Expert answer:Statistics assignment

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hw2.docx

output_in_word_fall2017_2_.pdf

variable_definition_section_2_fall_2017_1_.pdf

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Name:
Directions : For Section One you will be asked to respond to a set of multiple choice items and a few short answer
items. The second section you will use three SPSS outputs to answer the homework questions. These outputs are
provided to you and will just need to be printed out. NOTE: Some values (e.g., degrees of freedom, significance
levels) have been intentionally deleted from the output and will need to be computed to answer the homework
questions. To assist in understanding the meaning and metric of the variables there is a variable definition sheet that
also must be printed out. Be sure to write your name on all pieces of paper and turn everything back in (i.e.,
agreement form, homework and all output).
SECTION ONE – Choose the best answer for each multiple choice question. Then, provide a one
paragraph justification or an illustrative example for why your selected answer is the correct one.
(Each multiple choice item is worth 2 points)
1.
The Y-intercept is the value of a person’s predicted score when X equals:
a. 1.0
b. 0.0
c. mean of Y
d. mean of X
Justification:
2.
The Y-intercept of a regression line is:
a. the value of X at the point where the regression line crosses the X-axis.
b. the value of X at the point where the regression line crosses the Y-axis.
c. the value of Y at the point where the regression line crosses the X-axis.
d. the value of Y at the point where the regression line crosses the Y-axis.
Justification:
3.
In general, the greater the proportion of variance accounted for:
a. the more error there is in the data.
b. the less accurately we can predict or explain behavior.
c. the more accurately we can predict or explain behavior.
d. the less important the relationship to our ability to make predictions.
Name:
Justification:
4.
In general, as independent variables are added to a regression model, the unstandardized regression
coefficients previously entered are expected to:
a. become smaller in value or magnitude.
b. become larger in value or magnitude.
c. remain the same value regardless of the number of independent variables.
d. approach the value of the zero order correlation coefficient.
Justification:
5.
The coefficient of determination is interpreted as:
a. the amount of variance explained in all of the independent variable scores.
b. the degree to which the dependent variable scores are reliable.
c. the proportion of variance in the dependent variable scores that has been accounted for .
d. the proportion of variance in the dependent variable scores that has not been accounted for.
Justification:
6.
In order to have a high multiple correlation (R) or a high R squared value, a researcher would want
independent variables that correlate _______ with the dependent variable and correlate _______ with each
other.
a. low, low
b. low, high
c. high, low
d. high, high
Justification:
7.
For a set of paired (X,Y) values the Sum of Squares Total is equal to 40 and the zero order correlation
coefficient (Pearson correlation coefficient) between X and Y is .60. What is the value of the Sum of
Squares Regression?
a.
b.
c.
.36
.60
14.4
2
Name:
d.
24.0
Justification:
8.
Imagine a set of data where the zero order correlation between Y (the dependent variable) and X1
(the first independent variable) = .10, the zero order correlation between Y (the dependent
variable) and X2 (the second independent variable) = .70 and the zero order correlation between
Y (the dependent variable) and X3 (the third independent variable) = -.20. For the same data set
assume that the zero order correlation between X1 and X2 =0; the zero order correlation between
X1 and X3 =0 and the zero order correlation between X2 and X3 =0, then what would be the value
of R2? Demonstrate and explain how you determined your answer. If you do not show your
work, no points will be awarded. (2 pts)
9. A panel of educators in a large urban community wanted to evaluate the effects of educational
resources on student performance. They examined the relationship between 12th grade mean verbal
SAT scores (Y) and the following independent variables for a random sample of 25 high schools: X1
3
Name:
= Per pupil expenditure in dollars; X2 = Percentage of teachers with a master’s degree or higher; and
X3 = Pupil to teacher ratio. The following sum of squares values can be used to summarize the key
results from using the three independent variables to explain the variability in the SAT scores.
