Question

In: Statistics and Probability

1) You conduct a stepwise regression according to the following procedure: Step 1:        HS_SCI only Step 2:        HS_SCI...

1) You conduct a stepwise regression according to the following procedure:

Step 1:        HS_SCI only

Step 2:        HS_SCI and HS_ENG

Step 3:        HS_SCI, HS_ENG and HS_MATH

Step 4:        HS_SCI, HS_ENG, HS_MATH and PARENT EDUC

Step 5:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC AND GENDER

Step 6:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC, GENDER and ATAR

Present the regression output for each of the six steps.

Choice of reference category: It is recommended that you choose U (undergraduate education) as the reference category for the categorical variable: PARENT EDUC.                                                   

2) For eachof the independent variables contained in the regression model in Step 5, fullyinterpret the regression (slope) coefficients and comment on their statistical significance.

In discussing statistical significance of a regression coefficient, you have to justify your choice of a one or two tail test.

3) In stepwise regression Step 6you noticed that the regression coefficient of ATAR is negative (!). Does this result surprise you, given the correlation of ATAR and GPA? Why/Why not? Does the inclusion of ATAR improve overall model fit? Discuss fully.   

DATA SAET:

Student ID GPA HS_SCI HS_ENG HS_MATH ATAR PARENT EDUC GENDER
1 6.75 10 10 10 91.6 P M
2 3.78 6 6 6 55.3 S M
3 4.11 6 8 8 74.95 U M
4 3.64 10 7 9 84.05 U M
5 5.91 9 8 8 77.55 U M
6 5.75 8 8 10 78.3 U M
7 5.35 10 10 8 89.75 S M
8 1.99 10 7 10 85.45 S M
9 4.81 10 10 10 90.25 P M
10 4.09 7 6 7 64.8 U M
11 5.39 10 6 9 84.55 U M
12 5.84 9 7 5 67.95 U M
13 1.59 5 7 6 61.95 S M
14 2.50 9 9 10 89.85 U M
15 4.09 9 7 8 74.05 S M
16 6.52 10 9 10 96.75 U M
17 6.65 10 9 10 93.9 U M
18 7.00 9 8 9 86.55 U M
19 3.50 6 5 9 66.95 U M
20 5.25 10 9 10 96 P M
21 4.06 7 8 9 74.05 U M
22 4.58 8 7 9 79.25 P M
23 5.37 4 7 7 58.3 S M
24 5.18 7 6 9 66.3 U M
25 6.56 9 9 10 92.35 U M
26 5.46 10 7 10 89.4 S M
27 3.93 7 4 9 68.3 S M
28 5.30 8 7 8 74.95 S M
29 1.35 6 6 7 57.65 S M
30 5.60 5 7 9 68.6 P M
31 2.45 8 8 6 68.35 S M
32 4.60 10 6 10 81.95 S M
33 3.36 10 8 9 86 S M
34 5.12 10 10 10 97.45 U M
35 6.54 10 9 9 84.85 P M
36 4.95 9 9 10 92.75 U M
