Question

In: Statistics and Probability

Does undergraduate success predict graduate success? While most people complete their bachelor's degree during the daytime...

Does undergraduate success predict graduate success? While most people complete their bachelor's degree during the daytime while taking multiple classes and not working full-time, those getting an MBA are typically taking one or two courses at a time, in the evening or on weekends, and while working and even supporting a family. Yet one would expect those who perform better in their bachelor's degree will perform better in their master's. Using a significance level of .05, test whether there is a correlation between the BS GPA and the MBA GPA. Also, answer the following:

a) What is the correlation coefficient & how strong is it?
b) What is the best fit regression equation that can predict the MBA GPA from the BS GPA?
c) What percent of the variability in the MBA GPA can be explained by the regression model?
d) What would you expect a student's MBA GPA to be if he/she had a 3.50 BS GPA?

Data File

ID Gender Major Employ Age MBA_GPA BS GPA Hrs_Studying Works FT
1 0 No Major Unemployed 39 2.82 3 10 0
2 1 No Major Full Time 55 4 4 15 0
3 0 No Major Part Time 43 3.45 3.5 3 0
4 0 No Major Full Time 56 2.61 4 4 0
5 1 No Major Full Time 38 3.5 3.3 5 0
6 0 No Major Unemployed 54 4 3.05 5 1
7 0 No Major Full Time 30 3 4 6 0
8 0 No Major Full Time 37 2.5 3.6 6 0
9 0 No Major Part Time 38 2.84 3.05 6 0
10 0 No Major Full Time 42 3.72 3.7 6 0
11 0 No Major Part Time 52 3.21 3.5 6 0
12 0 No Major Full Time 35 3.44 3.55 6 0
13 0 No Major Full Time 37 3.65 2.78 6 0
14 0 No Major Full Time 53 3.02 3.3 6 0
15 0 No Major Part Time 51 3.03 3.25 6 0
16 1 No Major Full Time 40 3.8 4 6 0
17 0 Finance Full Time 33 4 3.5 6 1
18 0 No Major Part Time 53 3.26 3.5 7 0
19 0 No Major Full Time 43 3.53 3.75 6 0
20 0 Finance Unemployed 35 3.75 3.9 7 0
21 0 No Major Full Time 57 3.15 3.2 6 0
22 1 No Major Part Time 32 3.66 3.75 8 0
23 1 No Major Full Time 59 3.36 3.45 8 0
24 1 No Major Full Time 48 3.79 2.55 8 0
25 1 No Major Part Time 34 2.85 3.05 8 0
26 1 No Major Full Time 53 3.74 3.9 8 0
27 1 No Major Part Time 35 3.23 4 2 0
28 1 No Major Unemployed 38 3.52 3.7 2 0
29 1 No Major Part Time 37 3.32 3.45 2 0
30 0 Finance Full Time 46 2.89 3.1 2 0
31 0 No Major Full Time 44 2.83 3.05 1 0
32 0 No Major Unemployed 31 2.93 3.1 1 0
33 0 No Major Full Time 51 3.71 3.8 1 0
34 0 Finance Full Time 47 3.47 2.6 4 0
35 0 No Major Part Time 56 3.52 3.8 4 0
36 1 Finance Part Time 42 2.83 4 4 0
37 0 Finance Full Time 44 3.64 3.55 6 1
38 0 No Major Unemployed 54 2.96 3.1 6 0
39 0 Finance Full Time 51 3.59 3.9 6 1
40 0 No Major Part Time 42 3.33 3.9 6 1
41 0 Finance Full Time 45 3.38 3.6 6 0
42 0 Finance Full Time 55 3.44 3.35 6 1
43 0 No Major Full Time 47 3.31 3.9 7 0
44 1 Finance Unemployed 43 3.03 3.25 7 0
45 0 Finance Full Time 57 3.26 3.4 7 1
46 1 Finance Full Time 36 3.04 4 7 0
47 1 No Major Part Time 58 2.98 3.1 7 0
48 1 Finance Full Time 46 2.8 3.05 7 0
49 1 Finance Full Time 53 3.75 3.75 3 1
50 0 Finance Full Time 59 3.64 3.65 3 1
51 0 No Major Full Time 49 3.65 3.8 3 1
52 0 Finance Full Time 34 3.18 3.3 3 0
53 0 No Major Full Time 46 3.44 4 3 1
54 1 Finance Unemployed 46 3.06 3.15 3 1
55 1 Finance Full Time 33 3.51 3.75 10 0
56 1 Marketing Part Time 56 3.33 3.4 2 1
57 1 Marketing Full Time 39 2.81 3.05 2 0
58 1 Marketing Full Time 51 3.64 3.8 8 1
59 1 Leadership Part Time 55 3.05 3.4 7 0
60 1 Leadership Full Time 38 2.85 3.25 3 1
61 1 Marketing Full Time 33 3.56 3.6 7 1
