Question

This question was answered a while ago, but I feel something is still missing for some reason, so I will be adding it again for another opinion.

Thank you!

You are given the data which consists of SAT math scores and University GPA at time of graduation with a four-year degree for fifteen students. Perform a regression analysis on your collected data and submit a written report. The SAT_Math column (variable) is the independent (explanatory) variable. The SAT_Univ column (variable) is the dependent (response) variable,

                           

SAT_Math	GPA_Univ
643	3.52
558	2.91
583	2.4
685	3.47
592	3.47
562	2.37
573	2.4
559	2.24
552	3.02
617	3.32
684	3.59
568	2.54
604	3.19
619	3.71
642	3.58

Your report should include the computer printout of your statistical analysis as well as a word-processed summary of your findings and conclusions. Your report should be one single file into which the software input and output are pasted. The data that you collect should be included in your report. Make sure that the following questions/items are included in your report:

             

1. Plot a scatterplot.
2. Discuss the direction of the association between the variables, the form of the relationship, and the strength of the relationship
3. Does the scatterplot show any outliers?
4. Perform a correlation analysis and discuss, i.e., find the correlation coefficient (provided by the software) and interpret it.
5. Perform a regression analysis making sure your project contains a plot of the regression line, and regression equation. Discuss these two items.
6. Use your ofund regression equation to predict the GPA_univ for a student with SAT_Math of 600.
7. What is the value (given by the software) of R-squared? What does it mean (its interpretation)?
8. Conclusion-- A summative paragraph. What are the interpretations? What are your conclusions? Are they expected or surprising? What were the difficulties encountered in carrying out this project and how were they handled?

Your project should have a front page (title and other informative items) and an abstract. Use a font size of 12, double spacing, and NEW YORK TIMES font.

                           

Answer 1

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.7558
R Square	0.5712
Adjusted R Square	0.5382
Standard Error	0.3595
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.2382	2.2382	17.3175	0.0011
Residual	13	1.6802	0.1292
Total	14	3.9184
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.3647	1.3041	-1.8132	0.0929	-5.1821	0.4528
SAT_Math	0.0090	0.0022	4.1614	0.0011	0.0043	0.0136

scatter-plot

r = 0.7558 , since r > 0 positive relationship .

strength - strong

p-value = 0.0011

since p-value < alpha

hence the model is significant

GPA^= -2.3647 + 0.0090 SAT_Math

= -2.3647 + 0.0090 *600 = 3.0353

R^2 = 0.5712

this means 57.12 % of variation in GPA_university is explained by this model