Running head: MULTIPLE REGRESSION ANALYSIS
Multiple Regression Analysis
Michael Hartman and Gerald Stannard Jr.
Long Island University
1

MULTIPLE REGRESSION ANALYSIS
*******************************************************
** Data Analysis Project 2 **
** Multiple Regression Analysis **
** **
*******************************************************
* STEP 1
* Stata session set up set more off cap set autotabgraphs on
*STEP 2 use "http://datalibrary.us/reportcards200405.dta", clear
*Step 3 describe
*STEP 4 codebook, compact
*Step 5 tab pct4col
*Step 6 sum pct4col
*Step 7 tab1 pct4col enroll000 ppexp000 csize attend pass4 passregents medtchexp co
*Step 8 regress pct4col enroll000 ppexp000 csize attend pass4 passregents medtchexp co, beta
*Step 9 regress, level(90)
*Step 10 graph twoway (scatter pct4col ppexp000, msize(1)), legend(off) xlabel(0(5)26, format(%4.0f)) ylabel(0(5)100, format(%4.0f)) xtitle("% Grads Who Go to College in
Year after Graduation ") ytitle("Per Pupil Expenditures in $1000s")
*Step 11 graph twoway (scatter pct4col passregents, msize(1)), legend(off) xlabel(0(5)100, format(%4.0f)) ylabel(0(5)100, format(%4.0f)) xtitle("% Grads Who Go to College in
Year after Graduation ") ytitle("Avg Pass Rate Eng Math SocStud Regents")
*Step 12 estat vif
2

MULTIPLE REGRESSION ANALYSIS
___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 12.1 Copyright 1985-2011 StataCorp LP
Statistics/Data Analysis StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC http://www.stata.com
979-696-4600 stata@stata.com
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 30120594797
Licensed to: Gerald Stannard Jr.
Notes:
. * STEP 1
. * Stata session set up
. set more off
. cap set autotabgraphs on
.
. *STEP 2
. use "http://datalibrary.us/reportcards200405.dta", clear
. *Step 3
. describe
Contains data from http://datalibrary.us/reportcards200405.dta
obs: 92
vars: 22 29 Feb 2012 12:35
size: 6,256
--------------------------------------------------------------------------------------
------------------------------------
storage display value variable name type format label variable label
--------------------------------------------------------------------------------------
------------------------------------ district str25 %25s School District Name co byte %11.0g coval County enroll int %8.0g Enrollment enroll000 float %9.0g Enrollment in 1000s ppexp long %8.0g Per Pupil Expenditures ppexp000 float %9.0g Per Pupil Expenditures in $1000s povrate byte %8.0g Poverty Rate attend byte %8.0g Average Percent Attendance csize byte %8.0g Average Class Size medtchexp float %9.0g Median Teacher Workforce Experience in
Years passeng4 byte %8.0g 4th Grade Pass Rate Eng Regents passmat4 byte %8.0g 4th Grade Pass Rate Math Regents passeng8 byte %8.0g 8th Grade Pass Rate Eng Regents passmat8 byte %8.0g 8th Grade Pass Rate Math Regents passengr byte %8.0g English Regents Pass Rate passmathr byte %8.0g Math Regents Pass Rate passsocsr byte %8.0g Social Studies Regents Pass Rate
3