37 5.42 10 9 9 86.25 U M
38 4.20 6 6 7 59.2 S M
39 4.88 6 7 9 70.45 S M
40 3.37 6 8 8 76.05 S M
41 3.79 7 7 10 74.2 U M
42 3.13 7 5 7 66.05 S M
43 5.86 10 10 10 84.25 U M
44 6.31 10 9 10 88.9 P M
45 4.81 7 5 10 73.65 U M
46 6.26 7 8 10 77.8 P M
47 4.83 10 10 10 90.35 P M
48 6.42 10 10 10 97.3 U M
49 6.66 10 7 10 90.2 U M
50 5.53 9 8 10 87 S M
51 5.53 7 7 9 77.6 P M
52 6.33 10 8 10 92 U M
53 3.93 9 10 6 81.8 S M
54 4.46 8 8 7 74 U M
55 4.93 9 9 10 91.45 U M
56 5.68 7 8 9 73.5 U M
57 3.71 7 8 7 73.95 S M
58 3.29 6 6 10 75.95 S M
59 4.63 10 8 8 82 S M
60 3.22 6 6 9 64 S M
61 3.86 7 8 7 73.65 S M
62 5.18 7 8 9 72.8 P M
63 4.23 6 8 6 61.3 S M
64 5.96 4 7 9 62.8 P M
65 5.81 10 10 10 90.4 P M
66 4.74 7 9 8 76.1 U M
67 5.95 10 9 9 84.25 U M
68 4.34 9 6 8 75.55 S M
69 4.34 8 7 8 71.85 U M
70 1.00 10 9 7 86.15 P M
71 5.56 10 8 9 88.1 P M
72 5.95 8 4 7 61.1 S M
73 5.61 8 7 8 74.25 S M
74 4.72 8 6 6 65.35 S M
75 5.35 6 5 8 59.95 U M
76 7.00 10 10 9 95.05 U M
77 6.12 7 8 8 69.8 S M
78 4.91 7 4 9 68.35 U M
79 3.16 9 9 9 87.5 P M
80 6.47 10 10 10 96.45 U M
81 5.04 7 6 9 71.35 S M
82 4.62 9 8 9 82.85 U M
83 5.40 10 8 10 84.2 U M
84 4.93 5 7 4 51.15 S M
85 5.19 10 10 10 95.55 U M
86 4.91 10 10 10 98.25 U M
87 5.81 9 10 10 91.5 U M
88 5.61 9 8 7 75.8 S M
89 6.47 10 8 8 87.9 S M
90 5.35 9 9 5 73.95 S M
91 5.02 9 9 9 81.15 S M
92 3.71 6 7 7 69.55 P M
93 3.95 7 7 5 63.55 U M
94 3.55 7 9 6 74.4 U M
95 4.25 10 10 7 82.3 U M
96 4.37 9 9 10 90.35 S M
97 2.90 4 3 8 49.75 U M
98 5.96 9 9 9 88.9 U M
99 3.41 8 9 7 77.25 S M
100 5.82 6 7 7 64.1 U M
101 2.78 9 7 8 77.5 S M
102 4.30 7 7 6 66.9 U M
103 6.02 10 9 10 96.35 S M
104 2.95 7 7 8 75.05 S M
105 1.30 7 7 9 72.8 U M
106 4.88 8 7 8 70.6 P M
107 1.00 6 6 4 58.05 S M
108 3.57 7 7 8 70.15 S M
109 3.50 5 6 6 57 S M
110 2.34 7 8 6 64.25 U M
111 4.02 10 10 9 90.65 P M
112 5.70 10 9 10 95.75 P M
113 5.49 8 9 9 83.2 U M
114 3.93 10 10 10 93.6 U M
115 1.75 9 10 8 91 U M
116 4.86 9 10 9 89.75 S M
117 3.95 8 5 6 65.7 S M
118 3.69 9 9 6 72.4 S M
119 4.95 7 7 6 63.85 S M
120 1.00 7 7 5 59.45 S M
121 4.37 9 9 9 81.1 U M
122 4.77 8 7 9 79.05 S M
123 4.27 8 8 8 73.55 U M
124 1.94 7 7 7 69.35 U M
125 5.46 10 10 10 96.3 U M
126 3.79 7 8 8 70.25 U M
127 3.50 7 6 3 53.25 S M
128 3.18 8 6 6 64.2 S M
129 5.63 7 9 9 84.2 U M
130 5.39 10 8 9 82.85 S M
131 1.40 10 9 8 85 S M
132 4.51 9 9 10 87.95 U M
