Simple Linear Regression
It is believed that caste plays an important role in Indian elections. Data is collected from 2019
elections from 37 parliamentary constituencies of Tamil Nadu for the political party called
A2ZMK (A-to-Z Munnetra Kazhagam) and number of people belonging A to Z (A2Z) caste in
each of the 37 constituencies. Note that, depending on the candidate, they also get large number
of votes from people belonging to other castes. Data description is provided in Table 1.1 and
descriptive statistics are shown in Table 1.2.
Table 1.1. Data Description
Variable Name
Description
NVP
Votes polled for A2ZMK in a constituency
A2Z
Number of voters belonging to A2Z caste
in a constituency
ln(NVP)
= ln(NVP)
ln(A2Z)
= ln(A2Z)
Table 1.2. Descriptive Statistics
N
Mean
A2Z
37
17536.000
NVP
37
94623.35
LNA2Z
37
9.5855
LNNVP
37
11.4550
Valid N (listwise)
37
Std. Deviation
11303.7003
6924.458
.6298
.0733
A simple linear regression model was developed between the variable NVP as dependent variable
and A2Z as independent variable. The regression outputs are shown in Tables 1.3 and 1.4.
Table 1.3 Model Summaryb
Model
R
R Square
Adjusted R
Square
Std. Error of
the Estimate
1
4722.744
a. Predictors: (Constant), A2Z
b. Dependent Variable: NVP
Table 1.4 Coefficientsa
Model
1
Unstandardized Coefficients
(Constant)
B
Std. Error
86673.0292
1447.0391
A2Z
a. Dependent Variable: NVP
.070
Standardized
Coefficients
t
Sig.
Beta
59.897
.740
6.511
.000
(a) Is there a statistically significant relationship between votes polled (NVP) for A2ZMK and
the number of voters belonging to A2Z caste in the constituency at a 1% significance level?
(b) A constituency has 50000 voters belonging the A2Z caste. Predict the votes polled for
A2ZMK in this constituency.
(c) What proportion of the variation in votes polled for A2ZMK is explained by the number
of people belonging the A2Z caste?
(d) The President of the A2ZMK party believes that at least 40% of the people belonging to
the A2Z caste vote for them. Check whether the President’s claim is true at a 10%
significance level. Clearly write all the steps.
The normal P-P plot and residual plots are shown in Figures 1.1 and 1.2.
Figure 1.1 Normal P-P Plot
Figure 1.2 Residual plot
(e) Based on the P-P plot (Figure 1.1) and Residual Plot (Figure 1.2), comment on the validity
of model shown in Tables 1.3 and 1.4. Clearly identify any potential problem with the
model.
A second model is developed between ln(NVP) and ln(A2Z). The model outputs are provided in
Tables 1.5 and 1.6 and Figures 1.3 and 1.4.
Table 1.5 Model Summaryb
Model
R
R Square
1
.754a
Adjusted R
Square
Std. Error of
the Estimate
.0488
a. Predictors: (Constant), LNA2Z
b. Dependent Variable: LNNVP
Table 1.6. Coefficientsa
Model
Unstandardized Coefficients
B
1
(Constant)
LNA2Z
Std. Error
10.614
.124
.088
.013
Standardized
Coefficients
t
Sig.
Beta
85.500
.000
a. Dependent Variable: LNNVP
(f) Coimbatore has 50,000 voters belonging A2Z caste, what is the number of the votes polled
for A2ZMK in Coimbatore using Model 2?