MULTIPLE REGRESSION ANALYSIS 4 gradrate byte %8.0g Graduation Rate pct4col byte %8.0g % Grads Who Go to College in Year after
Graduation pass8 float %9.0g Avg Pass Rate 8th Grade Eng & Math
Regents pass4 float %9.0g Avg Pass Rate 4th Grade Eng & Math
Regents passregents float %9.0g Avg Pass Rate Eng Math SocStud Regents
--------------------------------------------------------------------------------------
------------------------------------
Sorted by:
.
. *STEP 4
. codebook, compact
Variable Obs Unique Mean Min Max Label
--------------------------------------------------------------------------------------
------------------------------------ district 92 92 . . . School District Name co 92 2 1.434783 1 2 County enroll 92 92 4627.261 249 17158 Enrollment enroll000 92 92 4.627261 .249 17.158 Enrollment in 1000s ppexp 92 91 16927.52 12799 25022 Per Pupil Expenditures ppexp000 92 91 16.92752 12.799 25.022 Per Pupil Expenditures in $1000s povrate 92 33 12.93478 0 89 Poverty Rate attend 92 8 94.93478 90 97 Average Percent Attendance csize 92 10 21.47826 16 25 Average Class Size medtchexp 92 12 11.15217 7 18 Median Teacher Workforce
Experience in Years passeng4 92 34 83.72826 52 99 4th Grade Pass Rate Eng Regents passmat4 92 21 93.38043 72 100 4th Grade Pass Rate Math Regents passeng8 92 42 66.97826 18 90 8th Grade Pass Rate Eng Regents passmat8 92 39 74.23913 23 93 8th Grade Pass Rate Math Regents passengr 92 31 87.5 30 100 English Regents Pass Rate passmathr 92 34 86.05435 21 99 Math Regents Pass Rate passsocsr 92 34 86.52174 24 100 Social Studies Regents Pass Rate gradrate 92 39 84.05435 33 100 Graduation Rate pct4col 92 43 63.26087 11 100 % Grads Who Go to College in Year after Graduation pass8 92 61 70.6087 22 91 Avg Pass Rate 8th Grade Eng &
Math Regents pass4 92 41 88.55435 64 99.5 Avg Pass Rate 4th Grade Eng &
Math Regents passregents 92 60 86.69203 25 99.66666 Avg Pass Rate Eng Math SocStud
Regents
--------------------------------------------------------------------------------------
------------------------------------
.
. *Step 5
. tab pct4col
% Grads Who |
Go to |
College in |
Year after |
Graduation | Freq. Percent Cum.
------------+-----------------------------------
11 | 1 1.09 1.09
31 | 2 2.17 3.26

MULTIPLE REGRESSION ANALYSIS
38 | 2 2.17 5.43
41 | 3 3.26 8.70
45 | 5 5.43 14.13
46 | 1 1.09 15.22
48 | 1 1.09 16.30
49 | 2 2.17 18.48
50 | 2 2.17 20.65
51 | 3 3.26 23.91
54 | 3 3.26 27.17
55 | 5 5.43 32.61
56 | 5 5.43 38.04
57 | 1 1.09 39.13
58 | 1 1.09 40.22
59 | 2 2.17 42.39
60 | 2 2.17 44.57
61 | 2 2.17 46.74
62 | 3 3.26 50.00
63 | 3 3.26 53.26
64 | 2 2.17 55.43
65 | 2 2.17 57.61
66 | 2 2.17 59.78
67 | 3 3.26 63.04
69 | 3 3.26 66.30
70 | 2 2.17 68.48
71 | 2 2.17 70.65
73 | 3 3.26 73.91
75 | 3 3.26 77.17
77 | 2 2.17 79.35
78 | 2 2.17 81.52
79 | 3 3.26 84.78
82 | 1 1.09 85.87
84 | 1 1.09 86.96
85 | 2 2.17 89.13
86 | 1 1.09 90.22
87 | 1 1.09 91.30
88 | 2 2.17 93.48
89 | 1 1.09 94.57
90 | 2 2.17 96.74
91 | 1 1.09 97.83
95 | 1 1.09 98.91
100 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
.
. *Step 6
. sum pct4col
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
pct4col | 92 63.26087 16.19311 11 100
.
. *Step 7
. tab1 pct4col enroll000 ppexp000 csize attend pass4 passregents medtchexp co
-> tabulation of pct4col
% Grads Who |
Go to |
College in |
5

MULTIPLE REGRESSION ANALYSIS
Year after |
Graduation | Freq. Percent Cum.
------------+-----------------------------------
11 | 1 1.09 1.09
31 | 2 2.17 3.26
38 | 2 2.17 5.43
41 | 3 3.26 8.70
45 | 5 5.43 14.13
46 | 1 1.09 15.22
48 | 1 1.09 16.30
49 | 2 2.17 18.48
50 | 2 2.17 20.65
51 | 3 3.26 23.91
54 | 3 3.26 27.17
55 | 5 5.43 32.61
56 | 5 5.43 38.04
57 | 1 1.09 39.13
58 | 1 1.09 40.22
59 | 2 2.17 42.39
60 | 2 2.17 44.57
61 | 2 2.17 46.74
62 | 3 3.26 50.00
63 | 3 3.26 53.26
64 | 2 2.17 55.43
65 | 2 2.17 57.61
66 | 2 2.17 59.78
67 | 3 3.26 63.04
69 | 3 3.26 66.30
70 | 2 2.17 68.48
71 | 2 2.17 70.65
73 | 3 3.26 73.91
75 | 3 3.26 77.17
77 | 2 2.17 79.35
78 | 2 2.17 81.52
79 | 3 3.26 84.78
82 | 1 1.09 85.87
84 | 1 1.09 86.96
85 | 2 2.17 89.13
86 | 1 1.09 90.22
87 | 1 1.09 91.30
88 | 2 2.17 93.48
89 | 1 1.09 94.57
90 | 2 2.17 96.74
91 | 1 1.09 97.83
95 | 1 1.09 98.91
100 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of enroll000
Enrollment |
in 1000s | Freq. Percent Cum.
------------+-----------------------------------
.249 | 1 1.09 1.09
.679 | 1 1.09 2.17
.934 | 1 1.09 3.26
1.014 | 1 1.09 4.35
1.266 | 1 1.09 5.43
1.267 | 1 1.09 6.52
1.386 | 1 1.09 7.61
1.465 | 1 1.09 8.70
1.628 | 1 1.09 9.78
6

