Question

Please write the answer legibly. Thank you.

The age (X) and glucose levels (Y) of 6 patients are calculated in order to see if there is a relationship
between these two variables. The following data was collected:
SP xy = 478
SS x = 1241
SS y = 656
Calculate the correlation coefficient using the formula: r = SPxy / √ SSx SSy => [sq root of SSx SSy ]

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Using the correlation coefficient (r) derived from above and the data indicated below, determine
(1) the regression equation and (2) the standard error of the estimate using the following formulas:
_ _
Least Squares Regression Equation: Y’ = bX + a where a = Y - bX and b = SSy/SSx • r => sq rt of SSy/SSx

Standard Error of the Estimate: Sy|x = SSy (1 – r 2 )/n-2 [take sq root of entire fraction]
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also, X = 4.2
_
Y = 81

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Given the regression equation determined in problem immediately above, answer the following:
A. What is the predicted glucose level of a patient whose age is 43?
B. What is the predicted glucose level of a patient whose age is 59?

Answer 1

Calculate the correlation coefficient

r = SPxy / √ SSx SSy

r= 478 / sqrt(1241*656)

r= 0.5298

(1) the regression equation and (2) the standard error of the estimate using the following formulas:

b = SSy/SSx

b = 656/1241

b = 0.5286

a = Y – bX

a = 81 -0.5286*4.2

a=78.7799

y=78.7799 + 0.5286*x

Given the regression equation determined in problem immediately above, answer the following:

A. What is the predicted glucose level of a patient whose age is 43?

y=78.7799 + 0.5286*x

y=78.7799 + 0.5286*43

y= 101.5097

B. What is the predicted glucose level of a patient whose age is 59?

y=78.7799 + 0.5286*x

y=78.7799 + 0.5286*59

y= 109.9673