Egwald Statistics: Multiple Regression

Egwald's popular web pages are provided without cost to users.

The Canadian Federal Election — 2006

by

Elmer G. Wiens

Pre-Election Analysis

I am interested in analyzing how regional voting patterns affect and are influenced by the Canada wide percentage of seats that the winning party takes in an election. In particular I want to look at the relationship between the winning party's percentage of seats across Canada in relation to the percentage of seats it won in Eastern Canada, Ontario and Quebec, the Prairie Provinces, and British Columbia.

Moreover, I want to use any statistical regularity this relationship reveals to predict the number of seats that the winning party will take in the Canadian federal election to be held on January 23, 2006.

Using the eighteen Canadian federal elections from 1949 to 2004 (Canadian Election 2004), I obtain the following linear relation:

C = -17.321 + 0.13 * E + 0.857 * OQ + 0.117 * P + 0.113 * BC

where C = percentage of seats of Canada taken by the winning party, E = percentage of seats of Eastern Canada taken by the winning party, OQ = percentage of seats of Ontario and Quebec taken by the winning party, P = percentage of seats of the Prairie Provinces taken by the winning party, and BC = percentage of seats of B.C. taken by the winning party. (I ignore Nunavut, the Northwest Territories, and the Yukon in the regression equation estimates.)

2004 Federal Election

The Liberal Party won the 2004 Canadian federal election.

 Liberal Party - 2004 Canada Eastern Canada Ontario & Quebec Prairie Provinces British Columbia NU+NWT+YUK % Seats Taken 43.8 69 53 11 22 100 Seats Taken 135 22 96 6 8 3 Seats Available 308 32 181 56 36 3

Predicting the 2006 Federal Election

Predicting the number of seats the Liberal Party takes on January 23, 2006

To predict the number of seats that the Liberal Party takes in the 2006 Canadian federal election using the equation above, one must estimate the number of seats that the Liberal Party wins in each region of Canada. Technically, one could then just add these seats to obtain an estimate of the total number of seats the winning party will take across Canada. However, this approach does not exploit the information contained in the data from previous Canadian federal elections. Moreover, the data as captured in the linear regression equation sheds light on successful strategies of political parties in previous elections.

Examining the equation

C = -17.321 + 0.13 * E + 0.857 * OQ + 0.117 * P + 0.113 * BC

one sees that the coefficient of the variable OQ, 0.857, is much larger than the coefficients of the other regions.

To win an election in Canada, a political party must win a majority of seats in Ontario and Quebec combined!

Despite their rhetoric supporting the regions of Canada, the Conservatives and Liberals focus most of their election policies, expenditures, energy, and time on the provinces of Quebec and Ontario.

The Prairie Provinces and British Columbia have more seats available than Eastern Canada. Traditionally the winning party of a federal election, however, has placed more weight on winning in Eastern Canada than on winning in either the Prairie Provinces or in British Columbia. One can see this by comparing the coefficient of E, 0.13, with the coefficient of P, 0.117, and with the coefficient of BC, 0.113.

Traditionally, the winning party wins a majority of seats in Eastern Canada,
and a majority of seats in Central Canada — Ontario and Quebec combined.

One can construct a possible scenario for the 2006 election by analyzing swing ridings, where the winning candidate won by a small margin of votes.

A scenario for the Liberal Party might be the following. The Liberal Party loses 3 seats in British Columbia, 2 seats in the Prairie Provinces, 10 seats in Quebec and 2 seats in Eastern Canada.

 Liberal Party - 2006 - Scenario Canada Eastern Canada Ontario & Quebec Prairie Provinces British Columbia NU+NWT+YUK % Seats Taken 38.3 62.5 47.5 0.07 14 100 Seats Taken 118 20 86 4 5 3 Seats Available 308 32 181 56 36 3

Using the regression equation to predict the seats taken by the Liberal Party in this scenario:

C = -17.321 + 0.13 * E + 0.857 * OQ + 0.117 * P + 0.113 * BC

C = -17.321 + 0.13 * 62.5 + 0.857 * 47.5 + 0.117 * 0.07 + 0.113 * 14

C = -17.321 + 8.125 + 40.7 + 0.01 + 1.58 = 33.1

Traditional voting patterns give the Liberal Party 33.1% of the seats (about 102 seats), while adding seats for each region of Canada gives the Liberal Party 38.3% of the seats (118 seats).