MULTIPLE REGRESSION ANALYSIS
1.663 | 1 1.09 10.87
1.711 | 1 1.09 11.96
1.73 | 1 1.09 13.04
1.752 | 1 1.09 14.13
1.833 | 1 1.09 15.22
1.957 | 1 1.09 16.30
1.975 | 1 1.09 17.39
2.132 | 1 1.09 18.48
2.254 | 1 1.09 19.57
2.284 | 1 1.09 20.65
2.372 | 1 1.09 21.74
2.437 | 1 1.09 22.83
2.537 | 1 1.09 23.91
2.606 | 1 1.09 25.00
2.702 | 1 1.09 26.09
2.75 | 1 1.09 27.17
2.755 | 1 1.09 28.26
2.819 | 1 1.09 29.35
2.843 | 1 1.09 30.43
2.851 | 1 1.09 31.52
2.865 | 1 1.09 32.61
2.945 | 1 1.09 33.70
3.035 | 1 1.09 34.78
3.063 | 1 1.09 35.87
3.104 | 1 1.09 36.96
3.14 | 1 1.09 38.04
3.219 | 1 1.09 39.13
3.283 | 1 1.09 40.22
3.355 | 1 1.09 41.30
3.535 | 1 1.09 42.39
3.553 | 1 1.09 43.48
3.589 | 1 1.09 44.57
3.617 | 1 1.09 45.65
3.622 | 1 1.09 46.74
3.647 | 1 1.09 47.83
3.66 | 1 1.09 48.91
3.662 | 1 1.09 50.00
3.946 | 1 1.09 51.09
4.013 | 1 1.09 52.17
4.077 | 1 1.09 53.26
4.126 | 1 1.09 54.35
4.16 | 1 1.09 55.43
4.203 | 1 1.09 56.52
4.212 | 1 1.09 57.61
4.399 | 1 1.09 58.70
4.483 | 1 1.09 59.78
4.786 | 1 1.09 60.87
4.787 | 1 1.09 61.96
4.801 | 1 1.09 63.04
4.896 | 1 1.09 64.13
4.911 | 1 1.09 65.22
4.999 | 1 1.09 66.30
5.161 | 1 1.09 67.39
5.309 | 1 1.09 68.48
5.472 | 1 1.09 69.57
5.482 | 1 1.09 70.65
5.811 | 1 1.09 71.74
5.874 | 1 1.09 72.83
6.137 | 1 1.09 73.91
6.189 | 1 1.09 75.00
6.242 | 1 1.09 76.09
6.323 | 1 1.09 77.17
6.41 | 1 1.09 78.26
7

MULTIPLE REGRESSION ANALYSIS
6.453 | 1 1.09 79.35
6.475 | 1 1.09 80.43
6.677 | 1 1.09 81.52
6.913 | 1 1.09 82.61
6.951 | 1 1.09 83.70
7.125 | 1 1.09 84.78
7.482 | 1 1.09 85.87
7.561 | 1 1.09 86.96
7.972 | 1 1.09 88.04
7.987 | 1 1.09 89.13
8.004 | 1 1.09 90.22
8.353 | 1 1.09 91.30
9.144 | 1 1.09 92.39
9.745 | 1 1.09 93.48
9.974 | 1 1.09 94.57
10.191 | 1 1.09 95.65
10.541 | 1 1.09 96.74
11.52 | 1 1.09 97.83
15.528 | 1 1.09 98.91
17.158 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of ppexp000
Per Pupil |
Expenditure | s in $1000s | Freq. Percent Cum.
------------+-----------------------------------
12.799 | 1 1.09 1.09
12.814 | 1 1.09 2.17
12.863 | 1 1.09 3.26
13.086 | 1 1.09 4.35
13.148 | 1 1.09 5.43
13.227 | 1 1.09 6.52
13.229 | 1 1.09 7.61
13.295 | 1 1.09 8.70
13.433 | 1 1.09 9.78
13.467 | 1 1.09 10.87
13.594 | 1 1.09 11.96
13.633 | 1 1.09 13.04
13.775 | 1 1.09 14.13
13.78 | 1 1.09 15.22
13.795 | 1 1.09 16.30
14.023 | 1 1.09 17.39
14.126 | 1 1.09 18.48
14.194 | 1 1.09 19.57
14.225 | 1 1.09 20.65
14.274 | 1 1.09 21.74
14.398 | 1 1.09 22.83
14.456 | 1 1.09 23.91
14.487 | 1 1.09 25.00
14.494 | 1 1.09 26.09
14.526 | 1 1.09 27.17
14.596 | 1 1.09 28.26
14.651 | 1 1.09 29.35
14.704 | 1 1.09 30.43
14.707 | 1 1.09 31.52
14.822 | 1 1.09 32.61
14.841 | 1 1.09 33.70
14.993 | 1 1.09 34.78
15.034 | 1 1.09 35.87
15.142 | 1 1.09 36.96
8

