The analysis used data from 25 Women’s Issues PACs, with variables including: - Financial_Support (Total donations) - Ideology_Encoded (1 for Republican/Conservative, 0 for Democrat/Liberal) - Affiliate_DEM (1 for Democratic-affiliated PACs, 0 otherwise) - Affiliate_REP (1 for Republican-affiliated PACs, 0 otherwise) - Interaction_Dem_Support (Democratic support in thousands of dollars)
Call:
lm(formula = Financial_Support ~ Ideology_Encoded + Affiliate_DEM +
Affiliate_REP + Interaction_Dem_Support, data = data_clean)
Residuals:
Min 1Q Median 3Q Max
-26578 -10051 -1781 6261 58975
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4506.8 15982.9 0.282 0.781
Ideology_Encoded 9946.2 74169.9 0.134 0.895
Affiliate_DEM 3367.3 24430.7 0.138 0.892
Affiliate_REP 67319.3 35651.9 1.888 0.073 .
Interaction_Dem_Support 1213.4 56.1 21.623 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 19370 on 20 degrees of freedom
Multiple R-squared: 0.9814, Adjusted R-squared: 0.9777
F-statistic: 263.4 on 4 and 20 DF, p-value: < 2.2e-16 Ideology_Encoded Affiliate_DEM Affiliate_REP Interaction_Dem_Support
4.48739 4.84697 3.05487 1.50761 VIF values are generally below 5, indicating acceptable levels of multicollinearity.
studentized Breusch-Pagan test
data: model
BP = 6.7953, df = 4, p-value = 0.1471The p-value is greater than 0.05, suggesting no significant heteroscedasticity.
Shapiro-Wilk normality test
data: residuals(model)
W = 0.73486, p-value = 3.251e-05The p-value is less than 0.05, indicating residuals are not normally distributed.
Durbin-Watson test
data: model
DW = 2.3654, p-value = 0.8055
alternative hypothesis: true autocorrelation is greater than 0The Durbin-Watson statistic is close to 2 with p-value > 0.05, suggesting no significant autocorrelation.
2.5 % 97.5 %
(Intercept) -28896.6697 37910.2558
Ideology_Encoded -145194.9072 165087.2979
Affiliate_DEM -47673.1861 54407.8397
Affiliate_REP -7023.7294 141662.3748
Interaction_Dem_Support 1096.0711 1330.7571Analysis of Variance Table
Response: Financial_Support
Df Sum Sq Mean Sq F value Pr(>F)
Ideology_Encoded 1 5.1290e+10 5.1290e+10 136.663 4.090e-11 ***
Affiliate_DEM 1 1.5129e+09 1.5129e+09 4.031 0.05837 .
Affiliate_REP 1 3.6200e+09 3.6200e+09 9.646 0.00559 **
Interaction_Dem_Support 1 1.7539e+11 1.7539e+11 467.284 < 2.2e-16 ***
Residuals 20 7.5042e+09 3.7521e+08
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1=================================================================================
OLS Regression Results
=================================================================================
Dep. Variable: Financial Support R-squared: 0.981
Model: OLS Adj. R-squared: 0.978
Method: Least Squares F-statistic: 263.4
Date: Fri, 12 Apr 2025 Prob (F-statistic): 2.22e-17
Time: 14:23:17 Log-Likelihood: -243.09
No. Observations: 25 AIC: 496.2
Df Residuals: 20 BIC: 503.0
Df Model: 4
Covariance Type: nonrobust
=================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------
const 4.507e+03 1.598e+04 0.282 0.781 -2.890e+04 3.791e+04
Ideology_Encoded 9.946e+03 7.417e+04 0.134 0.895 -1.452e+05 1.651e+05
Affiliate_DEM 3.367e+03 2.443e+04 0.138 0.892 -4.767e+04 5.441e+04
Affiliate_REP 6.732e+04 3.565e+04 1.888 0.073 -7.024e+03 1.417e+05
Interaction_Dem_ 1.213e+03 5.610e+01 21.623 0.000 1.096e+03 1.331e+03
=================================================================================
Omnibus: 45.176 Durbin-Watson: 2.365
Prob(Omnibus): 0.000 Jarque-Bera (JB): 45.176
Skew: 2.875 Prob(JB): 1.58e-10
Kurtosis: 10.962 Cond. No. 2.46e+03
=================================================================================
Notes:
1. Standard Errors assume that the covariance matrix of the errors is correctly specified.
2. The condition number is large (2.46e+03). This might indicate multicollinearity or other numerical problems.The model explains 98.1% of variance in financial support (R² = 0.981).
The Interaction_Dem_Support variable is highly significant (p < 0.001) with a coefficient of approximately 1,213, indicating that for every $1,000 Democrats donate to Democratic candidates, there’s an associated increase of about $1,213 in total financial support.
The Affiliate_REP variable is marginally significant (p = 0.073) with a coefficient of approximately 67,319, suggesting Republican-affiliated PACs tend to provide more financial support overall.
Neither Ideology_Encoded nor Affiliate_DEM variables are statistically significant predictors of financial support when controlling for other variables.
The ANOVA table shows that each variable contributes significantly to explaining the variance in financial support when entered sequentially, with Interaction_Dem_Support having the largest effect.
The residuals show some non-normality, as indicated by the significant Shapiro-Wilk test, but no significant heteroscedasticity or autocorrelation was detected.
The condition number (2.46e+03) is relatively high, suggesting potential numerical problems or multicollinearity, although individual VIF values are below critical thresholds.