62 1 Marketing Full Time 34 2.92 3.1 5 0
63 1 Marketing Full Time 31 3.35 3.5 7 1
64 1 Marketing Full Time 37 3.46 3.35 10 1
65 1 Marketing Full Time 46 3.59 3.75 8 1
66 1 No Major Unemployed 31 3.11 3.2 6 0
67 1 No Major Full Time 47 3.65 3.7 8 1
68 1 No Major Part Time 54 3.17 3.5 7 0
69 1 No Major Full Time 52 2.97 3.1 5 1
70 1 Marketing Part Time 43 3.77 3.9 8 1
71 1 Leadership Full Time 44 3.21 3.2 6 1
72 1 Leadership Part Time 34 3.17 3.15 6 0
73 1 Leadership Full Time 59 3.65 3.65 10 0
74 1 Leadership Full Time 45 2.94 3.1 5 0
75 1 Leadership Full Time 30 3.53 3.7 8 1
76 1 No Major Full Time 32 3.65 3.6 7 1
77 1 Leadership Full Time 32 3.61 3.7 8 1
78 1 No Major Full Time 40 3.7 3.9 8 1
79 1 Leadership Full Time 48 2.91 3.1 5 1
80 1 Leadership Unemployed 51 3.09 3.25 6 0
81 1 Leadership Full Time 30 3.77 3.95 9 1
82 1 Leadership Full Time 31 3.79 3.8 8 1
83 1 Leadership Full Time 35 3.59 3.6 7 )
84 1 Leadership Full Time 33 3.38 3.5 8 1
85 1 No Major Full Time 35 4 3.5 8 1
86 1 Marketing Full Time 31 2.97 3.1 8 0
87 1 Marketing Full Time 38 3.44 3.65 8 1
88 1 No Major Part Time 46 3.64 3.55 8 1
89 1 Finance Full Time 45 3.48 3.4 8 1
90 1 Finance Full Time 59 2.76 3.1 8 1
91 1 Finance Full Time 58 3.73 3.8 8 1
92 1 Finance Full Time 46 2.91 3.05 8 1
93 1 Finance Full Time 35 3.78 3.95 9 1
94 1 Finance Part Time 53 3.5 3.4 7 1
95 1 Finance Full Time 31 3.13 3.15 6 1
96 1 Finance Full Time 50 3.14 3.25 6 1
97 1 Finance Full Time 38 3.24 3.3 6 1
98 1 Finance Full Time 50 3.56 3.5 7 1
99 1 Finance Full Time 48 3.16 3.25 6 1
100 1 Finance Full Time 53 3.53 3.55 7 1
101 0 No Major Unemployed 53 3.7 3.15 6 0
102 0 Marketing Full Time 30 3.3 3.35 6 1
103 0 Marketing Part Time 32 4 3.6 7 0
104 0 Leadership Full Time 42 3.5 3.4 7 0
105 0 Leadership Full Time 56 3.39 3.4 7 1
106 0 No Major Full Time 46 3.65 3.8 8 1
107 0 Leadership Full Time 49 2.78 3.7 8 1
108 0 No Major Part Time 32 3.44 3.6 7 0
109 0 No Major Full Time 36 3.88 3.95 9 1
110 0 No Major Full Time 42 2.84 3.95 9 1
111 0 No Major Part Time 37 3.53 3.6 7 1
112 0 No Major Full Time 31 3.22 3.3 6 0
113 0 No Major Full Time 31 3.56 3.8 8 1
114 0 No Major Unemployed 42 3.2 3.25 6 1
115 0 No Major Full Time 39 3.56 3.3 6 1
116 0 No Major Full Time 47 3.41 3.6 7 1
117 0 Leadership Part Time 28 3.56 3.7 8 1
118 0 Leadership Unemployed 28 3.34 3.6 7 0
119 0 Leadership Full Time 52 2.56 3.6 7 1
120 0 Leadership Part Time 35 3.76 3.8 8 1
121 1 Finance Full Time 38 3.55 3.45 7 1
122 1 No Major Full Time 44 3.88 3.9 8 1
123 1 No Major Part Time 38 3.31 3.45 7 1
124 1 Finance Full Time 52 3.09 3.15 6 1
125 1 Finance Unemployed 53 3.82 4 9 0
126 1 Finance Part Time 53 3.01 3.2 6 1
127 1 Finance Full Time 31 3.66 3.85 8 1
128 1 Finance Part Time 47 3.64 3.7 8 1
129 1 Finance Full Time 51 3.59 3.65 7 1
130 1 Finance Unemployed 37 3.49 3.55 7 1
131 1 Finance Part Time 46 3.13 3.2 6 1
132 1 Finance Full Time 48 3.83 3.9 8 1
133 1 Leadership Full Time 54 3.04 3.15 6 1
134 1 Leadership Full Time 48 3.91 4 10 1
135 1 Leadership Full Time 36 3.56 3.7 8 1
136 1 Finance Unemployed 39 3.96 4 9 1
137 1 Finance Full Time 28 3.46 3.4 7 1
138 1 Finance Part Time 45 3.22 3.15 6 0
139 1 Finance Full Time 31 3.27 3.2 6 0
140 1 Finance Full Time 47 3.43 3.45 7 1
141 1 Finance Part Time 35 3.85 3.95 9 1
142 1 Finance Full Time 52 3.89 3.9 8 1
143 0 Finance Part Time 52 3.37 3.45 7 1
144 1 Finance Unemployed 55 3.32 3.3 6 0
145 1 Finance Full Time 52 3.54 3.55 7 1
146 1 Finance Part Time 46 3.8 3.9 8 1
147 1 Leadership Full Time 31 3.74 3.85 8 1