MULTIPLE REGRESSION ANALYSIS
15.211 | 1 1.09 38.04
15.236 | 1 1.09 39.13
15.362 | 1 1.09 40.22
15.466 | 1 1.09 41.30
15.573 | 1 1.09 42.39
15.607 | 1 1.09 43.48
15.636 | 1 1.09 44.57
15.647 | 1 1.09 45.65
15.757 | 1 1.09 46.74
16.122 | 1 1.09 47.83
16.148 | 1 1.09 48.91
16.227 | 1 1.09 50.00
16.466 | 1 1.09 51.09
16.502 | 1 1.09 52.17
16.53 | 1 1.09 53.26
16.663 | 1 1.09 54.35
16.932 | 1 1.09 55.43
17 | 1 1.09 56.52
17.003 | 1 1.09 57.61
17.081 | 1 1.09 58.70
17.204 | 1 1.09 59.78
17.324 | 1 1.09 60.87
17.325 | 2 2.17 63.04
17.368 | 1 1.09 64.13
17.37 | 1 1.09 65.22
17.513 | 1 1.09 66.30
17.552 | 1 1.09 67.39
17.615 | 1 1.09 68.48
17.768 | 1 1.09 69.57
17.833 | 1 1.09 70.65
17.916 | 1 1.09 71.74
18.02 | 1 1.09 72.83
18.027 | 1 1.09 73.91
18.178 | 1 1.09 75.00
18.388 | 1 1.09 76.09
18.404 | 1 1.09 77.17
18.864 | 1 1.09 78.26
19.181 | 1 1.09 79.35
19.434 | 1 1.09 80.43
19.634 | 1 1.09 81.52
19.688 | 1 1.09 82.61
19.917 | 1 1.09 83.70
21.038 | 1 1.09 84.78
21.296 | 1 1.09 85.87
21.664 | 1 1.09 86.96
21.695 | 1 1.09 88.04
21.705 | 1 1.09 89.13
21.91 | 1 1.09 90.22
22.245 | 1 1.09 91.30
22.301 | 1 1.09 92.39
22.419 | 1 1.09 93.48
22.529 | 1 1.09 94.57
23.162 | 1 1.09 95.65
24.063 | 1 1.09 96.74
24.654 | 1 1.09 97.83
24.981 | 1 1.09 98.91
25.022 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of csize
Average |
9

MULTIPLE REGRESSION ANALYSIS
Class Size | Freq. Percent Cum.
------------+-----------------------------------
16 | 1 1.09 1.09
17 | 1 1.09 2.17
18 | 4 4.35 6.52
19 | 4 4.35 10.87
20 | 12 13.04 23.91
21 | 19 20.65 44.57
22 | 26 28.26 72.83
23 | 17 18.48 91.30
24 | 7 7.61 98.91
25 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of attend
Average |
Percent |
Attendance | Freq. Percent Cum.
------------+-----------------------------------
90 | 1 1.09 1.09
91 | 2 2.17 3.26
92 | 2 2.17 5.43
93 | 6 6.52 11.96
94 | 22 23.91 35.87
95 | 19 20.65 56.52
96 | 33 35.87 92.39
97 | 7 7.61 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of pass4
Avg Pass |
Rate 4th |
Grade Eng & |
Math |
Regents | Freq. Percent Cum.
------------+-----------------------------------
64 | 1 1.09 1.09
66 | 1 1.09 2.17
71 | 1 1.09 3.26
72.5 | 1 1.09 4.35
73 | 1 1.09 5.43
73.5 | 1 1.09 6.52
78 | 1 1.09 7.61
78.5 | 3 3.26 10.87
79.5 | 1 1.09 11.96
80 | 1 1.09 13.04
81.5 | 1 1.09 14.13
82.5 | 2 2.17 16.30
83 | 3 3.26 19.57
83.5 | 1 1.09 20.65
84 | 3 3.26 23.91
84.5 | 1 1.09 25.00
85 | 1 1.09 26.09
85.5 | 2 2.17 28.26
86 | 2 2.17 30.43
86.5 | 1 1.09 31.52
88 | 6 6.52 38.04
89 | 2 2.17 40.22
89.5 | 3 3.26 43.48
10

