Business Statistics: Correlation Coefficient and Linear Regression
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I need help resolved the following problem. Thank you in advance!
NOTE: I tried uploaded the data on my excel sheet but it continuously says uploading. I have done everything and it won't let me upload the sheet.
Use the Student_Data.xls file to solve the following.
Problem 1)
Does studying really help with grades? Using a significance level of .05, test whether there is a correlation between the Hours Studying and the BS GPA. Also, answer the following:
a) What is the correlation coefficient and how strong is it?
b) What is the best fit regression equation that can predict the BS GPA from the Hours Studying?
c) What would you expect a student's BS GPA to be if he/she studies 8 hours per week?
************** DATA ************************
ID Gender Major Employ Age MBA_GPA BS GPA Hrs_Studying Works FT
1 1 No Major Unemployed 39 2.82 3.05 3 1
2 1 No Major Full Time 55 3.49 3.45 7 1
3 1 No Major Part Time 43 3.28 3.5 7 0
4 1 No Major Full Time 56 3.25 3.55 7 1
5 1 No Major Full Time 38 3.26 3.3 6 0
6 1 No Major Unemployed 54 2.87 3.05 4 1
7 1 No Major Full Time 30 3.16 3.35 6 1
8 1 No Major Full Time 37 3.4 3.35 6 0
9 1 No Major Part Time 38 2.84 3.05 3 0
10 1 No Major Full Time 42 3.72 3.7 7 1
11 1 No Major Part Time 52 3.22 3.5 7 1
12 1 No Major Full Time 35 3.44 3.55 7 1
13 1 No Major Full Time 37 3.65 3.9 8 0
14 1 No Major Full Time 53 3.02 3.3 6 0
15 1 No Major Part Time 51 3.03 3.25 6 1
16 1 No Major Full Time 40 3.8 3.8 8 1
17 1 No Major Full Time 33 3.23 3.5 7 1
18 1 No Major Part Time 53 3.26 3.5 7 1
19 1 No Major Full Time 43 3.53 3.75 8 0
20 1 No Major Unemployed 35 3.75 3.9 8 1
21 1 No Major Full Time 57 3.15 3.2 6 0
22 1 No Major Part Time 32 3.66 3.75 8 1
23 1 No Major Full Time 59 3.36 3.45 7 0
24 1 No Major Full Time 48 3.79 3.85 8 0
25 1 No Major Part Time 34 2.85 3.05 3 0
26 1 No Major Full Time 53 3.74 3.9 8 1
27 1 No Major Part Time 35 3.23 3.25 6 0
28 1 No Major Unemployed 38 3.52 3.7 7 1
29 1 No Major Part Time 37 3.32 3.45 7 1
30 1 No Major Full Time 46 2.89 3.1 4 0
31 1 No Major Full Time 44 2.83 3.05 3 1
32 1 No Major Unemployed 31 2.93 3.1 5 1
33 1 No Major Full Time 51 3.71 3.8 8 1
34 1 No Major Full Time 47 3.47 3.75 8 1
35 1 No Major Part Time 56 3.52 3.65 7 1
36 1 Finance Part Time 42 2.83 3.05 3 0
37 1 Finance Full Time 44 3.64 3.55 7 1
38 1 Finance Unemployed 54 2.96 3.1 4 0
39 1 Finance Full Time 51 3.59 3.8 8 1
40 1 Finance Part Time 42 3.33 3.55 7 1
41 1 Finance Full Time 45 3.38 3.6 7 0
42 1 Finance Full Time 55 3.44 3.35 6 1
43 1 Finance Full Time 47 3.31 3.45 7 0
44 1 Finance Unemployed 43 3.03 3.25 6 0
45 1 Finance Full Time 57 3.26 3.4 7 1
46 1 Finance Full Time 36 3.04 3.25 6 0
47 1 Finance Part Time 58 2.98 3.1 5 0
48 1 Finance Full Time 46 2.8 3.05 2 0
49 1 Finance Full Time 53 3.75 3.75 8 1
50 1 Finance Full Time 59 3.64 3.65 7 1
51 1 Finance Full Time 49 3.65 3.8 8 1
52 1 Finance Full Time 34 3.18 3.3 6 0
53 1 Finance Full Time 46 3.44 3.4 7 1
54 1 Finance Unemployed 46 3.06 3.15 6 1
55 1 Finance Full Time 33 3.51 3.75 8 0
56 1 Finance Part Time 56 3.33 3.4 7 1
57 1 Finance Full Time 39 2.81 3.05 2 0
58 1 Finance Full Time 51 3.64 3.8 8 1
59 1 Finance Part Time 55 3.05 3.4 7 0
60 1 Finance Full Time 38 2.85 3.05 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 6 1
65 1 Marketing Full Time 46 3.59 3.75 8 1
66 1 Marketing Unemployed 31 3.11 3.2 6 0
