Psych 541 Online Test 3 Summer 2017 59 points 1 (14 points) A researcher wanted to examine the degre

Psych 541 Online Test 3 Summer 2017 59 points

1 (14 points) A researcher wanted to
examine the degree to which IQ and Study Time (hours per week) predict grade
point average The data are presented below along with the results of a
simultaneous multiple regression (backwards and interpret model 1) Please
answer the following questions about the output

IQ
Study GPA

1100 80 10

1120 100 16

1180 60 12

1190 130 21

1220 140 26

1250 60 18

1270 130 26

1300 120 20

1320 130 32

1340 110 26

1360 120 30

1380 180 36

Descriptive
Statistics

Mean

Std
Deviation

N

GPA

22750

79901

12

IQ

1252500

922571

12

study

113333

344656

12

ANOVAb

Model

Sum of
Squares

df

Mean
Square

F

Sig

1

Regression

6389

2

3194

45353

000a

Residual

634

9

070

Total

7023

11

a Predictors: (Constant), study, IQ

b Dependent Variable: GPA

Model
Summary

Model

R

R Square

Adjusted
R Square

Std
Error of the Estimate

1

954a

910

890

26539

a Predictors: (Constant), study, IQ

Correlations

GPA

IQ

study

Pearson Correlation

GPA

1000

856

829

IQ

856

1000

560

study

829

560

1000

Sig (1-tailed)

GPA

000

000

IQ

000

029

study

000

029

N

GPA

12

12

12

IQ

12

12

12

study

12

12

12

Coefficientsa

Model

Unstandardized
Coefficients

Standardized
Coefficients

t

Sig

B

Std
Error

Beta

1

(Constant)

-5249

1166

-4501

001

IQ

049

010

570

4717

001

study

118

028

509

4209

002

a Dependent Variable: GPA

Coefficientsa

Model

Correlations

Zero-order

Partial

Part

1

IQ

856

844

472

study

829

814

422

a Dependent Variable: GPA

(2)
Write the regression equation below here

(1)
What percent of the variance is
unaccounted for by the above predictor variables?

(2) From the above analysis, if we take the
square root of the MS residual, what is that number called and what does it
reflect?

(2) Which predictor variable has the
strongest relationship to Y and how do you know this

(1) What percent of the total variability
is uniquely accounted for by IQ (hint examine the part correlations)

(1)
What number is in the
denominator of the t-test for testing the significance of the predictor study
time?

(2) With study
time in the model, for each unit change in IQ how much of a change occurs in Y
and in what direction

(2) With IQ in
the model, for each standard deviation change in Study time how much of a
standard deviation change in Y occurs and in what direction

(1) What number is in the denominator of
the t-test for testing the significance of the predictor IQ?

2 (10 Points) A statistics professor
conducts a study to investigate the relationship between the performance of
students on his exams and their anxiety Ten students from his class are
selected for the experiment Just prior to taking the final exam, the 10
students are given an anxiety questionnaire Here are final exam and anxiety
scores for the students

Anxiety Final
Exam

28 82

41 58

35 63

39 89

31 92

42 64

50 55

46 70

45 51

37 72

?X = 394 ?Y = 696 ?XY = 26,819

?X2 =
15,946 ?Y2 =50,248

a)
Pearson r for these two
variables is _________

b)
Write the least squares
regression equation using anxiety predicting the final exam

c)
If anxiety level was 20, what is
the predicted final exam score 97303

d)
Compute the Standard Error of estimate

e) If we restricted the range on
either Anxiety or final exam score, what is the most

likely thing to happen assuming the
relationship is linear

3 (20 points) A large corporation is
interested in predicting a measure of job satisfaction its employees It has
collected data on 15 employees who each supplied information on job
satisfaction, level of responsibility, number of people supervised, rating of
working environment and years of service

Satisfaction: 2 2 3
3 5 5
6 6 6
7 8 8
8 9 9

Responsibility: 4 2 3
6 2 8
4 5 8
8 9 6
3 7 9

No supervised: 5 3 4
7 4 8
6 5 9
8 9 3
6 9 9

Environment: 1 1 7
3 5 8
5 5 6
4 7 2
8 7 9

Years of 5 7
5 3 3
6 3 2
7 3 5
5 8 8
1

Service:

A simultaneous a multiple regression
analysis was computed using years of service, environment, numb supervised and
responsibility as predictors and satisfactory ratings as the dependent
variable Using the output below answer the questions for problem 4

Model Summary

Model

R

R Square

Adjusted R Square

Std Error of the Estimate

1

697a

486

281

205723

a Predictors: (Constant), yrsservice,
numsuper, environment, Responsibility

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig

B

Std Error

Beta

1

(Constant)

1669

2032

822

430

Responsibility

605

428

624

1414

188

numsuper

–334

537

–311

–622

548

environment

486

276

514

1758

109

yrsservice

070

262

063

268

794

a Dependent Variable: satisfaction

1
With all four variables in the
model what percent of the variance is accounted for?

2
With all other variables in the
model, for each unit change in responsibility how much of a change occurs in Y
and in what direction

3
With all other variables in the
model, for each standard deviation change in years of service how much of a
standard deviation change in Y occurs and in what direction

4
Which of the five predictor(s)
accounts for a significant amount of the variance in Y?

5
Using the simultaneous multiple
regression procedure, which of the five predictors accounts for the largest
amount of the variance in Y and how do you know this?

6
What number from the output
gives us the error in prediction (put an actual number in here)

7
Write the regression equation
below here

4 (6 points)
What is collinearity and multicollinearity? Why is it a problem? Be specific
and complete in your answer

5 (8 points)
describe what a partial and a part correlation is Give an example of each and
what they accomplish

6 (5 points) What are the standardized
regression coefficients and why do we need them?

____ 7 Satisfying the assumption of
homoscedasticity allows you to
_________

a Interpret
the standard error of estimate

b Calculate
multiple R

c Calculate
a standardized regression coefficient

d Decide
who has been naughty or nice

____ 8 The farther the points on a scatter
diagram fall from the regression line, the _________ between the scores

a higher
the correlation

b lower
the correlation

c correlation
doesn’t change

d need
more information

____ 9 The stronest degree of correlation
shown below is _________

a 075

b -033

c -087

d 015

____ 10 If the correlation between two variables
is 100 and the score of a given individual is 220 standard deviations above
the mean on one of the variables, we would predict a score on the second
variable of _________

a 220
standard deviations below the mean

b 220
standard deviations above the mean

c more
than 220 standard deviations above the mean