MULTIPLE REGRESSION ANALYSIS
90 | 5 5.43 48.91
90.5 | 6 6.52 55.43
91 | 4 4.35 59.78
91.5 | 3 3.26 63.04
92 | 4 4.35 67.39
92.5 | 6 6.52 73.91
93 | 2 2.17 76.09
93.5 | 2 2.17 78.26
94 | 1 1.09 79.35
94.5 | 5 5.43 84.78
95 | 2 2.17 86.96
95.5 | 2 2.17 89.13
96 | 1 1.09 90.22
96.5 | 4 4.35 94.57
97 | 1 1.09 95.65
98 | 1 1.09 96.74
99 | 2 2.17 98.91
99.5 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of passregents
Avg Pass |
Rate Eng |
Math |
SocStud |
Regents | Freq. Percent Cum.
------------+-----------------------------------
25 | 1 1.09 1.09
39.33333 | 1 1.09 2.17
49 | 1 1.09 3.26
57 | 1 1.09 4.35
66.66666 | 1 1.09 5.43
67 | 1 1.09 6.52
69 | 1 1.09 7.61
72 | 1 1.09 8.70
74 | 1 1.09 9.78
75.33334 | 1 1.09 10.87
76 | 1 1.09 11.96
77.33334 | 1 1.09 13.04
77.66666 | 1 1.09 14.13
78 | 1 1.09 15.22
79 | 1 1.09 16.30
79.33334 | 1 1.09 17.39
79.66666 | 1 1.09 18.48
80.66666 | 1 1.09 19.57
82 | 1 1.09 20.65
82.33334 | 1 1.09 21.74
82.66666 | 1 1.09 22.83
83 | 1 1.09 23.91
83.33334 | 1 1.09 25.00
83.66666 | 1 1.09 26.09
84.33334 | 1 1.09 27.17
85 | 1 1.09 28.26
85.33334 | 2 2.17 30.43
85.66666 | 1 1.09 31.52
86 | 1 1.09 32.61
86.33334 | 1 1.09 33.70
86.66666 | 2 2.17 35.87
87 | 1 1.09 36.96
87.33334 | 2 2.17 39.13
88 | 2 2.17 41.30
11

MULTIPLE REGRESSION ANALYSIS
88.33334 | 2 2.17 43.48
88.66666 | 3 3.26 46.74
89 | 1 1.09 47.83
90 | 1 1.09 48.91
90.33334 | 1 1.09 50.00
90.66666 | 2 2.17 52.17
91 | 1 1.09 53.26
91.33334 | 2 2.17 55.43
91.66666 | 1 1.09 56.52
92 | 2 2.17 58.70
92.33334 | 6 6.52 65.22
92.66666 | 2 2.17 67.39
93.33334 | 2 2.17 69.57
93.66666 | 1 1.09 70.65
94 | 3 3.26 73.91
94.33334 | 3 3.26 77.17
94.66666 | 2 2.17 79.35
95 | 4 4.35 83.70
95.33334 | 3 3.26 86.96
95.66666 | 3 3.26 90.22
96 | 1 1.09 91.30
96.66666 | 3 3.26 94.57
97.33334 | 2 2.17 96.74
98.66666 | 1 1.09 97.83
99 | 1 1.09 98.91
99.66666 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of medtchexp
Median |
Teacher |
Workforce |
Experience |
in Years | Freq. Percent Cum.
------------+-----------------------------------
7 | 3 3.26 3.26
8 | 11 11.96 15.22
9 | 14 15.22 30.43
10 | 12 13.04 43.48
11 | 10 10.87 54.35
12 | 18 19.57 73.91
13 | 9 9.78 83.70
14 | 6 6.52 90.22
15 | 3 3.26 93.48
16 | 4 4.35 97.83
17 | 1 1.09 98.91
18 | 1 1.09 100.00
------------+-----------------------------------
Total | 92 100.00
-> tabulation of co
County | Freq. Percent Cum.
------------+-----------------------------------
Suffolk Co. | 52 56.52 56.52
Nassau Co. | 40 43.48 100.00
------------+-----------------------------------
Total | 92 100.00
.
. *Step 8
12