67 1 Marketing Full Time 47 3.65 3.7 8 1
68 1 Marketing Part Time 54 3.17 3.5 7 0
69 1 Marketing 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 7 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 Leadership Full Time 32 3.65 3.6 7 1
77 1 Leadership Full Time 32 3.61 3.7 8 1
78 1 Leadership 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 1
84 1 Leadership Full Time 33 3.38 3.5 7 1
85 1 Leadership Full Time 35 3.57 3.5 7 1
86 1 Leadership Full Time 31 2.97 3.1 5 0
87 1 Leadership Full Time 38 3.44 3.65 7 1
88 1 Leadership Part Time 46 3.64 3.55 7 1
89 1 Leadership Full Time 45 3.48 3.4 7 1
90 1 Leadership Full Time 59 2.99 3.1 5 1
91 1 Leadership Full Time 58 3.73 3.8 8 0
92 1 Leadership Full Time 46 2.91 3.05 4 0
93 1 Leadership Full Time 35 3.78 3.95 9 1
94 1 Leadership Part Time 53 3.4 3.4 7 0
95 1 Leadership Full Time 31 3.13 3.15 6 0
96 1 Leadership Full Time 50 3.14 3.25 6 1
97 1 Leadership Full Time 38 3.24 3.3 6 0
98 1 Leadership Full Time 50 3.56 3.5 7 1
99 1 Leadership Full Time 48 3.16 3.25 6 0
100 1 Leadership Full Time 53 3.53 3.55 7 1
101 0 No Major Unemployed 53 3.01 3.15 6 0
102 0 Leadership Full Time 30 3.3 3.35 6 1
103 0 No Major Part Time 32 3.62 3.6 7 0
104 0 Leadership Full Time 42 3.21 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 3.47 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 Leadership Full Time 42 3.83 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 3.17 3.3 6 1
116 0 No Major Full Time 47 3.41 3.6 7 1
117 0 No Major Part Time 28 3.56 3.7 8 1
118 0 No Major Unemployed 28 3.34 3.6 7 0
119 0 No Major Full Time 52 3.44 3.6 7 1
120 0 No Major Part Time 35 3.76 3.8 8 1
121 0 Finance Full Time 38 3.55 3.45 7 1
122 0 Finance Full Time 44 3.88 3.9 8 1
123 0 Finance Part Time 38 3.31 3.45 7 1
124 0 Finance Full Time 52 3.09 3.15 6 1
125 0 Finance Unemployed 53 3.82 4 9 0
126 0 Finance Part Time 53 3.01 3.2 6 1
127 0 Finance Full Time 31 3.66 3.85 8 1
128 0 Finance Part Time 47 3.64 3.7 8 1
129 0 Finance Full Time 51 3.59 3.65 7 1
130 0 Finance Unemployed 37 3.49 3.55 7 1
131 0 Finance Part Time 46 3.13 3.2 6 1
132 0 Finance Full Time 48 3.83 3.9 8 1
133 0 Finance Full Time 54 3.04 3.15 6 1
134 0 Finance Full Time 48 3.91 4 10 1
135 0 Finance Full Time 36 3.56 3.7 8 1
136 0 Finance Unemployed 39 3.96 4 9 1
137 0 Finance Full Time 28 3.46 3.4 7 1
138 0 Finance Part Time 45 3.22 3.15 6 0
139 0 Finance Full Time 31 3.27 3.2 6 0
140 0 Finance Full Time 47 3.43 3.45 7 1
141 0 Finance Part Time 35 3.85 3.95 9 1
142 0 Finance Full Time 52 3.89 3.9 8 1
143 0 Finance Part Time 52 3.37 3.45 7 1
144 0 Finance Unemployed 55 3.32 3.3 6 0
145 0 Finance Full Time 52 3.54 3.55 7 1
146 0 Finance Part Time 46 3.8 3.9 8 1
147 0 Finance Full Time 31 3.74 3.85 8 1
148 0 Finance Full Time 33 3.17 3.45 7 1
149 0 Finance Part Time 45 3.27 3.55 7 1
150 0 Finance Full Time 50 3.32 3.3 6 1
151 0 Marketing Part Time 33 3.56 3.45 7 1
152 0 Marketing Full Time 37 3.95 4 9 1
153 0 Marketing Unemployed 33 3.56 3.75 8 0
154 0 Marketing Full Time 46 3.79 3.75 8 1
155 0 Marketing Part Time 55 3.93 4 9 1
156 0 Marketing Full Time 30 3.79 3.85 8 1
157 0 Marketing Full Time 51 3.71 3.85 8 1
158 0 Marketing Part Time 35 3.05 3.35 6 1
159 0 Marketing Unemployed 40 3.22 3.2 6 1
160 0 Marketing Part Time 29 3.85 3.95 9 1
161 0 Marketing Full Time 52 3.82 3.95 9 1
162 0 Marketing Full Time 27 3.23 3.95 9 1
163 0 Marketing Full Time 51 3.56 3.65 7 1
164 0 Marketing Part Time 56 3.53 3.65 7 1
