Emotional exhaustion or burnout is a significant problem for

Emotional exhaustion, or burnout, is a significant problem for people with careers in the field of human services. Regression analysis was used to investigate the relationship between burnout and aspects of the human services professional’s job and job related behavior (Journal of Applied Behavioral Science, Vol 22, 1986). The next table lists the values of the emotional ex- haustion index (higher values indicate greater exhaustion) and concentration for a sample of 25 human services professionals who work in a large public hospital. A SAS printout of the simple linear regression is provided below.

Find the correlation coefficient for the data and interpret its value.

Test the usefulness of the straight-line relationship with concentration

for predicting burnout. Use = .05.

Find the coefficient of determination for the model.

Find a 95% confidence interval for the slope 1. Interpret the result.

Use a 95% confidence interval to estimate the mean exhaustion level for all professionals who have 80% of their social contacts within their work groups. Interpret the interval.

Solution

R-SQUARE = 0.6123..so, R = correlation coefficient = sqrt( 0.6123) = 0.7825.....
and coeeficient of determiantion = R^2 = 0.6123..
so, corelation between y and x is + 0.7825 and 61.23% of variability of y will be expalined by variation in x!

Test H0 : 1 = 0 ag. H1 : 1 not equals to zero!...

test statistic = coefficient of slope / standard error of slope = 8.86547 / 1.47097 = 6.03 = t value

p-score = < 0.001.. ( from the sas output)

so, at   = .05 , p-score is way less than   = .05 = our level of significance!

so, the test is statistically significant!

i.e, the concentration for predicting burnout is very significant i.e, they are related , there exist a association or relation between them!!

95% confidence interval for slope 1.....

= [ slope estimate - ( t-score for d.f = 23) * ( std. error) , slope estimate + ( t-score for d.f = 23) * ( std. error) ]

= [ 8.86547 - ( 2.068658 * 1.47095) ,   8.86547 - ( 2.068658 * 1.47095) ]
=[ 5.822578 , 11.90836 ]

so, we can say with 95% confidence that the slope of the regression equation for any sample will fall between this interval!!.......

e) s.e = Root MSE * sqrt ( 1 + ( 1 / 25) + ( 80 - x-bar)^2 / ss(x) ) )...

= 174.20742 * sqrt ( 1 + ( 1/25) + (( 80- 68.56) ^2 / 14026.16 ) )
= 178.4526

WHEN, CONCENTRATION = 80 , estimated Exhaustion index = = - 29.49672 + ( 80 * 8.86547) = 679.7409

so, 95% conf. interval = [ 679.7409 - ( 2.068658 * 178.4526) , 679.7409 - ( 2.068658 * 178.4526) ]
= [ 310.5835 , 1048.89 ]

i.e, i can say with 95% confidence that when concentration will be equal to 80 for any observation in any sample , the value of the exhaustion index should lie inside this interval.......