MULTIPLE REGRESSION ANALYSIS 13
. regress pct4col enroll000 ppexp000 csize attend pass4 passregents medtchexp co, beta
Source | SS df MS Number of obs = 92
-------------+------------------------------ F( 8, 83) = 19.24
Model | 15503.6188 8 1937.95235 Prob > F = 0.0000
Residual | 8358.12034 83 100.700245 R-squared = 0.6497
-------------+------------------------------ Adj R-squared = 0.6160
Total | 23861.7391 91 262.216914 Root MSE = 10.035
------------------------------------------------------------------------------
pct4col | Coef. Std. Err. t P>|t| Beta
-------------+----------------------------------------------------------------
enroll000 | .0302549 .4037618 0.07 0.940 .0056507
ppexp000 | 2.082902 .5055581 4.12 0.000 .4054772
csize | .2630747 .7725277 0.34 0.734 .0272997
attend | 1.570267 .91467 1.72 0.090 .1369906
pass4 | .2538726 .2337281 1.09 0.281 .1113964
passregents | .7451234 .1280158 5.82 0.000 .560986
medtchexp | -1.3152 .5588814 -2.35 0.021 -.2003755
co | 1.073157 2.573468 0.42 0.678 .0330332
_cons | -200.811 83.39689 -2.41 0.018 .
------------------------------------------------------------------------------
.
. *Step 9
. regress, level(90)
Source | SS df MS Number of obs = 92
-------------+------------------------------ F( 8, 83) = 19.24
Model | 15503.6188 8 1937.95235 Prob > F = 0.0000
Residual | 8358.12034 83 100.700245 R-squared = 0.6497
-------------+------------------------------ Adj R-squared = 0.6160
Total | 23861.7391 91 262.216914 Root MSE = 10.035
------------------------------------------------------------------------------
pct4col | Coef. Std. Err. t P>|t| [90% Conf. Interval]
-------------+----------------------------------------------------------------
enroll000 | .0302549 .4037618 0.07 0.940 -.6413706 .7018805
ppexp000 | 2.082902 .5055581 4.12 0.000 1.241946 2.923857
csize | .2630747 .7725277 0.34 0.734 -1.021963 1.548113
attend | 1.570267 .91467 1.72 0.090 .0487862 3.091747
pass4 | .2538726 .2337281 1.09 0.281 -.1349154 .6426606
passregents | .7451234 .1280158 5.82 0.000 .5321793 .9580675
medtchexp | -1.3152 .5588814 -2.35 0.021 -2.244855 -.3855457
co | 1.073157 2.573468 0.42 0.678 -3.207602 5.353916
_cons | -200.811 83.39689 -2.41 0.018 -339.5351 -62.08694
------------------------------------------------------------------------------
.
.

MULTIPLE REGRESSION ANALYSIS 14
. *Step 10
. graph twoway (scatter pct4col ppexp000, msize(1)), legend(off) xlabel(0(5)26, format(%4.0f)) ylabel(0(5)100, format(%4.
> 0f)) xtitle("% Grads Who Go to College in Year after Graduation ") ytitle("Per Pupil
Expenditures in $1000s")

MULTIPLE REGRESSION ANALYSIS 15
.
. *Step 11
. graph twoway (scatter pct4col passregents, msize(1)), legend(off) xlabel(0(5)100, format(%4.0f)) ylabel(0(5)100, format
> (%4.0f)) xtitle("% Grads Who Go to College in Year after Graduation ") ytitle("Avg
Pass Rate Eng Math SocStud Regents")
. *Step 12
. estat vif
Variable | VIF 1/VIF
-------------+----------------------
pass4 | 2.49 0.401233
ppexp000 | 2.30 0.435703
passregents | 2.20 0.454311
medtchexp | 1.72 0.582081
csize | 1.52 0.656663
attend | 1.51 0.662773
co | 1.49 0.672539
enroll000 | 1.35 0.742098
-------------+----------------------
Mean VIF | 1.82
.