133 3.76 6 6 6 62.2 S M
134 4.37 10 10 7 89.2 U M
135 3.23 8 7 10 84.15 U M
136 1.87 8 6 7 66.55 S M
137 5.16 9 8 9 80.3 U M
138 6.51 8 7 7 70.8 U M
139 1.21 6 7 6 61.55 S M
140 4.67 9 10 9 93.35 U M
141 4.39 8 7 9 76.3 U M
142 2.55 7 8 7 72.1 S M
143 4.18 5 6 6 57.4 S M
144 5.25 3 4 4 35.05 S M
145 5.86 10 10 10 92.9 P M
146 4.27 9 9 10 86.25 S F
147 5.86 9 9 9 88.25 U F
148 6.65 9 8 10 90.4 U F
149 4.56 7 8 9 73.15 P F
150 4.90 9 9 10 92.45 P F
151 5.74 10 10 10 91 P F
152 5.02 8 7 8 69.65 U F
153 5.53 9 8 8 76.75 U F
154 5.37 8 9 9 79.4 U F
155 6.44 8 9 10 89.65 U F
156 5.84 9 10 10 88.1 U F
157 6.05 9 8 9 86.05 S F
158 4.25 5 9 9 72.65 U F
159 4.84 5 9 6 64.75 P F
160 6.40 10 10 10 90.7 U F
161 3.25 9 7 7 75.55 S F
162 3.41 6 9 6 68.2 S F
163 5.35 10 10 10 96.2 U F
164 3.39 8 8 8 73.95 S F
165 5.49 9 10 9 91.6 U F
166 4.98 8 8 10 79.45 U F
167 6.07 10 9 10 96.25 U F
168 5.93 10 10 10 86.25 S F
169 6.82 10 10 10 91.8 U F
170 6.38 9 9 9 83.15 U F
171 6.37 6 8 8 72.4 S F
172 4.83 10 10 10 96.35 S F
173 5.00 9 10 10 91.05 U F
174 4.39 9 10 8 85.85 U F
175 5.00 9 8 8 78.35 U F
176 5.84 9 9 10 85.1 U F
177 5.82 7 9 9 82.85 U F
178 6.45 10 8 10 90.65 U F
179 3.15 7 7 7 65.35 U F
180 4.49 10 10 9 90.85 U F
181 3.99 10 10 8 92.8 U F
182 3.50 4 6 2 44.55 S F
183 4.42 9 8 8 81 S F
184 2.95 6 7 7 60.25 U F
185 5.35 10 9 9 86.6 U F
186 4.81 9 8 8 81.9 U F
187 4.58 10 8 9 87.45 U F
188 3.74 4 8 5 54.85 U F
189 3.37 8 8 10 87.35 S F
190 5.00 4 8 9 70.35 S F
191 4.14 7 9 8 78.35 U F
192 2.18 8 6 7 66.75 U F
193 5.56 10 10 10 95.35 P F
194 5.77 10 9 10 88.9 S F
195 4.00 6 8 7 72.15 S F
196 4.74 7 10 9 84.05 U F
197 4.53 10 10 10 90.45 U F
198 5.93 9 10 9 85.35 P F
199 4.28 7 8 7 73.3 S F
200 4.53 4 7 5 51.5 S F
201 4.51 10 9 10 89.35 P F
202 4.70 6 9 8 70.2 U F
203 4.42 6 9 7 72.1 S F
204 5.25 8 9 10 86.2 U F
205 3.62 7 6 9 66.95 S F
206 3.23 8 10 10 92.75 U F
207 5.84 9 10 10 95.2 U F
208 4.76 5 7 6 61.55 P F
209 7.00 10 10 10 94.8 U F
210 5.95 9 9 6 75.55 P F
211 5.12 9 10 9 91.05 P F
212 3.83 5 6 6 57.5 S F
213 5.81 9 10 10 87.1 S F
214 5.96 6 8 8 69.85 S F
215 3.15 7 9 8 76.15 U F
216 2.66 9 10 9 86.1 U F
217 4.16 9 10 9 87.75 P F
218 3.65 7 8 9 74.35 S F
219 5.65 10 10 10 98.75 S F
220 2.31 8 9 9 81.4 S F
221 4.06 6 7 6 58.8 S F
222 1.48 7 9 7 72.35 S F
223 2.80 7 7 4 56.95 S F
224 3.99 8 9 9 79.45 U

