Question

The data set for your project is collected from 84 high school students and has two quantitative variables: SAT score and GPA score for each student.

1.For each variable, calculate the Mean, Standard Deviations, and the Five-Number-Summary.

2.Draw a box plot of each variable.

3.Create a scatter plot of the two variables and explain the type of relationship between the two variables.

4.Calculate the Correlation Coefficient of the both variables.

Project Data:

GPA	SAT
2.4	1714
2.52	1664
2.54	1760
2.74	1685
2.83	1693
2.91	1670
3	1764
3	1764
3.01	1792
3.01	1850
3.02	1735
3.07	1775
3.08	1735
3.08	1712
3.12	1773
3.17	1872
3.17	1755
3.17	1674
3.17	1842
3.19	1786
3.19	1761
3.19	1722
3.2	1663
3.21	1687
3.24	1974
3.28	1826
3.28	1787
3.28	1821
3.28	2020
3.28	1794
3.28	1769
3.28	1934
3.29	1775
3.29	1855
3.29	1880
3.31	1849
3.32	1808
3.34	1954
3.37	1777
3.37	1831
3.37	1865
3.38	1850
3.38	1966
3.39	1702
3.39	1990
3.4	1925
3.4	1824
3.4	1956
3.41	1857
3.41	1979
3.41	1802
3.42	1855
3.42	1907
3.42	1634
3.44	1879
3.47	1887
3.47	1730
3.47	1953
3.47	1781
3.48	1891
3.49	1964
3.49	1808
3.5	1893
3.51	2041
3.51	1893
3.52	1832
3.52	1850
3.54	1934
3.58	1861
3.58	1931
3.59	1933
3.59	1778
3.6	1975
3.6	1934
3.61	2021
3.62	2015
3.64	1997
3.65	2020
3.71	1843
3.71	1936
3.71	1810
3.73	1987
3.76	1962
3.81	2050

Answer 1

We can find the solution with the help of R -software.

The R commands are

(a)

(b)

(c)

From these plot , we can fit a straight line through it.So it's a good fit i.e. there is linear relation between them.

(d)