1. Introduction

1.1 The research question

What will be the predicted outcome for the party that receives the highest amount of votes in the upcoming election 2025 between the Conservative Party and the Liberal Party?

1.2 Importance of the research

Free and fair elections are considered important features contributing to a healthy democracy. Fairness of the election could be ensured as citizens can vote to reflect their wills without political interference. These conditions can contribute to a durable democracy in Canada and also improve the internal political efficacy of Canada (Elections Canada, 2023). The choice of who will form the government and which party’s policies will guide the government and legislation. These appointments and policies can influence various aspects of society, including the economy, public health initiatives, and environmental sustainability. The analysis of election outcomes helps encourage citizens to track the political process and promote their participation (Statistics Canada, 2022). Political parties and candidates can learn about competitors’ voting tendencies and concerns of voters so adjusting their electoral strategies.

Importantly, our analysis provides a demonstration of the relationship between the selected variables and the binary outcomes of voting decisions (vote or not vote) to see how the change of variables influences the change of probability change in vote. In this case, the result of the analysis can be an essential reference for future study of Canadian elections, and representatives of parties may set up relevant rules and benefits to increase their political reputation and construct campaign strategies according to the favorable factors considered by respondents. Furthermore, the government may refine relevant policy in terms of the races, employment, income, and other socioeconomic data presented in this study.

1.3 Terminology

Turnout in political elections means the probability or proportion of popular votes for a party.

The 45th Canadian federal election will be held on or before October 20, 2025. This date is determined by the Canada Elections Act (Parliament of Canada, 2006). There are currently 337 members in office in the 44th Parliament. Both the Liberal Party and Conservative Party have 275 members (158 and 117 respectively), and they are the two major Canadian parties(Members of Parliament, 2023).

The Liberal Party is the oldest active federal political party in Canada and has dominated federal politics for the majority of Canadian history (Liberal Party, 2019). The party espouses liberal principles and is generally central to center-left. Its main competitor, the Conservative Party, is right-leaned. Liberal Party is currently led by Justin Trudeau who has been the prime minister of Canada since 2015. Signature policies and legislation of the Liberal Party include universal health care, pension plans, bilingualism, gun control, related charters and acts that legalize same-sex marriage and cannabis usage, and expanding access to abortion (Liberal Party of Canada. n.d.).

The Conservative Party is one of the major political parties in Canada, known for its center-right political orientation. Its platform typically includes a commitment to fiscal responsibility, free-market principles, and a focus on individual liberties. The party has traditionally attracted support from a broad coalition of conservative voters, including those with social or economic conservative values. The party is currently led by Pierre Poilievre since 2022. Its signature policies involve reducing government debt, lowering taxes, and eliminating the long-gun registry (Dippel, 2016).

The Liberal Party leans on progressive policies and social transformation, and the Liberal encourages free-market competition in economics, diversity of minorities, and inclusion of immigrants. As opposed to the Liberal, the Conservative prefers traditional and preservative rules, imposes more government regulation on economics, and disagrees with social activism (Canada Guide, 2023).

Canada includes five distinct regions: The Atlantic Provinces (New Brunswick, Newfoundland and Labrador, Nova Scotia, and Prince Edward Island), Central Canada (Ontario and Quebec), The Prairie Provinces (Manitoba, Saskatchewan and Alberta), The West Coast (British Columbia), and The Northern Territories (Nunavut, Northwest Territories, and Yukon Territories) (Government of Canada, 2022). To more easily present the data, adjustments have been applied to the categories of five regions, and the Prairie Provinces have been renamed into western regions.

Visible minority refers to individuals who are non-Caucasian in race or non-white in color, except indigenous population groups. The visible minority group consists of South Asian, Chinese, Black, Filipino, Latin American, Arab, Southeast Asian, West Asian, Korean, and Japanese (Statistics Canada, 2021). To present data concisely, we adjusted the components of the visible minority group by also including the indigenous population.

1.4 Hypothesis

As the 45th Canadian Election is approaching, the competition between “Liberal” and “Conservative” is kicked off again. The Liberal and the Conservative parties dominate the political system of Canada and the show plays between these parties. Moreover, if we look at the recent 20 years of popular vote percentages, the Liberal Party almost beats the Conservative Party for each election with an outstanding difference (Simon Fraser University, 2021). Therefore, we hypothesize that the Liberal party is still going to win the election and it is exciting to see if there is any chance that the Conservative will probably present a surprise.