The results indicate that this scenario is at variance with what usually happens in Canada during an election. This suggests we should revise our scenario. How? Consult a table of 2004 Federal Election Results for possible alternative scenarios.

If the Conservative Party wins 35.7% of the seats, they win 110 seats, and the opportunity to form the government with the support of the Bloc Québécois Party.

Each scenario that one constructs will result in different estimates for the winning party's percentage of seats in each region of Canada, and consequently for the Canada wide winning percentage.

The 2006 Federal Election

Analysis of the 2006 Canadian Federal Election

The 2006 Canadian Federal Election resulted in a minority government for the Conservative Party. This election produced some very unusual results. The Conservatives 124 seats, or 40.3 percent of the total seats, represent the smallest percentage of government seats in Canadian history. Furthermore, the Consevatives won only 27.6 percent of the seats in Ontario and Quebec (OQ) combined. Over the last nineteen elections, the previous smallest percentage of seats of Ontario and Quebec won by the party forming the government was 49 percent. The Bloc Québécois held its seat total in Quebec, and the Conservatives increased their seats in Ontario and Quebec at the expense of the Liberals.

Esentially, the election in Ontario and Quebec resulted in a three-way-split among the Liberal, Bloc Québécois, and Conservative Parties. In previous elections, the party that won the most seats in Ontario and Quebec formed the government. These events constitute a shift in traditional voting patterns.

Consequently, the linear relation:

C = -17.321 + 0.13 * E + 0.857 * OQ + 0.117 * P + 0.113 * BC

based on the eighteen Canadian federal elections from 1949 to 2004 becomes problematic to predict elections.

The following table summarizes the 2006 election results for the Conservative and Liberal Parties.

 Federal Seats Available - 2006 Canada Eastern Canada Ontario & Quebec Prairie Provinces British Columbia NU+NWT+YUK Seats Available 308 32 181 56 36 3 Conservative Party - 2006 Canada Eastern Canada Ontario & Quebec Prairie Provinces British Columbia NU+NWT+YUK % Seats Taken 40.3 28 27.6 85.7 47 0 Seats Taken 124 9 50 48 17 0 Liberal Party - 2006 Canada Eastern Canada Ontario & Quebec Prairie Provinces British Columbia NU+NWT+YUK % Seats Taken 33.4 62.5 37 8.9 25 66.7 Seats Taken 103 20 67 5 9 2

The nineteen Canadian Federal Elections (1949-2006) resulted in eight minority governments and eleven majority governments. To investigate how traditional voting patterns depend on the event of a minority government, I look for a relationship between the winning party's percentage of seats across Canada in relation to the percentage of seats it won in Eastern Canada, Ontario and Quebec, the Prairie Provinces, and British Columbia — and whether the winning party won a majority of seats.

Using the nineteen Canadian federal elections from 1949 to 2006 (Canadian Election 2006 Results), I obtain the following linear relation:

C = 9.271 + 0.126 * E + 0.382 * OQ + 0.069 * P + 0.176 * BC + 8.028 * M

where C = percentage of seats of Canada taken by the winning party, E = percentage of seats of Eastern Canada taken by the winning party, OQ = percentage of seats of Ontario and Quebec taken by the winning party, P = percentage of seats of the Prairie Provinces taken by the winning party, BC = percentage of seats of B.C. taken by the winning party, and M = 1 if the winning party has a majority, while M = 0 if the winning party has a minority. (I ignore Nunavut, the Northwest Territories, and the Yukon in the regression equation estimates.)

The coefficients of this linear relation differ from those of the previous linear relation. While the coefficients for E and BC are almost the same, the intercept, OQ, and P coefficients have changed significantly, since these variables are correlated with the event of a minority or a majority government.

As a test, I will use the linear relation with the M variable to predict the 2006 Canadian Federal Election.

C = 9.271 + 0.126 * E + 0.382 * OQ + 0.069 * P + 0.176 * BC + 8.028 * M

C = 9.271 + 0.126 * 28 + 0.382 * 27.6 + 0.069 * 85.7 + 0.176 * 47 + 8.028 * 0

C = 9.271 + 3.528 + 10.54 + 5.9 + 8.27 + 0 = 37.51

The linear relation predicts the Conservative Party wins 37.5% of the votes (116 seats) versus the 40.3 percent of the votes (124 seats) the Conservative Party actually won in the 2006 election.