lm(formula = Large ~ college + prcapinc + urban, data = Data1)

Residuals:

    Min      1Q  Median      3Q     Max 

-6.3912 -1.5526  0.0647  1.4102  6.6222 

Coefficients:

              Estimate Std. Error t value Pr(>|t|)    

(Intercept) 45.5214967  2.6960841  16.884  < 2e-16 ***

college     -0.6030154  0.1389037  -4.341  7.7e-05 ***

prcapinc     0.0001281  0.0001468   0.873   0.3873    

urban       -0.0642188  0.0290102  -2.214   0.0318 *  

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.565 on 46 degrees of freedom

Multiple R-squared:  0.5655, Adjusted R-squared:  0.5371 

F-statistic: 19.96 on 3 and 46 DF,  p-value: 1.983e-08

Antonia Wright

Team Riff Raff (Henry Goettler, Griffin Hansen, Andrew Wise)

Hypothesis: (Taken from merge assignment) In a very inactive America we believe data on how physically active a state’s adult population is will influence a number of other societal and political factors. Specifically we wanted to look into how physical activity can affect the political party representation of a state. In order to do this we looked into how the percent of the adult population that is active leads to a more democratic state. Physical activity is telling of political identification for a variety of reasons, chiefly because more active people are are more concerned with the environmental health of their surroundings, with environmental regulations being a central issue to the democratic party it is no wonder physically active people are more likely to vote blue. 

Analysis: Examining our residual plot of the linear model showing the impact of physical activity on the state’s political alignment, there seems to be significant outliers and a weak pattern. The significant outliers marked in the table above, Colorado, Utah, Arkansas and Mississippi impact the relationship between a state’s political alignment and its level of activity. The residual plot we have is biased and homoscedastic shown by how the data points don’t follow a straight line and how the data points are distributed evenly across the plot. This means that our linear model was not great at explaining the variation in a state’s political alignment. If we had seen an even distribution of data points and a linear line instead of a parabolic line then we could say that there is less error in our linear model and the actual outcome better follow the predicted outcome better.

lm(formula = states$blkleg ~ states$blkpct08 + states$gay.support + 

    states$evm)

Residuals:

Percent of state legislators who are black 

     Min       1Q   Median       3Q      Max 

-10.2966  -1.0852  -0.3789   0.9918   5.9713 

Coefficients:

                       Estimate   Std. Error t value

(Intercept)        -0.093265125  3.659622128  -0.025

states$blkpct08     0.736346433  0.041049315  17.938

states$gay.support  0.000004468  0.062096712   0.000

states$evm         -0.035312939  0.074852081  -0.472

                              Pr(>|t|)    

(Intercept)                      0.980    

states$blkpct08    <0.0000000000000002 ***

states$gay.support               1.000    

states$evm                       0.639    

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.627 on 46 degrees of freedom

Multiple R-squared:  0.882, Adjusted R-squared:  0.8743 

F-statistic: 114.6 on 3 and 46 DF,  p-value: < 0.00000000000000022