Question

Using SPSS to solve the following questions

Reading-18,30,22,28,16,21,17,29,27,28,28,27,22,20,22,21,16,20,19,24,19,26,20,17,23,19,19,26,21,26,26,19,22,19,18,29,29,20,17,20,20,26,25,24,19,20,22,32,24,25,22,21,24,26,27,18,19,23,19,19,24,27,26,19,24,18,17,21,32,26,25,26,23,24,24,24,22,20,21,22,23,22,30,18,21,18,25,26,20,19,26,25,19,23,17,18,19,17,23,27

Math-21,34,20,24,19,19,21,30,28,30,30,25,18,19,23,18,17,23,20,26,24,21,19,18,22,20,16,25,23,25,29,16,18,18,17,27,33,23,18,18,19,28,24,26,17,24,23,28,27,29,17,22,22,27,32,16,20,20,23,18,25,27,33,19,23,19,21,17,25,26,28,25,31,24,27,26,17,21,18,19,17,16,25,19,19,21,21,32,21,18,33,26,23,24,21,17,22,23,25,24

GPA- 2.44,3.12,2.57,2.88,2.36,2.77,2.89,3.12,3.55,3.64,3.76,2.83,2.15,2.58,2.75,2.34,2.25,2.79,2.55,2.99,2.65,2.76,2.45,2.57,2.88,
2.44,2.45,2.88,2.56,3.12,3.44,2.33,2.68,2.63,2.29,3.76,3.76,2.45,2.57,2.28,2.30,3.66,3.22,2.89,2.44,2.35,2.54,3.47,3.00,3.03,
2.41,2.79,2.77,3.34,3.65,2.13,2.66,2.27,2.78,2.59,3.22,3.45,3.76,2.44,2.50,2.50,2.54,2.32,2.88,3.17,3.16,3.26,3.67,3.22,3.40,
3.11,2.22,2.65,2.44,2.47,2.12,2.18,2.84,2.75,2.54,2.65,2.78,3.64,2.89,2.56,3.54,3.02,2.56,3.33,2.99,2.88,3.10,2.98,3.40,3.75

1. Calculate all correlations for the following variables: Reading, Math, and GPA (there are 6 total). Identify and provide the correlations for each.

2. Which correlations are significant for a = 0.01? (Looking at the resulting sig value in ANOVA Table in SPSS, is the regression model significant)

3. Which correlations are positive?

4. Which correlations are “very high” (very strong) or “high” (strong)?

B. You are running a special program for students that perform above average academically. You are hoping to limit participation to students that have obtained a grade point average of at least 3.0 in your institution after 30 completed credits. A transfer student from another school would like to enroll in the program. However, without a GPA from your institution and knowing that GPAs between institutions may not be comparable, you must make an admission decision.

You noticed that the new student did take a standardized Math test and that you have GPA data at your institution paired with corresponding student Math scores. These data are contained in the file homework-2-data.sav under the headings GPA and Math. You would like to estimate GPA for a given Math score.

1. Produce a scatterplot of the data.

2. What is the resultant regression equation?

3. At the 0.01 level of significance, is the model statistically significant? That is, looking at the sig-value (i.e., significance) in the resulting ANOVA table, is the model “good” statistically?

4. For a Math score equal to 25, what GPA would you estimate?

5. Do you feel this student should be admitted to this special program? Explain your reasoning.

Answer 1

By using SPSS,Linear Regression

model summary
model	R	R^1	R^2	adjusted R^2	RMSE	R^2 Change	F change	df1	df2
	0.850	0.722	0.716	0.240	0.722		12701	2	98

p<0.01

ANOVA

MODEL	SUM OFsqares	df	mean square	F	P
1Regression	14.697	2	7.349	127.1	<0.01
Residual	5.668	98	0.058
Total	20.365	100

coefficients

model	unstandardized	standard error	standardized	t	p	0.5%	99.5%
1(intercept)	0.874	0.149		5.876	<0.01	0.483	1.265
reading	0.007	.008	0062	0.899	0.371	-0.014	.029
math	0.080	0.007	0.809	11.789	<0.01	0.062	0.097

B2]MODEL GPA=0.874+0.007*(Reading)+0.08*(math)

B3] Fron the ANOVA at 1% LOS,P value<.001,which conclude our model is statistically good

B4] At math score=25,model is

GPA=0.874+0.007*(READING)+0.08*(25)

=0.874+0.007*(READING)2

B5] Student should be admitted for this specialprogram because model is statistically good.