# Assignment On Post Secondary Degree

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Q U E S T I O N 1
Solution
Sum of X = 608.8
Sum of Y = 43715.4
Mean X = 38.05
Mean Y = 2732.2125
Sum of squares (SSX) = 973.34
Sum of products (SP) = -64987.55
Regression Equation = ŷ = bX + a
b = SP/SSX = -64987.55/973.34 = -66.76757
a = MY - bMX = 2732.21 - (-66.77*38.05) = 5272.71867
ŷ = -66.76757X + 5272.71867
Solution
Correlation Coefficient ( r ) = N x XY ( X )(Y )
N x ¿ ¿
Correlation Coefficient ( r ) =
16 1598383.42608.8 43715.4
(16 24138.1816 24138.182 )16 127198081.7243715.42 =-0.74785
Coefficient of Determination ( r2 ) = r x r.
Inputting the values obtained from d above:
Correlation Coefficient ( r ) =-0.74785
Hence:
Coefficient of Determination =0.55928
Solution
Correlation Coefficient ( r ) = N x XY ( X )(Y )
N x ¿ ¿
Correlation Coefficient ( r ) =
16 1598383.42608.8 43715.4
(16 24138.1816 24138.182 )16 127198081.7243715.42
Correlation Coefficient ( r ) =-0.74785

ŷ = -66.76757X + 5272.71867
Given the equation above, we can deduce that for every increase in percentage of adults
with a post-secondary degree, the rate of crime decreases by approximately 66.76757
hence the crime rate is 5205.95 for a 1% of adults with post-secondary degrees

Yes, using a multiple regression would be useful in further analysis since it would help in
understanding the relationship between the response variable and several other predictor
variables instead of a single predictor variable
Q U E S T I O N 2
1. Solution
Let p be the estimated probability of obtaining heads and r the maximum error which is
defined by |p-r| where p: we let h be the number of heads and t the number of tails then
p= h
h+t
32
50=0.64
Now using Z-tables, the value of z corresponding to 95% confidence interval is 1.960.
Now calculating the error:
E= Z
2 n = 1.96
2 50 =0.1386
Hence:
0.5014<r<0.7786 which closes out on 0.5 hence we can conclude with a 95% confidence
that the coin is biased.
Q U E S T I O N 3
1. Consider the following:

Chi Square
Coefficient of determination
Cramer’s V
Gamma
Kendall’s tau-b
Pearson’s correlation coefficient
t test
o Solution
In statistics, tests of statistical significance are used to calculate the probability that, “...a
relationship observed in the data occurred only by chance; the probability that the
variables are really unrelated in the population” (Devore, 2011) while, measures of
association, “..provide a means of summarizing the size of the
association between two variables” (Mahdavi Damghani, 2012)
o
According to (Göktaş & İşçi, 2011), a PRE Test (Proportional Reduction in Error) is, a
statistical criterion used to quantify the extent to which having knowledge on a given
variable can aid in the prediction of another variable.”
o Examples of PRE measures are: Cramer’s V and Gamma
o An asymmetrical measure of association is, a measure whose value is likely to vary depending
on the variable that is to be considered as independent variable and which the dependent
variable.

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