The goal of this study is to predict which political party in Canada is going to win the most popular votes in the 2025 Canadian Election based on the information from the previous 2021 Canadian Election. This study matches the survey data collected from the 2021 CES (Canadian Election Study) online survey with the census data collected from the Canada GSS (General Social Survey) and predicts the voting decision of respondents in the next 2025 Election in a logistic regression model based on demographic variables of respondents which include age, sex (male/female), language (English/French), income class (Low, Medium and High), the religious or atheist, and the races (the white or the other minorities). (Stephenson et al., 2021; Canada Statistics, 2020). To enhance the representatives of the population, we apply the stratification method that divides the survey respondents into strata by different variables and conclude the estimated voting probability for both the Liberal and the Conservative to infer the possible outcomes in the 2025 Election.

2. Data

2.1 Data description

Survey Data

The survey consists of the campaign period part and the post-election period part. The collection process started on August 7th, 2021, and ended on October 4th, 2021. To demonstrate, the campaign period survey data was collected on an online sample of 20,968 respondents of the Canadian general population at the Leger Opinion panel. The sampling process included three waves of panels in a modified rolling cross section. In this case, the survey data of three waves were merged into a whole sample at the end, but the respondents of the survey were randomly selected in three different periods. (Stephenson et al., 2021).

Census Data

The census data in this study is the 2020 General Social Survey, which provides detailed information on social trends for addressing interested social issues and improving the living conditions of Canadians, and it was released by September 2021. In addition, data was collected by both computer-based phone calls and electronic questionnaires through mail links from Statistics Canada offices in different regions from August 2020 to February 2021. According to the descriptive statistics, the overall response rate was 40.3%, and a total of 20,602 observations were collected. Moreover, the stratified sampling method was applied where each response was assigned to a province-level (a stratum). Then, a simple random sampling (SRS) was conducted in each stratum (Statistics Canada, 2020).

2.2 Data cleaning process

The sample survey data in this study was collected during the 2021 federal election campaign period and intended to gather the opinions of Canadian citizens and permanent residents aged 18 or older about election votes. Data cleaning was conducted on both survey and census datasets to enhance their suitability for analysis. Variables from both sources were aligned, allowing for the extrapolation of survey findings to the broader census population.

Initially, the survey dataset was filtered to include only Canadian citizens, excluding all Permanent Residents. Additionally, we filtered out respondents under 18 years old, as only Canadian citizens above 18 have the right to vote.

In the census dataset, age was already a present variable and was rounded for consistency.

Regarding gender, the survey dataset included an “Other” option, but this was minimally selected. Given its negligible proportion and lack of impact on key variables’ distribution, this category was excluded from the dataset. The survey’s gender data and the census’s sex data were thus streamlined to include only “Male” and “Female” options, with the term ‘sex’ in the census data being renamed to ‘gender’ for uniformity.

Both the survey and census datasets included information on respondents’ current province of residence. Considering Canada’s composition of 10 provinces and 3 territories, we streamlined the data based on geographic and demographic considerations to determine whether they are in the West. As mentioned earlier, we divided the country into five distinct regions. In the codebook, the western region initially included Manitoba, Saskatchewan, Alberta, and British Columbia, but we rearranged it to contain only the Prairie Provinces. It’s important to note that there were no responses from the Northern Territories (Nunavut, Northwest Territories, and Yukon Territories).

In both survey and census datasets, respondents provided information on their primary language. We matched the census’s ‘language_home’ data with the survey’s ‘UserLanguage’, as it likely represents the respondent’s first language or the language they are most proficient in.

Regarding income, we aligned the census’s ‘income_family’ data with the survey’s household income data, as both represent household income. Households earning less than $49,999 were classified as low income, those earning $50,000 to $124,999 as median income, and those earning above $125,000 as high income. (Springfield Financial, 2023).

Considering Canada’s diverse immigrant population, respondents were simply classified as having or not having a religious affiliation, without specifying particular beliefs. Responses of ‘Don’t Know’ were ignored.

Regarding visible minorities, we differentiated between ‘Not a visible minority’ and ‘visible minority’, disregarding ‘Don’t Know’ responses.

