Question

As part of an investigation into health service funding, a House subcommittee was concerned with the issue of whether mortality rates could be used to predict sickness rates. Data on standardized mortality rates and standardized sickness rates were collected for a sample of 10 regions and are shown in the table below:
Region Mortality rate x (per 10000)    Sickness rate y (per 1,000)
125   206.8
119.3 213.8
125.3   197.2
111.7 200.6
117.3 189.1
100.7 183.6
108.8    181.2
102.0 168.2
104.7 165.2
121.1 228.5

18. The sample correlation coefficient between the mortality rates and the sickness rates is equal to: A.) 0.1 B.) 0.54       C.) 0.76
19. For a region with mortality rate 125.0, the estimated sickness rate is equal to: A.) 212.12 B.) 215 C.) 225
20. The residual value in sickness rate, when the mortality rate is 125 is equal to: A.) 5.32       B.) 0           C.) -5.32

Answer 1

18. The correlation coefficient is obtained using the formula:

Here . Thus using these value the correlation coefficient is C) 0.76

19. The estimated regression line is:

, where y= sickness rate and x= mortality rate. Thus putting x=125 we have 212.12. Hence the answer is A) 212.12

20. Residual= observed - predicted = 206.8-212.12 = -5.32. Thus the answer is C) -5.32