SPSS part 4

Title: Modeling Project

Name

Institute:

Date:

Introduction:

One of the most affective application of statistics is describing data using regression. (Walpole, 1982). For instance the dataset of the 50 colleges/universities, the data is retrieved from the https://collegescorecard.ed.gov. In the data set there six variables the dependent variable (Y) is college enrollment. It is the current number of students that are enrolled in the college. The independent variables are X1 = Average Annual Cost, in $ (Costs tab), X2 = average salary 10 years after attending, X3 = a dummy variable where 1 = a public institution and 0 = a private institution, X4=Graduation Rate and X5=Students Paying down Their Debt. X6=Students Who Return After Their First Year, X7=Size,X8=Average Years to Graduation, X9=Ratings of the college

The independent variables I have picked are:

Variable Size:

1=Small (< 2,000)

2=Medium (2,000–15,000)

3=Large (> 15,000)

Variable Ratings of the college

1=Very unsatisfied

2=somewhat unsatisfied

3=Neutral

4= somewhat satisfied

5=satisfied

X4=Graduation Rate

X5=Students Paying Down Their Debt

X6=Students Who Return After Their First Year

X7=Size

X8=Average Years to Graduation

X9=Ratings of the college

Using excel the regression output is generated.

From the regression we can conclude that, to predict the current number of students that are enrolled in the college based on picked five independent variables is:

The units for slope are the units of the Y variable per units of the X variable. It’s a ratio of change in Y per change in X.

The R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. For this model the R square is 0.20 which indicates that there is 20% variance for a dependent variable that's explained by an independent variables in a regression model.

References

Walpole, R. (1982). Introduction to Statistics. (3rd ed.). Prentice Hall Publication.

Downie, N. M. & Heath, R. W. (1965). Basic Statistical Methods (2nd ed.). Harper & Row Publisher

Reid, H. (2013, August). Introduction to Statistics. SAGE Publication.

SUMMARY OUTPUT

Regression Statistics

Multiple R0.44

R Square0.20

Adjusted R Square0.02

Standard Error2683.41

Observations50

ANOVA

dfSSMSFSignificance F

Regression970369010.6278187791.0858390.394340455

Residual40288027145.47200679

Total49358396156

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept-1062.454614.98-0.230.82-10389.678264.77

X1 = Average Annual Cost0.150.081.820.08-0.020.31

X2 = average salary -0.020.02-1.170.25-0.060.02

X3 = a dummy variable -1239.31821.93-1.510.14-2900.49421.88

X4=Graduation Rate1002.342585.170.390.70-4222.506227.17

X5=Students Paying Down Their Debt880.461524.480.580.57-2200.633961.56

X6=Students Who Return After Their First Year807.141483.950.540.59-2192.053806.32

X7=Size-346.31496.99-0.700.49-1350.76658.14

X8=Average Years to Graduation407.05510.090.800.43-623.881437.98

X9=Ratings of the college-299.91291.97-1.030.31-889.99290.18