Finally, after the initial data-cleaning process, respondents with missing values were excluded for clarity and accuracy. This step was necessary as incomplete responses could be due to various factors, such as issues in reaching respondents or the survey’s design causing discomfort. Missing values could introduce anomalies, potentially reducing prediction accuracy. Although adjustments could have been made with more resources, omitting these respondents was considered the most appropriate approach for this study.

To glimpse the cleaned version of census data and survey data, please refer to Table 13 and Table 14 in the Appendix.

2.3 Data summary

The variables described in this section applied to both the CES survey data and GSS census data because we matched the variables in both datasets in the Data Cleaning section.

Response Variables
vote of conservative: The binary variable that whether the voter will vote for the Conservative Party in the 2025th election.

vote of liberal: The binary variable that whether the voter will vote for the Liberal Party in the 2025th election.

Independent Variables
age: This variable represents the age of the observations. It is a numerical variable.

sex: This variable represents the sex of the observations

language: A categorical variable indicating the primary language of individuals, with categories “FR” for French and “EN” for English.

west: A binary variable indicating whether an individual is from Western provinces (Manitoba, Saskatchewan, Alberta) or not.

income: A categorical variable categorizing individuals into “Low”, “Medium”, and “High” income groups based on their income category.

religion: A binary variable indicating whether individuals have a religious affiliation or not.

minority: A binary variable indicating whether individuals are part of a visible minority or not.

<Include a description of the numerical summaries. Remember you can use r to use inline R code.>

survey_data1$income <- factor(survey_data1$income, levels = c("Low", "Medium", "High"))
census_data1$income <- factor(census_data1$income, levels = c("Low", "Medium", "High"))
# Use this to create some plots. Should probably describe both the sample and population.
survey_age <- survey_data1 %>% ggplot(aes(x = age)) + geom_histogram(fill = "blue", color = "black", bins = 18) + theme_classic()+
  labs(x = "Age of the people that participated in the election", y = "Frequency", title = "Histogram of the age of the election participants")

census_age <- census_data1 %>% ggplot(aes(x = age)) + geom_histogram(fill = "blue", color = "black", bins = 18) + theme_classic()+
  labs(x = "Age of the people that participated in the election", y = "Frequency", title = "Histogram of the age of the election participants")

survey_income <- survey_data1 %>% ggplot(aes(x = income, fill = income)) + 
  geom_bar() + theme_classic() + coord_flip()+
  labs(x = "Income from survey data", y = "Frequency", title = "Histogram of ...")

census_income <- census_data1 %>% ggplot(aes(x = income, fill = income)) + 
  geom_bar() + theme_classic() + coord_flip()+
  labs(x = "Income from census data", y = "Frequency", title = "Histogram of ...")

survey_sex_count <- table(survey_data1$sex)

library(gridExtra)
library(patchwork)
survey_age | census_age

survey_income | census_income

par(mfrow = c(1, 2))
pie(survey_sex_count, main = "Sex Distribution in Survey", col = rainbow(length(survey_sex_count)))

census_sex_count <- table(census_data1$sex)
pie(census_sex_count, main = "Sex Distribution in Census", col = rainbow(length(census_sex_count)))

par(mfrow = c(1, 1))

3. Methods

<Include some text introducing the methodology, maybe restating the problem/goal of this analysis.>

3.1 Model selection and rationale

<Include some text introducing the methodology, maybe restating the problem/goal of this analysis.> Our study applies the logistic regression model to estimate the probability of voting of each voter for the Liberal Party and Conservative Party. Then, we use the post-stratification which divides the survey data in terms of the variables common in the census data and the survey, and yields the estimated overall probability of voting for the Liberal Party and Conservative Party respectively. In the end, we compare the estimated voting probability between the two parties to decide which one is going to win the election (i.e. the party has the higher estimated probability). In our model, to ensure the qualification of voting, we only keep the respondents who are at least 18 years old. In order to remove the influence of missing data, we delete the observations (record of respondents) which contain missing values of variables.

