Question

The following table represents a SRS of hospitals in a cross-sectional study looking at the relationship between the number of physicians employed and the number of independent research grants submitted in one fiscal quarter.

Number of Physicians Employed Full Time (X)	Number of Accepted Independent Grants (Y)
468	12
579	16
762	9
267	17
987	10
546	16

1. Calculate basic summary statistics for both your X and Y variables of interest.

2. Calculate a correlation coefficient describing the relationship between your X and Y variables. Interpret the statistic.

Answer 1

X Values
∑ = 3609
Mean = 601.5
∑(X - Mx)2 = SSx = 307669.5

Y Values
∑ = 80
Mean = 13.333
∑(Y - My)2 = SSy = 59.333

X and Y Combined
N = 6
∑(X - Mx)(Y - My) = -3237

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -3237 / √((307669.5)(59.333)) = -0.7576

The value of correlation coefficient is -0.7576.

This is a strong negative correlation, which means that higher the Number of Physicians Employed Full Time (X)  lower the Number of Accepted Independent Grants (Y).