Entering high school students make program choices among general program, vocational program and academic program. Their choice
Question:
Entering high school students make program choices among general program, vocational program and academic program. Their choice might be modeled using their writing score and their social economic status. For our data analysis example, we will expand the third example using the hsb demo data set. Let’s first read in the data. The data set contains variables on 200 students. The outcome variable is program type. The predictor variables are social economic status, , a three-level categorical variable and writing score, write, a continuous variable. Let’s start with getting some descriptive statistics of the variables of interest.
Question
Interpret the output
Snapshot of data
female | ses | schtyp | prog | read | write | math | science | socst | honors | awards | |
12 | male | high | public | 1 | 39 | 33 | 38 | 47 | 41 | not enrolled | 0 |
19 | male | middle | public | 1 | 34 | 46 | 45 | 39 | 36 | not enrolled | 0 |
25 | female | low | public | 1 | 47 | 37 | 43 | 42 | 46 | not enrolled | 0 |
26 | male | high | private | 1 | 44 | 38 | 49 | 39 | 46 | not enrolled | 0 |
29 | female | low | public | 1 | 47 | 41 | 46 | 40 | 41 | not enrolled | 0 |
Table 1.1Case Processing Summary | |||
N | Marginal Percentage | ||
prog | 1 | 105 | 52.5% |
2 | 45 | 22.5% | |
3 | 50 | 25.0% | |
female | female | 109 | 54.5% |
male | 91 | 45.5% | |
Valid | 200 | 100.0% | |
Missing | 0 | ||
Total | 200 | ||
Subpopulation | 200a | ||
a. The dependent variable has only one value observed in 200 (100.0%) subpopulations. |
Table 1.2 Model Fitting Information | ||||
Model | Model Fitting Criteria | Likelihood Ratio Tests | ||
-2 Log Likelihood | Chi-Square | df | Sig. | |
Intercept Only | 408.193 | |||
Final | 329.362 | 78.831 | 12 | .000 |
Table 1.3 Goodness-of-Fit | |||
Chi-Square | df | Sig. | |
Pearson | 422.540 | 386 | .097 |
Deviance | 329.362 | 386 | .983 |
Table 1.4Pseudo R-Square | |
Cox and Snell | .326 |
Nagelkerke | .374 |
McFadden | .193 |
Table 1.5 Likelihood Ratio Tests | ||||
Effect | Model Fitting Criteria | Likelihood Ratio Tests | ||
-2 Log Likelihood of Reduced Model | Chi-Square | df | Sig. | |
Intercept | 329.362a | .000 | 0 | . |
read | 331.819 | 2.457 | 2 | .293 |
write | 331.559 | 2.197 | 2 | .333 |
math | 343.486 | 14.124 | 2 | .001 |
science | 340.723 | 11.361 | 2 | .003 |
socst | 336.158 | 6.796 | 2 | .033 |
female | 329.951 | .589 | 2 | .745 |
The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model. The reduced model is formed by omitting an effect from the final model. The null hypothesis is that all parameters of that effect are 0. | ||||
a. This reduced model is equivalent to the final model because omitting the effect does not increase the degrees of freedom. |
Table1.6Parameter Estimates | |||||||||
proga | B | Std. Error | Wald | df | Sig. | Exp(B) | 95% Confidence Interval for Exp(B) | ||
Lower Bound | Upper Bound | ||||||||
1 | Intercept | -9.294 | 1.626 | 32.684 | 1 | .000 | |||
read | .033 | .032 | 1.076 | 1 | .300 | 1.034 | .971 | 1.101 | |
write | .048 | .033 | 2.086 | 1 | .149 | 1.049 | .983 | 1.119 | |
math | .114 | .037 | 9.755 | 1 | .002 | 1.121 | 1.044 | 1.205 | |
science | -.064 | .031 | 4.215 | 1 | .040 | .938 | .883 | .997 | |
socst | .067 | .026 | 6.458 | 1 | .011 | 1.070 | 1.016 | 1.127 | |
[female=female] | -.344 | .470 | .535 | 1 | .465 | .709 | .282 | 1.781 | |
[female=male] | 0b | . | . | 0 | . | . | . | . | |
2 | Intercept | -4.572 | 1.603 | 8.133 | 1 | .004 | |||
read | -.011 | .033 | .113 | 1 | .737 | .989 | .928 | 1.054 | |
write | .019 | .035 | .303 | 1 | .582 | 1.019 | .953 | 1.090 | |
math | .016 | .036 | .207 | 1 | .649 | 1.017 | .947 | 1.091 | |
science | .033 | .031 | 1.141 | 1 | .286 | 1.034 | .973 | 1.098 | |
socst | .035 | .025 | 1.917 | 1 | .166 | 1.036 | .985 | 1.089 | |
[female=female] | -.129 | .500 | .067 | 1 | .796 | .879 | .330 | 2.340 | |
[female=male] | 0b | . | . | 0 | . | . | . | . | |
a. The reference category is: 3. | |||||||||
b. This parameter is set to zero because it is redundant. |
Table.1.7 Classification | ||||
Observed | Predicted | |||
1 | 2 | 3 | Percent Correct | |
1 | 90 | 5 | 10 | 85.7% |
2 | 27 | 3 | 15 | 6.7% |
3 | 18 | 6 | 26 | 52.0% |
Overall Percentage | 67.5% | 7.0% | 25.5% | 59.5% |
Business Analytics Communicating With Numbers
ISBN: 9781260785005
1st Edition
Authors: Sanjiv Jaggia, Alison Kelly, Kevin Lertwachara, Leida Chen