3.2 Model Specifics

Our study creates two logistic regression models to predict the proportion of voters who will vote for the Liberal Party and the Conservative Party. Some assumptions are made before constructing our logistic regression models: The voting outcome of respondents is binary, that is, the respondents either vote for the party or not, and the selected categorical variables are independent in both the logistic models built for the Liberal and the Conservative. We select the following models because the variables are matched in both the census and the survey data, and the variability of the variables is similar in survey data compared to the census data as shown in the plots of Data Summary section (…). In addition, a previous study by Statistics Canada proposes that economic status, belief, and personal inborn identities such as sex, language, and race are the dominant factors that potentially influence the intention of voting, so we select the following variables as predictors to investigate the probability of each voter to vote (Uppal, S.& LaRochelle-Côté S., 2012). In the logistic regression models for both parties, we use the same variables as predictors.

\[ log(\frac{p_c}{1-p_c}) = \beta_0+\beta_1 x_{age}+\beta_2 x_{sex}+\beta_3 x_{French}+\beta_4 x_{west}+\beta5 x_{incomeMedium}\] \[+\beta6 x_{incomeHigh}+\beta7 x_{religion}+\beta8 x_{minority}\]

\[ log(\frac{p_l}{1-p_l}) = \beta_0+\beta_1 x_{age}+\beta_2 x_{sex}+\beta_3 x_{French}+\beta_4 x_{west}+\beta5 x_{incomeMedium}\] \[+\beta6 x_{incomeHigh}+\beta6 x_{religion}+\beta7 x_{minority}\]

\(p_c\) represents the probability of voting for the Conservative Party and \(p_l\) represents the probability of voting for the Liberal Party. The \(log(\frac{p_l}{1-p_l})\) and \(log(\frac{p_c}{1-p_c})\) are the log odds in both models.

\(\beta_0=\) is the intercept of the model. It represents the log odds of voting for the candidate or party when all the predictor variables are at their baseline level (which means that the respondent is aged at 0 years, sex category female, speaking the language of English, not living in Quebec, the default income class at low level of income, does not believe in religions, and is a minority other than the White.).

\(\beta_1\) represents the relationship between the age of the respondent and the log odds of voting for the parties. For every one-unit increase in age (typically one year), there is an expected \(\beta_1\) change in the log odds of voting for the parties, assuming all other variables are held constant.

\(\beta_2\) quantifies the average difference in the log odds of voting for the parties between two sex groups (e.g., male and female), controlling for other factors in the model. It shows how sex influences the likelihood of voting for the candidate or party.

For \(\beta_3\), this coefficient measures the average difference in log odds of voting for the parties between respondents who speak French and English when other predictors stay the same. It reflects how changes in language proficiency between English and French can affect the voting behavior of a respondent, with other factors being equal.

\(\beta_4\) represents the average difference of being in the western inland provinces (Alberta, Manitoba, Saskatchewan) or not on the log odds of voting for the candidate or party while holding other predictors constant. This could reflect regional differences in voting preferences, with all other variables held constant.

For\(\beta_5\), This coefficient measures the average difference of log odds of voting between the respondent who possesses a low and medium income level. Similarly, \(\beta_6\) measures the average difference of log odds of voting between the respondent who possesses a low and high income level when other predictors stay the same. They indicate how changes in income level impact the log odds of voting for the candidate or party. Both coefficients capture the relationship between economic status and voting behavior, controlling for other variables in the model.

\(\beta_7\) assesses the average difference in the log odds of voting for the parties between the respondents who are atheists or possess religious beliefs with the other predictors fixed. This factor might capture how the difference between a religious believer and a non-religious person on voting preferences.

Finally, \(\beta_8\) measures the average difference in the log odds of voting for the parties if a respondent is identified as a minority member compared to a non-minority one. This could reflect how membership in certain demographics or ethnic minorities influences voting patterns compared to the majority component of White people in the population of Canadian citizens (Statistics Canada, 2022).

3.3 Post-Stratification

<In order to estimate the proportion of voters…..>

<To put math/LaTeX inline just use one set of dollar signs. Example: \(\hat{y}^{PS}\) >

Post-stratification is a method to ensure that the results can accurately represent different groups within a population. It involves adjusting the weights for each estimated parameter within specific post strata based on their corresponding weights in the census population size.

