REGRESSION ANALYSIS
What is the relationship between the price of plots
and their distance from the CBD, plot size, and
altitude in Dar es Salaam City?
Dependent variable (y) = Price of Plots
Independent Variables:
Distance from CBD (X1)
Plot Size (X2)
Altitude (x3)
REGRESSION ANALYSIS
f(y) =𝛽𝑜 + 𝛽1 𝑋1 + 𝛽2 𝑥2 + 𝛽3 𝑥3 + 𝜀
f(Price of Plots)= 𝛽𝑜+ 𝛽1 Distance from CBD1 + 𝛽2 Plot Size + 𝛽3 Altitude +𝜀
𝛽𝑜 = Intercept
𝛽1, 𝛽2, 𝛽3 = Parameters
𝜀 =Error Term
Null hypothesis
there is no relationship between the independent variables and the dependent
variable
Alternative Hypothesis
The alternative hypothesis is that at least one of the coefficients is not equal to zero,
indicating that there is a relationship between the independent variables and the
Data (n=10)
ID
P_Price (Y)
(“00”Tsh)
Size (X1)
(“00”Sqm)
Distance from
CBD (X2)
Altitude (X3)
(00” m)
1
93
153
7
29
2
52
79
31
7
3
77
123
15
19
4
66
101
23
12
5
71
112
19
17
6
39
20
41
3
7
40
31
35
5
8
92
140
12
26
9
55
95
27
8
10
48
79
32
67
Step 1: Import Data to SAS Program (Run the
Data)
Step 1: Result of Imported Data
Step 2: Data Synthesis (Multiple Regression)
Linear Equation (Model).
f(Price of Plots)= 𝛽𝑜+ 𝛽1 Distance from CBD1 + 𝛽2 Plot Size +
𝛽3 Altitude +𝜀
f(y)= 103.8+( −1.7𝑋1)+ (0.02𝑋2) +(−0.02𝑋3)
Analysis
When the Plot size increases by 1 Sqm cause an increase of 2 Tsh on Plot
Price
When you go away from CBD by 1 km cause decrease of 172.5 m Tsh on
Plot Price
When the altitude increases by 1m cause decrease of 2m Tsh on Plot
Step 2:Multiple Regression (R-Square and Adj R-square)
R_Square.
It shows that this model can explain 96.58% of the variance of
dependence in the dependence variable,
Therefore it is a good model to explain relationship
between plot prices and location from CBD, Plot Size and
Altitude.
Adjusted R_Square. (It Measures the goodness of the model)
It shows that this model can explain 94.87% of the variance of
dependence in the dependence variable,
Therefore it is a good model to explain relationship
between plot prices and location from CBD, Plot Size and
Altitude.
Step 3: t- Value and p-value for beta
The t-value and p-value for the beta coefficient are used to
determine the statistical significance of the relationship
between each independent variable and the dependent
variable.
t-Value for beta
The t-value measures the strength of the relationship
between each independent variable and the dependent
variable
The P-Value for beta
p-value indicates the significance of the relationship
P< 0.05 suggests that the relationship is statistically
significant.
The t-value for DistanceCBD is -3.03, and the
p-value is 0.0231, indicating that the
relationship between DistanceCBD and the
dependent variable is statistically significant.
The t-value for SIZE is 0.11, and the p-value is
0.9154, indicating that the relationship between
SIZE and the dependent variable is not
statistically significant. The t-value for Altitude is
-0.18, and the p-value is 0.8648, also indicating
that the relationship between Altitude and the
dependent variable is not statistically
significant.
Step 3: P-Value for the model
The P-value for the model is used to determine
the statistical significance of the whole model.
The P-value for the model
If P< 0.05 then the relationship is statistically
significant.
Because the P-value for the model (0.0001) is less
than 0.05 that means the model is statistically
significant. Hence we reject the null hypothesis
Step 4: Variance Inflation Factor
The t-value and p-value for the beta coefficient are used to
determine the statistical significance of the relationship
between each independent variable and the dependent
variable.
The
t-Value for beta
The t-value measures the strength of the relationship
between each independent variable and the dependent
variable
The P-Value for beta
p-value indicates the significance of the relationship
P< 0.05 suggests that the relationship is statistically
significant.