MULTIPLE REGRESSION ANALYSIS
The New York State Report Card is an important part of the Board of Regents effort to
16 raise learning standards for all students ( Abrams, 2005 ). It provides information to the public on student performance and other measures of statewide performance. Knowledge gained from the report card can be used to improve instruction and services to students.
State assessments are designed to help ensure that all students reach high learning standards. They show whether students are getting the foundation knowledge they need to succeed at the elementary, middle, and commencement levels and beyond. The State requires that students who are not making appropriate progress toward the standards receive academic intervention services. Although the literature suggests that future oriented cognition of students shape their ultimate educational attainments, the underlying variables through which this occurs remain uncertain (Beal & Crockett, 2010).
Results and Discussion
The purpose of this study is to determine how multiple factors within school districts affect the rate at which its graduates enroll in four-year colleges in the year immediately after high school graduation. A set of selected variables from the 2004-05 New York State Education
Department school district report cards and other data available from http://nysed.gov are used as the data source to address a set of seven research questions to be identified. When students select advanced coursework in high school, there is an expectation that such courses will better prepare them for college and result in higher standardized test scores, greater probability of getting into college, and better performance while attending college (Sadler & Tai, 2007). The study’s findings indicate that the percentage of districts’ graduates who go to college in the year after graduation reflects a range from 11% to 100% ( M = 63.26, SD = 16.19).
Regression Model

MULTIPLE REGRESSION ANALYSIS
A multiple regression analysis was conducted on a set of selected variables from the
17
2004-05 New York State Education Department school district report cards and other data available from http://nysed.gov
to address a set of seven research questions concerning school district factors that affect the rates in which their students enroll in four-year colleges immediately after high school graduation.
The regression model shown Table 1 presents an analysis of all of the factors addressed in the research questions in this study. That model is highly statistically significant ( F
(8, 83)
=
19.24, p < .001) and explains about 65% of the variance in districts’ college-going rates ( R
2
=
.649, Adjusted R
2
= .616). The regression equation may be shown as : pct4col = -120.81 + .03
(enroll000) + 2.08 (ppexp000) + .26 (csize) + 1.57 (attend) + .25 (pass4) + .75 (passregents) + -
1.32 (medtchexp) + 1.07 (co).
[Insert Table 1 about here.]
The analysis of the Variable Inflation Factors (VIF) indicates that the model satisfies the regression assumptions related to Multicolinearity. All of VIFs are < 10 and the mean VIF for all variables = 1.82.
Research Question 1
There is insufficient evidence ( p = .946) to conclude that the size of a district, operationalized by its total enrollment, affects its college going rate in the year immediately after high school graduation.
Research Question 2
Budgetary investments (operationalized as expenditures variable per student) has a highly statistically significant (p < .001) influence on districts’ college-going rates and represent the second most important factor addressed in this study (ß = .405). Holding constant the effect of

MULTIPLE REGRESSION ANALYSIS the other factors considered in the study, for every $1,000 in per pupil expenditures, the percentage of students enrolling in a four-year college tends to increase by about 2.083% ( B =
18
2.083). The scatterplot shown in Figure 1 visually depicts the relationship between the collegegoing rate (pct4col) and per pupil expenditures in thousands of dollars (ppexp000).
[Insert Figure 1 about here.]
Research Question 3
Average class size ranged from 16 to 25 students ( M = 21.48, SD = 1.68). Holding the other variables in the model constant, average class size is not a significant predictor of district’s college enrollment rates. There is insufficient evidence ( p = .734) to conclude that average class sizes affect districts’ college-going rates.
Research Question 4
Average percentage of attendance ranged from 90 to 97%, ( M = 94.93, SD = 1.41).
There is insufficient evidence ( p = .09) to conclude that the percentage of average daily attendance affects a district’s college going rate in the year immediately after high school graduation.
Research Question 5
The average passing rate on the final Regents exams is a highly statistically significant ( p
< .001) predictor of a district’s college-going rate and is the single-most important factor (ß
=.561) considered in the analysis. As the results reflect, the percentage of students enrolling in four-year colleges after high school graduation tends to increase by about 0.745% for each percent of passing rate on the final Regents exams. Figure 2 reflects the relationship between districts’ final Regents passing rates and their college-going rates.
[Insert Figure 2 about here.]

