Just a quick questions relating to the further core, I got this in a practice exam and had no idea how to work it out:
"A set of bivariate data involves the independent variable x. The mean of x is 31.38 and the standard deviation is 5.38.
The other variable is y and the mean of y is 19.46 and the standard deviation is 5.46.
Pearson's correlation coefficient is -0.813.
The least squares regression line for this data would have an equation closest to:"
A) y=45.4-0.8x
B) y=0.8+43.2x
C) y=9.9-0.8x
D) y=0.8+9.6x
E) y=44.6-0.8x
The know the answer couldn't be B or C and apparently it is A but how do I work it out?
The equation of a least squares regression line is y = a + bx
a is the y-intercept. This can be found by doing:
a = (mean of y) - b x (mean of x).
b is the gradient. This can be found by:
(correlation coefficient) x (standard deviation of y)
b= __________________________________________
(standard deviation of x).
So substitute the given values:
b = (-0.831 x 5.46) / 5.38 = -0.8
a = 19.46 - (-0.8 x 31.38) = 45.92
Closest answer is A