Statistics Midterm Exam Paper
Question 1
a) Averages: = (10 + 4 + 9 - 6 + 8 – 4)/6 = 3.5; = (68.5 + 63.37 + 71.18 + 56.88 + 75.09 + 47.14)/6 = 63.69
= = = 0.09
b) = 63.69 – 0.09*3.5 = 63.375
c) Yi = + 1Xi + ɛ
ɛ = N*(0. σ) = 10 * 0.631 = 6.31
Yi = 63.375 + 0.09* Xi + 6.31
d) SE = ;
SE = 5.52
e) T = = 3.655
The T values obtained are connected to p values used to assess the statistical significance of effects. The p values corresponding to obtained p values are less than the conventionally used level of .05, which means that results are statistically significant.
f) The magnitude of the slope is quite small due to weakness of beta coefficient. In this way, the effect of democracy score on voter turnout is very small and thus does not explain the variances in turnout rate.
g) Yi = 63.375 + 0.09*2 + 6.31
Yi = 69,865
h) R Squared = 1 – (407.54/(407.54 + 122.04)) = 0.77
Question 2
a) Non-Linear relationship
b) Value “1” for Female variable means that participant who gave a certain response was a female. Value “2” for Female variable means that participant who gave a certain response was not a female. Value “1” for Liberal variable means that means that participant who gave a certain response had liberal political views. Value “2” for Liberal variable means that means that participant who gave a certain response did not have liberal political views.
b) For female liberal: ŷ = 40 + 5*1 + 4*1 + 10*1*1 = 59
For male liberal: ŷ = 40 + 5*0 + 4*1 + 10*0*1 = 44
For female conservative: ŷ = 40 + 5*1 + 4*0 + 10*1*0 = 45
For male conservative: ŷ = 40 + 5*0 + 4*0 + 10*0*0 = 40
d) The partial effect is the amount of favorability scores that go up when a variable rises by one point. As the variable “Female” cannot rise by more than 1 point in this case, then the partial effect of being a female for liberals accounts for the increase in 15 points as it is a part of 2 influences. The partial effect of being a female for conservatives accounts for 5 points increase, as it does not additionally contribute to combined effect of variables like in a previous case.
e) The results do not support the hypothesis. Women are more supportive of Hillary Clinton than men regardless of their views. Even the conservative females are more supportive than conservative males. In this way, the hypothesis should be modified. It should be formulated as: all women are more supportive of Hillary Clinton.
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