Sum of Squares Total = 28522.24
Sum of Squares Residual = 20391.75
a. Using any SPSS Linear Regression output as a guide, construct an ANOVA table from the Model
Summary section when X1, X2, and X3 are used to explain the variability in Y. (You do not need
to include the Sig column since you do not have access to the exact probability value.) (4 pts)
b. What is the value of the R2 for the model in part 9a? When using an alpha level of .05, is this
value significantly different than zero? Justify your answer. This includes providing the
parameter being estimated, the statistical test (F, t, etc.) and its value, degrees of freedom
associated with the statistical test, and the critical F value associated with this test. (4 pts)
c. Based on the R2 value in part b and your statistical decision, comment on whether the linear
composite of educational resources (the regression equation using your IVs) appears to be
associated with student performance. (1 pt)
SECTION TWO: For this portion of the exam use the SPSS outputs provided or a critical value
F or t table to answer the following questions. You will have to decide which of the outputs
that are provided to you best answer each specific question. Remember a variable definition
sheet is attached to this exam to aid in interpretation of the variables.
4
Name:
10.
11.
Among the six independent variables provided, which one would account for or explain the
greatest amount of variance in the STRESS variable if it were the only independent variable you
were allowed to use in a regression model? In other words, you could only conduct a bivariate
linear regression as opposed to a multiple linear regression. Calculate the proportion of variance
this variable would account for in the STRESS scores (the dependent variable). (4 pts)
Using the unstandardized regression coefficient and an alpha level of .05, interpret the correlation
(including the direction) between traditionality toward childrearing (TRAD) and the mother’s
reported level of stress with her child (STRESS) after controlling for locus of control
(LOCNTRL) and the reported quality of the relationship the mother has with her partner or
spouse (RELAT). In order to receive full credit you must interpret the correlation in the context
of the variable using the definition sheet. It is not acceptable to just say the correlation is positive
or the correlation is negative. Indicate the basis for your conclusion by identifying the value of
the test statistics (F, t, etc.), the degrees of freedom, and your statistical decision. (5 pts)
12. Identify and name the type of parameter (e.g., squared semi-partial correlation coefficient)
that is being estimated along with the values from your set of outputs for each of the
following: (10 pts) Hint: You will need to find the output that contains the model with only the
independent variable of interest for each question. Also, remember there is a difference between r,
r2, and R2 values.
a. r STRESS (RELAT∙ TRAD, LCONTROL)
b. r STRESS, LOCNTROL ∙ M_AGE, INCOME, GENDER, TRAD
c. R2 STRESS ∙ INCOME, GENDER, M_AGE
d. r2 STRESS, M_AGE ∙INCOME, GENDER
e. R2 STRESS ∙ M_AGE, INCOME, GENDER, LOCNTROL, TRAD
13. Use the SPSS output from the full model containing all six independent variables to respond to the
following set of questions.
5
Name:
a. What is the total proportion of STRESS variance accounted for by the full six independent
variable model? (2 pts)
b. Does the proportion in part a) represent a statistically significant amount of variance in the
STRESS scores? Indicate the basis for your conclusion by identifying the value of the test
statistics (F, t, etc.) the degrees of freedom, the critical value and/or the observed significance
level used in making the statistical decision. (4 pts)
c. Do any of the six individual variables contribute a statistically significant proportion of
unique variance (using an alpha level of .05) in the STRESS scores? Answer yes or no for
each of the six variables. For those that you have answered yes, what is the unique variance
associated with these variables?
Indicate the basis for your conclusion by identifying the values of the parameter being
estimated, the test statistics (F, t, etc.) the degrees of freedom, the critical value and/or the
observed significance level used in making the statistical decisions. (16 pts)
6
Name:
14. Using the appropriate unstandardized regression equation, what is the predicted STRESS score for a
mother whose observed scores on the independent variables are as follows: (3 pts)
It is important to show all of your work for full credit.
M_AGE = 30
INCOME = $42,800
GENDER = girl (X value would be coded as a 1)
LOCNTROL = 45
TRAD = 54
RELAT = 2
15. Use the SPSS outputs to assist in answering the following questions regarding variables entered as a
set of variables versus variables entered into a model one individual variable at a time.
a.
What is the unique contribution of the set of variables TRAD and LOCNTRL in the
STRESS scores over and above (or after accounting for) the three family demographic
variables (M_AGE, INCOME and GENDER)? Indicate the basis for your conclusion by
identifying the value(s) of the parameter being estimated, the test statistic(s) (F, t, etc.)
the degrees of freedom, the critical value(s) and/or the observed significance level(s)
used in making the statistical decision(s) (3 pts)
b.