In order to estimate the proportion of voters who will vote for … we will perform a post-stratification analysis by applying the following formula:

\[ \hat{y}^{P S}=\frac{\sum N_{j} \widehat{y}_{j}}{\sum N_{j}} \]

\(\hat{y}\) is the estimate in each cell, and \(N_j\) is the population size of the \(j^{th}\) cell based on demographics.
The estimated (\(\hat{y}\)) is \(\hat{p}\) that refer to the proportion of voting for… Post-stratification will conduct logistic regression in each cell and use the logistic model to estimate the \(\hat{p}\) within that cell. We firstly will create cells based on different ages, sex, and working status. Using the model described in the previous sub-section, we will estimate the proportion of voters in each cell. _Since there are ? categories in sex, ? in region, ? in education, and ? in religion, we will have ? cells for each age.
We will subsequently weight each proportion estimate within each cell by the respective population size of that cell and will then sum those values and divide that by the entire population size.

4. Results

4.1 Logistic Model Results

The following are the logistic regression model results (coefficients rounded to 3 decimals). For Liberal\[ log(\frac{p_l}{1-p_l}) = -2.267+0.010 x_{age}-0.227x_{sex}-0.485 x_{French}-0.867 x_{west}+0.811 x_{incomeMedium}\] \[+0.643x_{incomeHigh}+0.152x_{religion}-0.036x_{minority}\] According to the liberal model For Conservative\[ log(\frac{p_c}{1-p_c}) = -3.358+0.017x_{age}+0.327x_{sex}-0.637 x_{French}+0.799 x_{west}+0.646 x_{incomeMedium}\] \[+0.356 x_{incomeHigh}+0.734 x_{religion}-0.180 x_{minority}\]

1. The following are the logistic regression model results (coefficients rounded to 3 decimals). For Liberal\[ log(\frac{\hat p_l}{1-\hat p_l}) = -2.267+0.010 x_{age}-0.227x_{sex}-0.485 x_{French}-0.867 x_{west}+0.811 x_{incomeMedium}\] \[+0.643x_{incomeHigh}+0.152x_{religion}-0.036x_{minority}\]

\(\hat p_c\) represents the probability of voting for the Conservative Party and \(\hat p_l\) represents the probability of voting for the Liberal Party.

knitr::kable(summary1$coefficients, col.names = c("Estimates", "SE", "Test statistics", "p-value"), caption = "Table x.Summary of Logistic Regression Model for Liberal", align = "cccc", digits = 4)

\(\hat p_l\) represents the probability of voting for the Liberal Party.

\(\hat \beta_0=-2.2672\) means the expected log odds of voting for the candidate or party is -2.2672 when all the predictor variables are at their baseline level (which means that the respondent is aged at 0 years, sex category female, speaking the language of English, not living in Quebec, the default income class at low level of income, does not believe in religions, and is a minority other than the White.).

\(\hat \beta_1=0.100\) represents the relationship between the age of the respondent and the log odds of voting for the parties. For every one-unit increase in age (typically one year), there is an expected 0.100 change in the log odds of voting for the parties, assuming all other variables are held constant.

\(\hat \beta_2=-2.2274\) quantifies the expected difference in the log odds of voting for the parties between two sex groups (e.g., male and female) is -2.2274, controlling for other factors in the model. It shows how sex influences the likelihood of voting for the candidate or party.

\(\hat \beta_3=0.4846\), this coefficient means the expected difference in log odds of voting for the parties between respondents who speak French and English is 0.4846 when other predictors stay the same. It reflects how changes in language proficiency between English and French can affect the voting behavior of a respondent, with other factors being equal.

\(\hat\beta_4=-0.8669\) means the expected difference of being in the western inland provinces (Alberta, Manitoba, Saskatchewan) or not on the log odds of voting for the candidate or party is -0.8669 while holding other predictors constant. This could reflect regional differences in voting preferences, with all other variables held constant.

For\(\hat \beta_5=0.8107\), This coefficient means the expected difference of log odds of voting between the respondent who possesses a low and medium income level is 0.8107. Similarly, \(\beta_6=0.6433\) means the expected difference of log odds of voting between the respondent who possesses a low and high income level is 0.6433 when other predictors stay the same. They indicate how changes in income level impact the log odds of voting for the candidate or party. Both coefficients capture the relationship between economic status and voting behavior, controlling for other variables in the model.

