Correlation Analysis in Business Analytics

BUSINESS ANALYTICS

Question: 1
a. regression equation = y = bx + a
Y = height coefficient*x +intercept
Y = 0.182*x+12.49.
b. If for example, in the above equation, if we substitute x as 28 inches for height, then the
resulting head circumference would be as: y= 0.182*28+12.49= 17.586 inches. Here b is slope of
the regression line and a is the intercept, where the x is the independent and y is the dependent
variable.
c. In the data given as regression statistics, where the coefficient of determination has been given
as R-square and the corresponding value of this is 0.8300.
R-square measures the overall strength and not the extent of association between dependent and
independent variable. The strength of association between variables facilitates the identification
of the proportion of variance in dependent variable that can be resulted from independent
variable. Here the value of R-square is given as 0.83 which can be interpreted as, 83% of the
variance in dependent variable (head circumference) can be anticipated through independent
variable (height).
Also, the same can be calculated as: R2= 1 – RSS / TSS, where RSS is the sum of squares of
residuals and the TSS is the total of sum of squares. So the RSS is given as 0.0818 and the TSS
is given as 0.4818. The resulting value of R2 is 1 - .0818 / .4818 = .83 or 83%.
d. coefficient of correlation can be calculated as follows:
SQRT of coefficient of determination =√R2 = √0.83 = 0.911.
r = 0.911.
e. Head circumference (y) =?
Height (x) = 25.25 inches
b = 0.182, a = 12.49
y = bx + c = 0.182*25.25 + 12.49 = 17.085(head circumference).
Question: 2
1. a. P(0<Z<1.5) = 0.4332.
b. P(1<Z<2)
= P(Z=2) = 0.4772 and P(Z=1) = 0.3413,
P(1<Z<2) = 0.4772 – 0.3413 = 0.1359.
c. P (-1<Z<3) = 0.8399