What does the normal Q?Q plot show?

Question

Recent research has shown that lecturers are among the most stressed workers. A researcher wanted to know exactly what it was about being a lecturer that created this stress and subsequent burnout. She recruited 75 lecturers and administered several questionnaires that measured: Burnout (high score = burnt out), Perceived Control (high score = low perceived control), Coping Ability (high score = low ability to cope with stress), Stress from Teaching (high score = teaching creates a lot of stress for the person), Stress from Research (high score = research creates a lot of stress for the person), and Stress from Providing Pastoral Care (high score = providing pastoral care creates a lot of stress for the person). The outcome of interest was burnout, and Cooper’s (1988) model of stress indicates that perceived control and coping style are important predictors of this variable.

The remaining predictors were measured to see the unique contribution of different aspects of a lecturer’s work to their burnout. The R output is below and the remaining questions relate to this output.



summary(burnoutModel.1)

Call:

glm(formula = burnout ~ loc + cope, family = binomial(), data = burnoutData)

Deviance Residuals:

Min 1Q Median 3Q Max

-2.9217 -0.5163 -0.3730 0.1273 2.0848

Coefficients:

Estimate Std. Error z value Pr(>|z|)\

loc 0.061080 0.010915 5.596 2.19e-08 ***

cope 0.082714 0.009369 8.829 < 2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 530.11 on 466 degrees of freedom

Residual deviance: 364.18 on 464 degrees of freedom

AIC: 370.18

Number of Fisher Scoring iterations: 5

logisticPseudoR2s(burnoutModel.1)

Pseudo R^2 for logistic regression

Hosmer and Lemeshow R^2 0.313

Cox and Snell R^2 0.299

Nagelkerke R^2 0.441

exp(burnoutModel.1$coefficients)

(Intercept) loc cope

0.01128261 1.06298389 1.08623164

exp(confint(burnoutModel.1))

2.5 % 97.5 %

(Intercept) 0.005160721 0.02292526

loc 1.041229885 1.08691181

cope 1.067210914 1.10722003

summary(burnoutModel.2)

Call:

glm(formula = burnout ~ loc + cope + teaching + research + pastoral,

family = binomial(), data = burnoutData)

Deviance Residuals:

Min 1Q Median 3Q Max

-2.41592 -0.48290 -0.28690 0.02966 2.63636

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -4.43993 1.08565 -4.090 4.32e-05 ***

loc 0.11079 0.01494 7.414 1.23e-13 ***

cope 0.14234 0.01639 8.684 < 2e-16 ***

teaching -0.11216 0.01977 -5.673 1.40e-08 ***

research 0.01931 0.01036 1.863 0.062421 .

pastoral 0.04517 0.01310 3.449 0.000563 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 530.11 on 466 degrees of freedom

Residual deviance: 321.20 on 461 degrees of freedom

AIC: 333.2

Number of Fisher Scoring iterations: 6

modelChi; chidf; chisq.prob

[1] 208.9086

[1] 5

[1] 0

logisticPseudoR2s(burnoutModel.2)

Pseudo R^2 for logistic regression

Hosmer and Lemeshow R^2 0.394

Cox and Snell R^2 0.361

Nagelkerke R^2 0.531

exp(burnoutModel.2$coefficients)

(Intercept) loc cope teaching research pastoral

0.01179680 1.11715594 1.15296414 0.89389904 1.01949919 1.04620942

exp(confint(burnoutModel.2))

2.5 % 97.5 %

(Intercept) 0.001317788 0.09419003

loc 1.086274965 1.15212014

cope 1.118430575 1.19286786

teaching 0.858532732 0.92793154

research 0.999115252 1.04068582

pastoral 1.020119629 1.07403586





a. That the data are not normally distributed.

b. Homoscedasticity of errors only.

c. Independence of errors and homoscedasticity.

d. Heteroscedasticity and independence of errors.

Answer 1

a. That the data are not normally distributed.