\(\hat \beta_7=0.1523\) menas the expected difference in the log odds of voting for the parties between the respondents who are atheists or possess religious beliefs is 0.1523 with the other predictors fixed. This factor might capture how the difference between a religious believer and a non-religious person on voting preferences.

Finally, \(\hat\beta_8=-0.0358\) means the average difference in the log odds of voting for the parties if a respondent is identified as a minority member is -0.358 compared to a non-minority one. This could reflect how membership in certain demographics or ethnic minorities influences voting patterns compared to the majority component of White people in the population of Canadian citizens (Statistics Canada, 2022).

Finally, \(\hat\beta_8\) measures the average difference in the log odds of voting for the parties if a respondent is identified as a minority member compared to a non-minority one. This could reflect how membership in certain demographics or ethnic minorities influences voting patterns compared to the majority component of White people in the population of Canadian citizens (Statistics Canada, 2022).

\(\hat p_c\) represents the probability of voting for the Conservative Party and \(\hat p_l\) represents the probability of voting for the Liberal Party.

\(\hat \beta_0=-3.3577\) is the intercept of the model. It represents the log odds of voting for the Conservatives is -3.3577 when all the predictor variables are at their baseline level (which means that the respondent is aged at 0 years, sex category female, speaking the language of English, not living in Quebec, the default income class at low level of income, does not believe in religions, and is a minority other than the White.).

\(\hat \beta_1=0.0175\) represents the relationship between the age of the respondent and the log odds of voting for the parties. For every one-unit increase in age (typically one year), there is an expected \(\hat \beta_1\) increase of 0.0175 in the log odds of voting for the parties, assuming all other variables are held constant.

\(\hat \beta_2=0.3269\) quantifies the average difference in the log odds of voting for the parties between two sex groups (e.g., male and female), controlling for other factors in the model. It shows how sex influences the likelihood of voting for the candidate or party.

\(\hat \beta_3=-0.6371\), this coefficient measures the average difference in log odds of voting for the parties between respondents who speak French and English when other predictors stay the same. It reflects how changes in language proficiency between English and French can affect the voting behavior of a respondent, with other factors being equal.

\(\hat\beta_4=0.7986\) represents the average difference of being in the western inland provinces (Alberta, Manitoba, Saskatchewan) or not on the log odds of voting for the candidate or party while holding other predictors constant. This could reflect regional differences in voting preferences, with all other variables held constant.

For\(\hat \beta_5=0.6465\), This coefficient measures the average difference of log odds of voting between the respondent who possesses a low and medium income level. Similarly, \(\beta_6=0.3561\) measures the average difference of log odds of voting between the respondent who possesses a low and high income level when other predictors stay the same. They indicate how changes in income level impact the log odds of voting for the candidate or party. Both coefficients capture the relationship between economic status and voting behavior, controlling for other variables in the model.

\(\hat \beta_7=0.7340\) assesses the average difference in the log odds of voting for the parties between the respondents who are atheists or possess religious beliefs with the other predictors fixed. This factor might capture how the difference between a religious believer and a non-religious person on voting preferences.

Finally, \(\hat\beta_8=-0.1796\) measures the average difference in the log odds of voting for the parties if a respondent is identified as a minority member compared to a non-minority one. This could reflect how membership in certain demographics or ethnic minorities influences voting patterns compared to the majority component of White people in the population of Canadian citizens (Statistics Canada, 2022).

According to the liberal model For Conservative\[ log(\frac{\hat p_c}{1-\hat p_c}) = -3.358+0.017x_{age}+0.327x_{sex}-0.637 x_{French}+0.799 x_{west}+0.646 x_{incomeMedium}\] \[+0.356 x_{incomeHigh}+0.734 x_{religion}-0.180 x_{minority}\]

Tablex shows that .

Tablex shows the summary statistics of the both logistic regressions, which includes the estimated coefficients (slopes) of the logistic regression models, the corresponding standard errors, test statistics and p-values for the coefficients t-tests. Using a significance level of 0.05, we can see that p-values for the coefficient estimate of numerical variable age and dummy variables: sex of Male or not, Language of French or not, living in Western inland provinces (Alberta, Manitoba, Saskatchewan) or not, income class at Medium or not, income class at High or not, possess a religion or not, identified as a minority or not. Among these predictors, we can see that the age, language speaking and religion identification can form a significant relationship with the voting decision of voters (whether or not they will vote the Conservative and the Liberal) because their p-values are smaller than the 0.05 significant level cutoff.

