Shannon Hartmann

Shannon Hartmann

MAT 210

Prof. Hoensch

8 December 2010

Excel Project 2

1) The purpose of this project is to determine how a states percentage of democrats in the 111th Congress depend on various aspects of the state. These aspects are the bottoms of income tax rate range by state, the median age of the state and the percentage of homeowners. Information on the specific variables is given in table 1.

Variable/Type / Levels/Units of Measurement / Source
Percent of Democrats in the 111th Congress/Response / Quantitative/Percent /
Median Age of State in 2009/Explanatory / Quantitative/Year /
Percent of homeowners in 2009/Explanatory / Quantitative/Percent /
Bottom of Income Tax Rate Range of the State in 2009/Explanatory / Quantitative/Percent /

The data was collected using on November 28 2010. The data is relevant for 2009 and all data corresponds with that year. The data will provide a model for the association of the percentage of democrats a given state has in Congress and the three explanatory variables. If the association is strong enough (r2) this model can be used to predict the amount of democrats in Congress for any given state.

2)I am working alone and collected data for n=50, this is the corresponding value of each variable by state. This data is attached.

3)The proposed linear model is

Percentage of Democrats=0 + 1 (BIT) + 2  (MA) + 3  (HO)

Where BIT stands for bottom of income tax rate range of the state, MA for Median Age of residents in the state and HO as the percentage of homeowners in the state. The analysis (see attached) on excel gives the following model:

Percentage of Democrats=4.03714 + 3.7649  (BIT) + 5.8079  (MA) - 2.45001 (HO)

4)The coefficient 0=4.03714 cannot be interpreted. In the table below are the interpretations of the three other coefficients. These are valid within the observed range of data.

Coefficient and Value / Interpretation / Significant at C=0.95?
1=3.7649 / The percentage of democrats is expected to increase by 3.7649% every time Bottom of Income Tax Rate Range increases by 1%. / Association is Significant.
2=5.8079 / The percentage of democrats is expected to increase by 5.8079% for every year the median age increases. / Association is Significant.
3=-2.45001 / The percentage of democrats is expected to decrease by 2.45001% every 1% increase in homeowners. / Association is Significant.

The coefficient of association is r2=53.771%, therefore the model explains 53% of the variation in democrats in Congress. This is a medium association and all factors appear to be significant. The formula

Percentage of Democrats=4.03714 + 3.7649  (BIT) + 5.8079  (MA) - 2.45001  (HO)

Can be used to see how many democrats are in Congress for any given state, as long as values remain in the range of the observed values for the model.

Application: If you take a look at California, bottom of income tax rate range of the state in 2009 was 1.25%, the median age of the state was 34.8 years and the percent of homeowners was 57.0%. According to the linear model the percentage of democrats should be

Percentage of Democrats=4.03714 + 3.7649  (1.25) + 5.8079  (34.8) - 2.45001  (57.0)=71.21%