Provide and analysis from the information below; Study sample of 368 New York st

Question

Provide and analysis from the information below;

Study sample of 368 New York state resident college students.

Sample drawn from larger survey population of over 6,000 students

Population includes students from a variety of academic disciplines, such as business, communications, liberal arts and engineering.

Looking to view effect on retention status in terms of the following variables
Financial Aid Status
Type of High School
Housing

Retention Status: Whether or not the student was retained in college
Financial Aid Received: Whether or not the student received financial assistance
Housing: Whether the student lived on campus, in fraternity/sorority housing, off campus or commuted.
Type of High School: Whether the student attended public or private high school.

Retention Status: Retained 330 (89.7%) / Not retained 38 (10.3%)

Financial Aid Status: Received Aid 242 (65.8%) Did not receive aid 126 (34.2%)

Housing: On Campus 210 (57.1%), Off Campus 58 (15.8%), Fraternity/Sorority 14 (3.8%) Commuter 86 (23.4%)

Type of High School: Public 186 (50.5%), Private 182 (49.5%)

SUMMARY OUTPUT Regression Statistics Multiple R 0.265481024 R Square 0.070480174 Adjusted R Square 0.060237531 Standard Error 0.295393459 Observations 368 ANOVA df SS MS F Significance F Regression 4 2.401688543 0.600422136 6.881053664 2.39099E-05 Residual 363 31.67439841 0.087257296 Total 367 34.07608696 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.80395707 0.038038498 21.13535248 3.24935E-65 0.729153578 0.878760562 0.729153578 0.878760562 Housing (1=oncampus) 0.16339234 0.0312563 5.227501023 2.90627E-07 0.101926181 0.224858499 0.101926181 0.224858499 HS (1=public) 0.004823377 0.030903807 0.156077117 0.876058996 -0.055949598 0.065596352 -0.055949598 0.065596352 Finaid (1=yes) 0.002337063 0.032513087 0.071880699 0.942736437 -0.061600593 0.06627472 -0.061600593 0.06627472

Explanation / Answer

The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.

Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.

In our model, the p value of Intercept and Housing are greater than alpha (0.05) and thus render them insignificant.

Also, the overall model is not effective as R^2 value is only close to 7%. That says, there are other variable not included in the study that affect the dependent variable.

Coefficients tell us that:

Retention status is positively correlated to Housing, HS and Finaid

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