F

                                            

Solutions

Expert Solution

Spss used.

PARENT EDUC coded as edu1 with 0 for U , 1 for S and P for 2

Gender is coded as gender1 with M=1 and F=0.

1) You conduct a stepwise regression according to the following procedure:

Step 1:        HS_SCI only

Step 2:        HS_SCI and HS_ENG

Step 3:        HS_SCI, HS_ENG and HS_MATH

Step 4:        HS_SCI, HS_ENG, HS_MATH and PARENT EDUC

Step 5:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC AND GENDER

Step 6:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC, GENDER and ATAR

Present the regression output for each of the six steps.

Choice of reference category: It is recommended that you choose U (undergraduate education) as the reference category for the categorical variable: PARENT EDUC.   

Spss syntax.

REGRESSION

/MISSING LISTWISE

/STATISTICS COEFF OUTS R ANOVA

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT GPA

/METHOD=ENTER HS_SCI

/METHOD=ENTER HS_ENG

/METHOD=ENTER HS_MATH

/METHOD=ENTER edu1

/METHOD=ENTER gender1

/METHOD=ENTER ATAR.

                                              

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.344a

.119

.115

1.25303

2

.367b

.135

.127

1.24408

3

.464c

.215

.205

1.18761

4

.464d

.215

.201

1.19022

5

.465e

.216

.198

1.19232

6

.465f

.216

.195

1.19491

a. Predictors: (Constant), HS_SCI

b. Predictors: (Constant), HS_SCI, HS_ENG

c. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH

d. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1

e. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1, gender1

f. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1, gender1, ATAR

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

46.870

1

46.870

29.852

.000b

Residual

348.557

222

1.570

Total

395.427

223

2

Regression

53.380

2

26.690

17.245

.000c

Residual

342.047

221

1.548

Total

395.427

223

3

Regression

85.137

3

28.379

20.121

.000d

Residual

310.290

220

1.410

Total

395.427

223

4

Regression

85.185

4

21.296

15.033

.000e

Residual

310.242

219

1.417

Total

395.427

223

5

Regression

85.512

5

17.102

12.030

.000f

Residual

309.915

218

1.422

Total

395.427

223

6

Regression

85.594

6

14.266

9.991

.000g

Residual

309.833

217

1.428

Total

395.427

223

a. Dependent Variable: GPA

b. Predictors: (Constant), HS_SCI

c. Predictors: (Constant), HS_SCI, HS_ENG

d. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH

e. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1

f. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1, gender1

g. Predictors: (Constant), HS_SCI, HS_ENG, HS_MATH, edu1, gender1, ATAR

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

2.422

.408

5.935

.000

HS_SCI

.270

.049

.344

5.464

.000

2

(Constant)

1.875

.485

3.865

.000

HS_SCI

.198

.060

.253

3.297

.001

HS_ENG

.139

.068

.157

2.051

.041

3

(Constant)

.988

.499

1.979

.049

HS_SCI

.067

.064

.085

1.049

.295

HS_ENG

.086

.066

.097

1.310

.192

HS_MATH

.286

.060

.352

4.745

.000

4

(Constant)

1.011

.516

1.960

.051

HS_SCI

.067

.064

.085

1.043

.298

HS_ENG

.086

.066

.097

1.308

.192

HS_MATH

.285

.061

.351

4.702

.000

edu1

-.021

.113

-.011

-.184

.854

5

(Constant)

1.116

.561

1.989

.048

HS_SCI

.074

.066

.095

1.127

.261

HS_ENG

.073

.071

.083

1.033

.303

HS_MATH

.284

.061

.349

4.670

.000

edu1

-.018

.113

-.009

-.157

.875

gender1

-.087

.181

-.031

-.480

.632

6

(Constant)

1.153

.583

1.978

.049

HS_SCI

.094

.105

.120

.894

.372

HS_ENG

.092

.104

.104

.880

.380

HS_MATH

.303

.101

.373

2.992

.003

edu1

-.019

.113

-.010

-.169

.866

gender1

-.084

.182

-.030

-.460

.646

ATAR

-.006

.027

-.060

-.240

.811

a. Dependent Variable: GPA

2) For eachof the independent variables contained in the regression model in Step 5, fullyinterpret the regression (slope) coefficients and comment on their statistical significance.

All two tailed test is used.

To test the significance of HS_SCI, calculated t=1.127, P=0.261 which is > 0.05 level. This is not significant.

To test the significance of HS_ENG, calculated t=1.033, P=0.303 which is > 0.05 level. This is not significant.

To test the significance of HS_MATH, calculated t=4.670, P=0.000 which is < 0.05 level. This is significant.

To test the significance of PARENT EDUC, calculated t=-0.157, P=0.875 which is > 0.05 level. This is not significant.

To test the significance of GENDER, calculated t=-0.480, P=0.632 which is > 0.05 level. This is not significant

5

(Constant)

1.116

.561

1.989

.048

HS_SCI

.074

.066

.095

1.127

.261

HS_ENG

.073

.071

.083

1.033

.303

HS_MATH

.284

.061

.349

4.670

.000

edu1

-.018

.113

-.009

-.157

.875

gender1

-.087

.181

-.031

-.480

.632

In discussing statistical significance of a regression coefficient, you have to justify your choice of a one or two tail test.

3) In stepwise regression Step 6you noticed that the regression coefficient of ATAR is negative (!). Does this result surprise you, given the correlation of ATAR and GPA? Why/Why not? Does the inclusion of ATAR improve overall model fit? Discuss fully.   

regression coefficient of ATAR is -0.006 which is negative.

Correlations

GPA

ATAR

GPA

Pearson Correlation

1

.424**

Sig. (2-tailed)

.000

N

224

224

ATAR

Pearson Correlation

.424**

1

Sig. (2-tailed)

.000

N

224

224

**. Correlation is significant at the 0.01 level (2-tailed).

Correlation of ATAR and GPA is 0.424 which is positive.

But regression coefficient of ATAR is -0.006 which is negative shows that some other independent variable is in the model is highly correlated with ATAR. After including ATAR, the R square value remains same as 0.216. There fore inclusion of ATAR does not improve overall model fit.

orchestra answered 1 year ago
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