Egwald Statistics: Multiple Regression
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Canadian Election 1997 | Canadian Election 2000 | Canadian Election 2004 | Canadian Election 2006
Canadian Federal Elections 1949-1997
Elmer G. Wiens
The following study demonstrates a practical application of the statistical technique of regression 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. To this end, I collected data and calculated percentages for the 16 Canadian elections between 1949 and 1997. The data were taken from:
Colombo, John C., ed. The Canadian Global Almanac. Toronto: Macmillan, 1999.
I use the following notation:
Pty = Winning party
Lib = Liberal Party
PC = Progressive Conservative Party
M = Winning party has a majority of federal seats
C = Percent of seats of Canada taken by the winning party
E = Percent of seats of Eastern Canada taken by the winning party
OQ = Percent of seats of Ontario and Quebec taken by the winning party
P = Percent of seats of the Prairie Provinces taken by the winning party
BC = Percent of seats of B.C. taken by the winning party
I want to predict Canadian elections using the linear equation:
If I use the data from the 16 Canadian elections during 1949 to 1997 to estimate this equation's parameters I get:
C = ß0 + ß1 * E + ß2 * OQ + ß3 * P + ß4 * BC
where the symbols, ß0, ß1, ß2, ß3, and ß4, represent parameters whose values I will determine from previous elections.
C = -21.691 + 0.117 * E + 0.937 * OQ + 0.136 * P + 0.087 * BC
The following pages explain how these parameter estimates for the linear equation were obtained.
The Winning Party's Percentage of Seats by Year and by Region
Year Pty M C E OQ P BC
1997 Lib Yes 52 34 72 17 18
1993 Lib Yes 60 97 67 39 19
1988 PC Yes 57 34 63 67 38
1984 PC Yes 75 78 74 80 68
1980 Lib Yes 52 63 74 4 0
1979 PC No 48 56 58 78 68
1974 Lib Yes 54 41 71 11 35
1972 Lib No 41 31 56 7 17
1968 Lib Yes 59 22 74 25 70
1965 Lib No 50 45 69 2 32
1963 Lib No 49 61 62 6 32
1962 PC No 44 55 49 88 27
1958 PC Yes 79 76 73 95 82
1957 PC No 42 64 52 29 32
1953 Lib Yes 64 34 78 35 38
1949 Lib Yes 73 74 78 58 61
Average 56 54 67 40 40
Ave Lib 55 50 70 20 32
Ave PC 57 61 62 73 53
Notice that the number of elections = 16, which equals the number of observations. Since we are interested in the extent to which the four regions determine the winning party in a Canadian election, the number of independent variables = 4 (number of regions: E, OQ, P and BC). C, the percentage of seats taken across Canada by the winning party, is the dependent variable.
When you are using my regression package for a study of your own, you must fill in the tables in the same way that I have done below.
To keep things manageable, in my package the number of observations must be less than 20 and the number of independent variables less than 6. Also, the number of observations must be greater than or equal to the number of variables. I'll explain what the intercept term means on the next page.
So you give your study a name and enter it with the number of observations and independent variables into the table. Then you click 'submit parameters'.
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