$\hat p_l$ represents the probability of voting for the Liberal Party. 

$\hat \beta_0=-2.2672$ means the expected log odds of voting for the candidate or party is -2.2672 when all the predictor variables are at their baseline level (which means that the respondent is aged at 0 years, sex category female, speaking the language of English, not living in Quebec, the default income class at low level of income, does not believe in religions, and is a minority other than the White.). 

$\hat \beta_1=0.100$ represents the relationship between the age of the respondent and the log odds of voting for the parties. For every one-unit increase in age (typically one year), there is an expected 0.100 change in the log odds of voting for the parties, assuming all other variables are held constant.

$\hat \beta_2=-2.2274$ quantifies the expected difference in the log odds of voting for the parties between two sex groups (e.g., male and female) is -2.2274, controlling for other factors in the model. It shows how sex influences the likelihood of voting for the candidate or party.

$\hat \beta_3=0.4846$, this coefficient means the expected difference in log odds of voting for the parties between respondents who speak French and English is 0.4846 when other predictors stay the same. It reflects how changes in language proficiency between English and French can affect the voting behavior of a respondent, with other factors being equal.

$\hat\beta_4=-0.8669$ means the expected difference of being in the western inland provinces (Alberta, Manitoba, Saskatchewan) or not on the log odds of voting for the candidate or party is -0.8669 while holding other predictors constant. This could reflect regional differences in voting preferences, with all other variables held constant.

For$\hat \beta_5=0.8107$, This coefficient means the expected difference of log odds of voting between the respondent who possesses a low and medium income level is 0.8107. Similarly, $\beta_6=0.6433$ means the expected difference of log odds of voting between the respondent who possesses a low and high income level is 0.6433 when other predictors stay the same. They indicate how changes in income level impact the log odds of voting for the candidate or party. Both coefficients capture the relationship between economic status and voting behavior, controlling for other variables in the model.

$\hat \beta_7=0.1523$ menas the expected difference in the log odds of voting for the parties between the respondents who are atheists or possess religious beliefs is 0.1523 with the other predictors fixed. This factor might capture how the difference between a religious believer and a non-religious person on voting preferences.

Finally, $\hat\beta_8=-0.0358$ means the average difference in the log odds of voting for the parties if a respondent is identified as a minority member is -0.358 compared to a non-minority one. This could reflect how membership in certain demographics or ethnic minorities influences voting patterns compared to the majority component of White people in the population of Canadian citizens (Statistics Canada, 2022).


Table: Table x.Summary Logistic Regression Model for Conservative

|             | Estimates |   SE   | Test statistics | p-value |
|:------------|:---------:|:------:|:---------------:|:-------:|
|(Intercept)  |  -3.3577  | 0.4549 |     -7.3816     | 0.0000  |
|age          |  0.0175   | 0.0057 |     3.0476      | 0.0023  |
|sexMale      |  0.3269   | 0.1950 |     1.6760      | 0.0937  |
|languageFR   |  -0.6371  | 0.2575 |     -2.4737     | 0.0134  |
|west         |  0.7986   | 0.2200 |     3.6298      | 0.0003  |
|incomeMedium |  0.6465   | 0.3793 |     1.7044      | 0.0883  |
|incomeHigh   |  0.3561   | 0.2959 |     1.2033      | 0.2288  |
|religion     |  0.7340   | 0.2505 |     2.9305      | 0.0034  |
|minority     |  -0.1796  | 0.2149 |     -0.8357     | 0.4033  |
**Tablex** shows the summary statistics of the both logistic regressions, which includes the estimated coefficients (slopes) of the logistic regression models, the corresponding standard errors, test statistics and p-values for the coefficients t-tests. Using a significance level of 0.05, we can see that p-values for the coefficient estimate of numerical variable age and dummy variables: sex of Male or not, Language of French or not, living in Western inland provinces (Alberta, Manitoba, Saskatchewan) or not, income class at Medium or not, income class at High or not, possess a religion or not, identified as a minority or not. Among these predictors, we can see that the age, language speaking and religion identification can form a significant relationship with the voting decision of voters (whether or not they will vote the Conservative and the Liberal) because their p-values are smaller than the 0.05 significant level cutoff. 