Would you expect M_AGE, INCOME, and GENDER taken as a set to contribute a
significant amount of unique variance to the STRESS scores in a model already
containing LOCNTROL, TRAD, and RELAT? (NOTE: You do not have an output
directly matching this question. You should be able to make an educated guess based on
the output that you do have.) Indicate the basis and rationale for your decision. (2 pts)
7
GET
FILE=’C:EPSY 810Fall2017EPSY 810 Exam data.sav’.
DATASET NAME DataSet1 WINDOW=FRONT.
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA CHANGE ZPP
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT stress
/METHOD=ENTER income m_age /METHOD=ENTER gender /METHOD=ENTER locntrl
trad /METHOD=ENTER relat .
Regression
[DataSet1] ‘C:EPSY 810Fall2017EPSY 810 Exam data.sav’
Descriptive Statistics
stress
income
m_age
gender
locntrl
trad
relat
Mean
63.0208
30767.54
28.2632
.5000
47.9561
58.1754
3.8991
Std. Dev iat ion
12.63602
19428.01324
5.66006
.50221
7.39815
14.73257
.77910
N
114
114
114
114
114
114
114
Correlations
Pearson Correlation
Sig. (1-tailed)
N
stress
1.000
-.188
-.027
-.052
.465
.295
-.271
.
.022
.389
.292
.000
.001
.002
114
114
114
114
114
114
114
stress
income
m_age
gender
locntrl
trad
relat
stress
income
m_age
gender
locntrl
trad
relat
stress
income
m_age
gender
locntrl
trad
relat
income
-.188
1.000
.497
-.146
-.074
-.285
.175
.022
.
.000
.060
.217
.001
.031
114
114
114
114
114
114
114
m_age
-.027
.497
1.000
.053
.149
-.330
.029
.389
.000
.
.288
.056
.000
.378
114
114
114
114
114
114
114
gender
-.052
-.146
.053
1.000
.042
-.047
-.089
.292
.060
.288
.
.330
.311
.174
114
114
114
114
114
114
114
locntrl
.465
-.074
.149
.042
1.000
.078
-.130
.000
.217
.056
.330
.
.206
.084
114
114
114
114
114
114
114
trad
.295
-.285
-.330
-.047
.078
1.000
-.250
.001
.001
.000
.311
.206
.
.004
114
114
114
114
114
114
114
relat
-.271
.175
.029
-.089
-.130
-.250
1.000
.002
.031
.378
.174
.084
.004
.
114
114
114
114
114
114
114
Variabl es Entered/Removedb
Model
1
2
3
4
Variables
Entered
m_age, a
income
gender a
locntrl, trada
relat a
Variables
Remov ed
Method
.
Enter
.
.
.
Enter
Enter
Enter
a. All requested v ariables entered.
b. Dependent Variable: stress
2
Model Summary
Change Statistics
Model
1
2
3
R
R Square
.203a
.223b
.050
c
4
d
Adjusted
R Square
.024
.024
Std. Error of
the Est imat e
12.48300
12.48350
R Square
Change
.041
.009
F Change
2.394
.991
.266
10.82757
.248
19.109
.282
10.70352
.022
3.518
df 1
2
1
df 2
111
110
Sig. F Change
.096
.322
1
107
.063
a. Predictors: (Const ant ), m_age, income
b. Predictors: (Const ant ), m_age, income, gender
c. Predictors: (Const ant ), m_age, income, gender, locntrl, t rad
d. Predictors: (Const ant ), m_age, income, gender, locntrl, t rad, relat
ANOVAe
Model
1
2
3
4
Regression
Residual
Total
Regression
Residual
Total
Regression
Residual
Total
Regression
Residual
Total
Sum of
Squares
745.983
17296.608
18042.591
900.433
17142.158
18042.591
5381.065
12661.526
18042.591
df
2
111
113
3
110
113
5
108
113
Mean Square
372.992
155.825
F
2.394
Sig.