165 0 Marketing Full Time 35 3.62 4 9 1
166 0 Leadership Full Time 46 3.8 3.95 9 1
167 0 Leadership Part Time 39 3.47 3.35 6 0
168 0 Leadership Full Time 31 3.64 3.65 7 1
169 0 Leadership Full Time 52 3.03 3.15 5 1
170 0 Leadership Unemployed 32 3.17 3.25 6 1
171 0 Leadership Part Time 32 3.22 3.2 6 1
172 0 Leadership Full Time 44 3.92 4 10 1
173 0 Leadership Full Time 43 3.82 3.95 9 1
174 0 Leadership Part Time 38 3.26 3.55 7 1
175 0 Leadership Full Time 54 3.8 3.85 8 1
176 0 Leadership Full Time 27 3.2 3.2 6 0
177 0 Leadership Part Time 38 3.46 3.35 6 1
178 0 Leadership Full Time 45 3.67 3.75 8 1
179 0 Leadership Unemployed 48 3.06 3.4 7 0
180 0 Leadership Full Time 43 3.66 3.85 8 0
181 0 Leadership Full Time 34 3.96 4 10 1
182 0 Leadership Full Time 54 3.75 3.85 8 1
183 0 Leadership Full Time 36 3.83 3.85 8 1
184 0 Leadership Full Time 45 3.22 3.2 6 1
185 0 Leadership Unemployed 28 3.36 3.35 6 1
186 0 Leadership Full Time 37 3.21 3.25 6 1
187 0 Leadership Full Time 27 3.02 3.15 5 1
188 0 Leadership Full Time 31 3.99 4 10 1
189 0 Leadership Unemployed 45 3.07 3.15 6 1
190 0 Leadership Full Time 48 3.65 3.65 7 1
191 0 Leadership Full Time 50 3.67 3.85 8 1
192 0 Leadership Full Time 32 3.06 3.35 6 0
193 0 Leadership Unemployed 33 3.98 3.7 8 1
194 0 Leadership Full Time 49 3.93 4 10 1
195 0 Leadership Unemployed 27 3.41 3.3 6 0
196 0 Leadership Part Time 28 3.43 3.5 7 1
197 0 Leadership Full Time 36 3.7 3.65 7 0
198 0 Leadership Full Time 35 3.76 3.75 8 1
199 0 Leadership Part Time 47 3.9 3.9 8 0
200 0 Leadership Full Time 33 3.23 3.3 6 1
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Solution Summary
This problem focuses on simple linear regression and the steps used to arrive at the best fit equation and how to then predict the dependent variable when given an independent variable using that equation. Additionally, it covers how to calculate a correlation coefficient in order to assess how closely related - either positively or negatively - two variables are. It discusses what your results from calculating a correlation coefficient imply about the relationship of those two variables.
Solution Preview
This question is asking you to consider if the statistical tests of the data set reflects if studying actually helps students get better grades. As you've learned in class, I assume, "correlation" is how closely related two variables are. Here, those variables are "Hours Studying" and "BS GPA".
(A) A correlation coefficient, sometimes denoted as "r", is between 1 and (1) where a 1 mean a perfect positive correlation and a (1) is a perfectly negative correlation. So, when thinking about what your result is, see where it sits within -1 to 1 and that will identify if the two variables are correlated or not.
You state that you have the data set in Excel but cannot attach it; the best thing to do is use that as a starting point and you can add additional information and a few columns that you'll need to fill in.
To calculate the correlation coefficient, (1) you first have to calculate the average (mean) of both variables in question ("Hours Studying" and "BS GPA") and then calculate the difference between each person's data point for that variable and the average (mean). Average the "BS GPA" and "Hours Studying" at the bottom of the data set in the applicable columns. Let "X*" = the average/mean of "Hours Studying" and "Y*" = the ...
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