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.
orchestra answered 2 years agoRelated Solutions
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