148 1 Leadership Unemployed 33 3.6 3.45 7 1
149 1 Leadership Part Time 45 2.6 3.55 7 1
150 1 Leadership Unemployed 50 3.8 3.3 6 1
151 1 No Major Part Time 33 2.67 3.45 7 1
152 1 No Major Full Time 37 3.95 4 9 1
153 1 No Major Unemployed 33 3.56 3.75 8 0
154 1 Marketing Full Time 46 3.79 3.75 8 1
155 1 Marketing Unemployed 55 3.93 4 9 1
156 1 Marketing Full Time 30 3.79 3.85 8 1
157 1 Marketing Full Time 51 3.71 3.85 8 1
158 1 Marketing Unemployed 35 3.05 3.35 6 1
159 1 Marketing Unemployed 40 3.22 3.2 6 1
160 0 Marketing Part Time 29 3.85 3.95 9 1
161 1 Marketing Full Time 52 3.82 3.95 9 1
162 1 Marketing Unemployed 27 3.23 3.95 9 1
163 1 Marketing Full Time 51 3.56 3.65 7 1
164 0 Marketing Part Time 56 3.53 3.65 7 1
165 1 Marketing Unemployed 35 3.62 4 9 1
166 1 Leadership Full Time 46 3.8 3.95 9 1
167 1 Leadership Part Time 39 3.47 3.35 6 0
168 1 Leadership Full Time 31 3.64 3.65 7 1
169 1 Leadership Part Time 52 3.03 3.15 5 1
170 1 Leadership Unemployed 35 3.17 3.25 6 1
171 1 Leadership Full Time 32 3.22 3.2 6 1
172 0 Leadership Part Time 44 3.92 4 10 1
173 1 Leadership Unemployed 43 3.82 3.95 9 1
174 1 Leadership Part Time 38 3.26 3.55 7 1
175 1 Leadership Full Time 54 3.8 3.85 8 1
176 1 Leadership Full Time 30 3.2 3.2 6 0
177 0 Leadership Part Time 38 3.46 3.35 6 1
178 1 Leadership Full Time 45 3.67 3.75 8 1
179 1 Leadership Unemployed 48 4 3.4 7 0
180 1 Leadership Full Time 43 3.66 3.85 8 0
181 0 Leadership Full Time 34 3.96 4 10 1
182 1 Leadership Full Time 54 3.75 3.85 8 1
183 1 Leadership Full Time 36 3.83 3.85 8 1
184 1 Leadership Full Time 45 3.55 3.2 6 1
185 0 Leadership Unemployed 55 3.36 3.35 6 1
186 1 Leadership Part Time 45 3.21 3.25 6 1
187 1 Leadership Part Time 34 2.97 3.15 5 1
188 0 Leadership Part Time 54 3.99 4 10 1
189 1 Leadership Full Time 36 3.07 3.15 6 1
190 1 Leadership Full Time 24 3.65 3.65 7 1
191 1 Leadership Full Time 34 3.67 3.85 8 1
192 1 Leadership Full Time 45 3.06 3.35 6 0
193 1 Leadership Unemployed 33 3.98 3.7 8 1
194 1 Leadership Full Time 22 3.93 4 10 1
195 1 Leadership Unemployed 27 3.41 3.3 6 0
196 1 Leadership Unemployed 33 3.43 3.5 7 1
197 1 Leadership Unemployed 36 3.7 3.65 7 0
198 1 Leadership Unemployed 34 3.76 3.75 8 1
199 1 Leadership Unemployed 55 3.9 3.9 8 0
200 1 Leadership Full Time 33 3.23 3.3 6 1

Solutions

Expert Solution

I have used R software:

Correlation test:

Let be the population correlation coefficient and r be the sample correlation coefficient.

n be the sample size.

Here our null hypothesis

which means no correlation between variables

the alternative hypothesis

Which means variables are correlated.

The test statistic

R syntax and output for the test

the crittical value is

As,

we woul reject null hypothesis and conclude that there exists correlations between BS GPA and the MBA GPA at 0.05 level of significance.

a)

We can see there is positive correlation between the variables . By positive correlation we mean if the value of one variable increases the value of the other also increases and vice versa.

and as the correlation is greater than 0.5 we can say there exists a moderate positive correlation.

b)

Regression Equation

MBA_GPA = 1.26815 + 0.61012 BS GPA

c)

from the R output in (b) we have

Multiple R-squared: 0.3052, Adjusted R-squared: 0.3017

The percent of the variability in the MBA GPA can be explained by the regression model is 30.17%.

d)

a student's MBA GPA is to be 3.403566   if he/she had a 3.50 BS GPA

PLEASE UPVOTE IF YOU LIKE MY ANSWER.

THANK YOU.


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