Question

Use the SAT data and create a multiple regression table but this time as input use ONLY two variables: Letters and SAT. Answer questions 1 to 4. Choose the best fitting answer. Note: numbers are truncated unless specified.

1. If an incoming student has Letters = 7 and SAT = 1000 what would his predicted College GPA be?

a. 1.99

b. 2.01

c. ​​2.18

d. 2.39

2. What is the approximate error of this prediction?

a. 0.58

b. ​​0.61

c. 0.55

d. 0.63

3. If this student increases his SAT score by 300 points how much higher would be his predicted College GPA?

a. 0.58

b. 0.48

c. 0.40

d. 0.37

4. If two students have the identical SAT scores but one has a letter score 2 points lower than the other, how much changes will his College GPA be?

a. 0.012

b. - 0.012

c. 0.24

d. - 0.24

SAT DATA

C ollege GPA    HighSchl GPA    SAT     Letters
2.04    2.01    1070    5
2.56    3.4     1254    6
3.75    3.68    1466    6
1.1     1.54    706     4
3       3.32    1160    5
0.05    0.33    756     3
1.38    0.36    1058    2
1.5     1.97    1008    7
1.38    2.03    1104    4
4.01    2.05    1200    7
1.5     2.13    896     7
1.29    1.34    848     3
1.9     1.51    958     5
3.11    3.12    1246    6
1.92    2.14    1106    4
0.81    2.6     790     5
1.01    1.9     954     4
3.66    3.06    1500    6
2       1.6     1046    5
2.05    1.96    1054    4
2.6     1.96    1198    6
2.55    1.56    940     3
0.38    1.6     456     6
2.48    1.92    1150    7
2.74    3.09    636     6
1.77    0.78    744     5
1.61    2.12    644     5
0.99    1.85    842     3
1.62    1.78    852     5
2.03    1.03    1170    3
3.5     3.44    1034    10
3.18    2.42    1202    5
2.39    1.74    1018    5
1.48    1.89    1180    5
1.54    1.43    952     3
1.57    1.64    1038    4
2.46    2.69    1090    6
2.42    1.79    694     5
2.11    2.72    1096    6
2.04    2.15    1114    5
1.68    2.22    1256    6
1.64    1.55    1208    5
2.41    2.34    820     6
2.1     2.92    1222    4
1.4     2.1     1120    5
2.03    1.64    886     4
1.99    2.83    1126    7
2.24    1.76    1158    4
0.45    1.81    676     6
2.31    2.68    1214    7
2.41    2.55    1136    6
2.56    2.7     1264    6
2.5     1.66    1116    3
2.92    2.23    1292    4
2.35    2.01    604     5
2.82    1.24    854     6
1.8     1.95    814     6
1.29    1.73    778     3
1.68    1.08    800     2
3.44    3.46    1424    7
1.9     3.01    950     6
2.06    0.54    1056    3
3.3     3.2     956     8
1.8     1.5     1352    5
2       1.71    852     5
1.68    1.99    1168    5
1.94    2.76    970     6
0.97    1.56    776     4
1.12    1.78    854     6
1.31    1.32    1232    5
1.68    0.87    1140    6
3.09    1.75    1084    4
1.87    1.41    954     2
2       2.77    1000    4
2.39    1.78    1084    4
1.5     1.34    1058    4
1.82    1.52    816     5
1.8     2.97    1146    7
2.01    1.75    1000    6
1.88    1.64    856     4
1.64    1.8     798     4
2.42    3.37    1324    6
0.22    1.15    704     6
2.31    1.72    1222    5
0.95    2.27    948     6
1.99    2.85    1182    8
1.86    2.21    1000    6
1.79    1.94    910     6
3.02    4.25    1374    9
1.85    1.83    1014    6
1.98    2.75    1420    7
2.15    1.71    400     6
1.46    2.2     998     7
2.29    2.13    776     6
2.39    2.38    1134    7
1.8     1.64    772     4
2.64    1.87    1304    6
2.08    2.53    1212    4
0.7     1.78    818     6
0.89    1.2     864     2

Answer 1

applying multiple regression on above:

Regression Statistics
Multiple R	0.5761
R Square	0.3319
Adjusted R Square	0.3181
Standard Error	0.6187
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	2	18.44455	9.222277	24.09389	3.2E-09
Residual	97	37.12812	0.382764
Total	99	55.57268
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%
Intercept	-0.3043	0.336	-0.907	0.367	-0.970	0.362	-0.970
SAT	0.0016	0.000	5.513	0.000	0.001	0.002	0.001
letters	0.1243	0.043	2.918	0.004	0.040	0.209	0.040

1)

predicted College GPA =-0.3043+0.0016*1000+0.1243*7=2.18

2)

approximate error of this prediction =0.61

3)

If this student increases his SAT score by 300 points how much higher would be his predicted College GPA

=0.0016*300=0.48

4)

changes will his College GPA be -2*0.1243 =-0.24