MULTIPLE REGRESSION ANALYSIS
The regression analysis further indicates that the 4th Grade Regents exam is not a statistically significant ( p =2.81) predictor of college-going rates after other factors (including
19 the final Regents exam passing rate) are taken into account. This should not be interpreted to indicate that the 4 th
grade exam is unimportant in understanding a district’s college-going rate.
Rather, this reflects the shared variance between pass4 and passregents ( r = .68, p < .001).
Essentially, pass4 and passregents are both indicators of the same effect.
Research Question 6
The median number of years of teaching experience across all teachers in the district ranged from 7 to 18 years ( M = 11.15, SD = 2.47). The median years of teaching experience in a district is a statistically significant ( p = .03) predictor of the college-going rate of its students, after holding all other variables in the model constant. For each additional year of a district’s median teaching experience, the rate at which its graduates enroll in four-year colleges in the year following high school tends to decrease by about 1.32%. This is the third most important factor (ß = -0.19) considered in the study.
Research Question 7
The county independent variable is dichotomous and categorizes the observations into the respective Suffolk and Nassau Counties. Of the 92 participating school districts, Suffolk County represented 52 (56.50%) and Nassau County represented 40 (43.50%). Holding the other variables in the model constant, local culture (as operationalized by county location) is not a significant predictor of district’s college enrollment rates. There is insufficient evidence ( p =
.678) to conclude that average class sizes affect districts’ college-going rates.
Summary and Conclusion

MULTIPLE REGRESSION ANALYSIS
This study found that the most important factors associated with the determination of a
20 school district's college going rate are its academic quality (and achievement), its budgetary investments, and its teaching workforces. District size, class sizes, daily attendance, and county location do not appear to affect the districts' successes in sending their graduates to four-year colleges in the year immediately after graduation. This study has a number of implications for additional research with regard to the determination and understanding of what constitutes academic quality, the fundamental reasons for attaining a college education relative to rewards, effectiveness with regard to budgetary investments for various school districts, and the correlation of teaching experience to teaching effectiveness as it relates to the percentage of high school graduates attending college. Limitations of the study involve the lack of data submission by some school districts and the fact that, from a national perspective, the study was only representative of one state.

MULTIPLE REGRESSION ANALYSIS
References
21
Abrams, D. (2005) 2004-05 New York State Statewide Report Cards. University of State of New
York State Education Department. http://www.p12.nysed.gov/repcrd2005/home.shtml
Beal, S. J., & Crockett, L. J. (2010). Adolescents’ occupational and educational aspirations and expectations: Links to high school activities and adult educational attainment.
Developmental Psychology , 46 , 258-265. doi:10.1037/a0017416
Sadler, P. M., & Tai, R. H. (2007). Weighting for recognition: Accounting for advanced placement and honors courses when calculating high school grade point average. NASSP
Bulletin , 91 , 5-32. doi:10.1177/0192636506298726

MULTIPLE REGRESSION ANALYSIS
Works Consulted as Examples
Fuchs, L. S., Geary, D., Compton, D. C., Fuchs, D. L., Hamlett, C., Seethaler, P. M, . . .
22
Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Advance online publication. Developmental Psychology , 46 , 1731-1746. doi:10.1037/a0020662
Halbesleben, J. R. B., Wakefield, B. J., Wakefield, D. S., & Cooper, L. B. (2008). Nurse burnout and patient safety outcomes: Nurse safety perception versus reporting behavior. Western
Journal of Nursing Research , 30 , 560-577. doi:10.1177/0193945907311322
Onwuegbuzie, A. J., & Jiao, Q. G. (1998). The relationship between library anxiety and learning styles among graduate students: Implications for library instruction. Library and
Information Science Research , 20 , 235-249. doi:10.1016/S0740-8188(98)90042-1

MULTIPLE REGRESSION ANALYSIS
Table 1
Regression Predicting
% Grads Who Go to College in Year after
Graduation
Enrollment in 1000s
Per Pupil Expenditures in $1000s
Average Class Size
Average Percent Attendance
Avg Pass Rate 4th Grade Eng & Math Regents
Avg Pass Rate Eng Math SocStud Regents
Median Teacher Workforce Experience in Years
County
_cons
23
Coef.
Std. Err.
0.03
2.08
0.26
1.57
0.25
0.75
-1.32
1.07
-200.81
t
0.40
0.51
0.77
0.91
0.07
4.12
0.34
1.72
0.23
0.13
1.09
5.82
0.56
-2.35
2.57
0.42
83.40
-2.41
P>t
0.94
0.00
0.73
0.09
0.28
0.00
0.02
0.68
0.02
[90% Conf.
-0.64
1.24
-1.02
0.05
-0.13
0.53
-2.24
-3.21
-339.54
Interval]
0.70
2.92
1.55
3.09
0.64
0.96
-0.39
5.35
-62.09

MULTIPLE REGRESSION ANALYSIS 24
Figure 1. Scatter plot of percentage of students who go to college in year after graduation vs. per pupil expenditures in 1,000’s of dollars.

MULTIPLE REGRESSION ANALYSIS 25
Figure 2 . Scatter plot of percentage of students who go to college in year after graduation vs. average pass rate English Math Social Studies Regents.