.096a
300.144
155.838
1.926
.130b
1076.213
117.236
9.180
.000c
964.017
8.415
5784.101
12258.490
18042.591
d
114.565
113
a. Predictors: (Constant), m_age, income
b. Predictors: (Constant), m_age, income, gender
c. Predictors: (Constant), m_age, income, gender, locntrl, trad
d. Predictors: (Constant), m_age, income, gender, locntrl, trad, relat
e. Dependent Variable: stress
3
Coeffici entsa
Model
1
2
3
4
(Constant)
income
m_age
(Constant)
income
m_age
gender
(Constant)
income
m_age
gender
locntrl
trad
(Constant)
income
m_age
gender
locntrl
trad
relat
Unstandardized
Coef f icients
B
Std. Error
62.062
6.102
.000
.000
.198
.239
62.690
6.134
.000
.000
.234
.242
-2.379
2.390
15.706
9.537
.0000
.000
.124
.221
-2.017
2.077
.737
.142
.206
.075
29.340
11.904
.000
.000
.087
.219
-2.294
2.058
.715
.141
.174
.076
-2.554
1.361
Standardized
Coef f icients
Beta
-.232
.089
-.254
.105
-.095
-.127
.056
-.080
.432
.240
-.105
.039
-.091
.419
.202
-.157
t
10.171
-2.169
.830
10.219
-2.324
.967
-.996
1.647
-1.308
.562
-.971
5.182
2.760
2.465
-1.081
.398
-1.115
5.068
2.290
-1.876
Sig.
.000
.032
.408
.000
.022
.336
.322
.102
.194
.575
.334
.000
.007
.015
.282
.691
.267
.000
.024
.063
Correlations
Zero-order
Part ial
Part
-.188
-.027
-.202
.079
-.202
.077
-.188
-.027
-.052
-.216
.092
-.094
-.216
.090
-.093
-.188
-.027
-.052
.465
.295
-.125
.054
-.093
.446
.257
-.105
.045
-.078
.418
.222
-.188
-.027
-.052
.465
.295
-.271
-.104
.038
-.107
.440
.216
-.178
-.086
.032
-.089
.404
.182
-.149
a. Dependent Variable: stress
Excluded Variablesd
Model
1
2
3
gender
locntrl
trad
relat
locntrl
trad
relat
relat
Beta In
-.095a
.458a
.297a
-.242a
.458b
.292b
-.248b
-.157c
t
-.996
5.366
3.093
-2.623
5.371
3.031
-2.688
-1.876
Sig.
.322
.000
.003
.010
.000
.003
.008
.063
Part ial
Correlation
-.094
.455
.283
-.243
.457
.279
-.249
-.178
Collinearity
Stat istics
Tolerance
.958
.948
.872
.965
.948
.868
.962
.901
a. Predictors in t he Model: (Constant), m_age, income
b. Predictors in t he Model: (Constant), m_age, income, gender
c. Predictors in t he Model: (Constant), m_age, income, gender, locntrl, trad
d. Dependent Variable: stress
4
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA CHANGE ZPP
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT stress
/METHOD=ENTER relat locntrl trad.
Regression
[DataSet1] ‘C:EPSY 810Fall2017EPSY 810 Exam data.sav’
Descriptive Statistics
stress
relat
locntrl
trad
Mean
63.0208
3.8991
47.9561
58.1754
Std. Dev iat ion
12.63602
.77910
7.39815
14.73257
N
114
114
114
114
Correlations
Pearson Correlation
Sig. (1-tailed)
N
stress
1.000
-.271
.465
.295
.
.002
.000
.001
114
114
114
114
stress
relat
locntrl
trad
stress
relat
locntrl
trad
stress
relat
locntrl
trad
relat
-.271
1.000
-.130
-.250
.002
.
.084
.004
114
114
114
114
locntrl
.465
-.130
1.000
.078
.000
.084
.
.206
114
114
114
114
trad
.295
-.250
.078
1.000
.001
.004
.206
.
114
114
114
114
Variables Entered/Removedb
Model
1
Variables
Entered
trad,
locntrl,
a
relat
Variables
Remov ed
.
