % change and
since the gradient is also positive then for most data as the annual % change increases, the
market price also increases.
b) Making a scatter plot of Market price ($000) by total number of square meters.

140 160 180 200 220 240 260 280 300 320
0
200
400
600
800
1000
1200
Scatter plot of Market Price ($000)
by Total number of square meters
Total number of square meters
Market Price ($000)
Figure-3
We also notice from figure 3 above that most data points lies within 150 to 250.
The straight-line doesn’t pass through most points of the graph hence the graph
doesn’t show a strong relationship between market price and total number of
square meters.
c) Making a scatter plot of market price by age of house (years).
0 5 10 15 20 25 30 35 40 45 50
0
200
400
600
800
1000
1200
Scatter plot of Market Price ($000)
by age of house (years)
Age of house (years)
Market price ($000)
Figure-4
From the figure-4 above the straight-line have a negative gradient indicating that
as age of house increases, the market price decreases. The two variables are
indirectly proportional.