## 4.2 Post-stratification Results



```r
# Here I will perform the post-stratification calculation for Conservative
census_data_counts <- census_data1 %>% group_by(age, sex, language, west, income, religion, minority) %>% 
  summarise(N=n())

census_data_counts$estimate2 <-
  model2 %>%
  predict(newdata = census_data_counts, type = "response") # get proportion
# prof's code can only provide log ratio

result_conservative <- census_data_counts %>% 
  mutate(conservative_predict_prop = estimate2*N) %>% ungroup() %>% 
  summarise(conservative_predict = sum(conservative_predict_prop)/sum(N))

table <- tibble(result_liberal, result_conservative)

knitr::kable(table, col.names = c("Liberal", "Conservative"), caption = "Table x.Estimated probability of voting for the Parties", align = "cccc", digits = 4)

<Here you present your results. You may want to put them into a well formatted table. Be sure that there is some text describing the results.>

<Note: Alternatively you can use the knitr::kable function to create a well formatted table from your code. See here: https://rmarkdown.rstudio.com/lesson-7.html.>

<Remember you can use r to use inline R code.>

<Include an explanation/interpretation of the visualizations. Make sure to comment on the appropriateness of the assumptions/results.>

5. Conclusions

<Here you should give a summary of the Hypotheses, Methods and Results>

<Highlight Key Results.>

<Talk about big picture.>

<Comment on any Weaknesses.>

<End with a concluding paragraph to wrap up the report.>

Bibliography

1. Grolemund, G. (2014, July 16) Introduction to R Markdown. RStudio. https://rmarkdown.rstudio.com/articles_intro.html. (Last Accessed: April 4, 1991)

2. RStudio Team. (2020). RStudio: Integrated Development for R. RStudio, PBC, Boston, MA URL http://www.rstudio.com/.

3. Allaire, J.J., et. el. References: Introduction to R Markdown. RStudio. https://rmarkdown.rstudio.com/docs/. (Last Accessed: April 4, 1991)

4. OpenAI. (2023). ChatGPT (September 13 version) [Large language model]. https://chat.openai.com/chat (Last Accessed: September 13, 2023)

Members of Parliament. (2023). Current Members. [https://www.ourcommons.ca/Members/en]

Parliament of Canada. (2006). Amendment to Canada Elections Act. [https://www.parl.ca/]

Simon Fraser University. (2021). Canadian Election Results by Party 1867 to 2021. https://www.sfu.ca/~aheard/elections/1867-present.html (Last Accessed: November 11, 2023)

Statistics Canada. (2022). Chapter 6: Political participation, civic engagement and caregiving among youth in Canada. [https://www150.statcan.gc.ca/n1/pub/42-28-0001/2021001/article/00006-eng.htm]

Statistics Canada. (October, 2022). The Canadian census-A rich portrait of the country’s religious and ethnocultural diversity. Statistics Canada. https://www150.statcan.gc.ca/n1/daily-quotidien/221026/dq221026b-eng.htm (Last Accessed: November 12, 2023)

Stephenson, Laura B., Allison Harell, Daniel Rubenson and Peter John Loewen. (2021). The 2021 Canadian Election Study. Consortium on Electoral Democracy. [dataset]

Tossutti, L. & Elections Canada. (2007). La participation électorale des membres des communautés ethnoculturelles. Élections Canada.

Uppal, S. & LaRochelle-Côté S. (February, 2012). Factors associated with voting. Statistics Canada. https://www150.statcan.gc.ca/n1/en/pub/75-001-x/2012001/article/11629-eng.pdf?st=nuV9FTRH (Last Accessed: November 12, 2023)

Appendix

Generative AI Statement

Here is where you can explain your usage of Generative AI tool(s). Be sure to reference it. For instance, including something like:

I used the following generative artificial intelligence (AI) tool: Bing AI Version 2.0 for Chrome [4]. I used the tool only in the Results section of this assignment and I gave it the following prompt of What should I eat for breakfast? and it gave me a list of 10 breakfast items which I then asked it to: Please only list breakfast items that do not include eggs. I then chose my 3 favourite items from the produced list and included those in the Results section.