Method
Enter
a. All requested v ariables entered.
b. Dependent Variable: stress
5
Model Summary
Change Statistics
Model
1
R
R Square
.555a
.308
Adjusted
R Square
.289
Std. Error of
the Est imat e
10.65722
R Square
Change
.308
F Change
16.286
df 1
3
df 2
110
Sig. F Change
.000
a. Predictors: (Const ant ), trad, locntrl, relat
ANOVAb
Model
1
Regression
Residual
Total
Sum of
Squares
5549.190
12493.402
18042.591
df
3
110
113
Mean Square
1849.730
113.576
F
16.286
Sig.
.000a
a. Predictors: (Constant), trad, locntrl, relat
b. Dependent Variable: stress
Coeffi ci entsa
Model
1
(Constant)
relat
locntrl
trad
Unstandardized
Coef f icients
B
St d. Error
27.140
10.181
-2.605
1.338
.729
.137
.191
.070
St andar
dized
Coef f ici
ents
Beta
-.161
.427
.222
t
2.666
-1.947
5.327
2.709
Sig.
.009
.054
.000
.008
Correlations
Zero-order Part ial
-.271
.465
.295
-.183
.453
.250
Part
-.155
.423
.215
a. Dependent Variable: stress
6
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA CHANGE ZPP
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT stress
/METHOD=ENTER gender income m_age .
Regression
[DataSet1] ‘C:EPSY 810Fall2017EPSY 810 Exam data.sav’
Descriptive Statistics
stress
gender
income
m_age
Mean
63.0208
.5000
30767.54
28.2632
Std. Dev iat ion
12.63602
.50221
19428.01324
5.66006
N
114
114
114
114
Correlati ons
Pearson Correlation
Sig. (1-tailed)
N
stress
1.000
-.052
-.188
-.027
.
.292
.022
.389
114
114
114
114
stress
gender
income
m_age
stress
gender
income
m_age
stress
gender
income
m_age
gender
-.052
1.000
-.146
.053
.292
.
.060
.288
114
114
114
114
income
-.188
-.146
1.000
.497
.022
.060
.
.000
114
114
114
114
m_age
-.027
.053
.497
1.000
.389
.288
.000
.
114
114
114
114
Variabl es Entered/Removedb
Model
1
Variables
Entered
m_age,
gender, a
income
Variables
Remov ed
.
Method
Enter
a. All requested v ariables entered.
b. Dependent Variable: stress
7
Model Summary
Change Statistics
Model
1
R
R Square
.223a
.050
Adjusted
R Square
.024
Std. Error of
the Est imat e
12.48350
R Square
Change
.050
F Change
1.926
df 1
3
df 2
110
Sig. F Change
.130
a. Predictors: (Const ant ), m_age, gender, income
ANOVAb
Model
1
Regression
Residual
Total
Sum of
Squares
900.433
17142.158
18042.591
df
3
110
113
Mean Square
300.144
155.838
F
1.926
Sig.
.130a
a. Predictors: (Constant), m_age, gender, income
b. Dependent Variable: stress
Coeffici entsa
Model
1
(Constant)
gender
income
m_age
Unstandardized
Coef f icients
B
Std. Error
62.690
6.134
-2.379
2.390
.000
.000
.234
.242
Standardized
Coef f icients
Beta
-.095
-.254
.105
t
10.219
-.996
-2.324
.967
Sig.
.000
.322
.022
.336
Correlations
Zero-order
Part ial
-.052
-.188
-.027
-.094
-.216
.092
Part
-.093
-.216
.090
a. Dependent Variable: stress
8
EPSY 810
Fall 2017
Exam Section 2
Variable Definitions
STRESS = Abidin Parenting Stress Index
– This variable represents the level of day-to-day stress reported by mothers when
they are raising a young child. Higher scores represent higher stress; lower scores
represent lower levels of reported stress. Scores can range from 30 to 150.
M_AGE = mother’s age in years
INCOME = total family income per year
GENDER = child gender (when X = 0 the child is a boy; when X = 1 the child is girl)
LOCNTRL = Locus of control
-This variable represents parental beliefs of having control over their baby’s
behavior. The scale contains 20 items on a 5-point Likert scale; scores can vary
from 20 to 100. High scores represent parental beliefs that the baby is in control
over the parents’ lives; low scores represent parental control over their own lives.
TRAD = Traditional ideas toward childrearing
-This variable represents parental ideas toward childrearing with high scores
meaning more traditional feelings toward childrearing and low scores
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