1.) You are interested in predicting the final grade of students in a business course. You collect data on the number of hours studied and final grade for 8 students. Using the data provided below, find the predicted linear regression equation. Do this long hand on notebook paper. You must show all of your calculations. Take calculations out to the 4th decimal place. Do not round up or round down.
Your answers must clearly show your answers for bo, b1, and the predicted linear regression equation.
Data Definitions:
Student - student identifying number
Hours of study - number of hours studied
Final Grade - based on 0-100 scale
Student |
Hours Studying |
Final Grade |
1 |
42 |
92 |
2 |
58 |
95 |
3 |
32 |
81 |
4 |
39 |
78 |
5 |
37 |
75 |
6 |
51 |
88 |
7 |
49 |
85 |
8 |
45 |
85 |
2.) Using the predicted linear regression equation from #1, find the predicted final grade for a student who studied 40 hours.
4.) Refer back to Question #1, what is another explanatory variable that you could use to predict final grade? Why did you chose this variable? In other words, justify your decision.
(1)
From the given data, the following Table is calculated:
X | Y | XY | X^{2} |
42 | 92 | 3864 | 1764 |
58 | 95 | 5510 | 3364 |
32 | 81 | 2592 | 1024 |
39 | 78 | 3042 | 1521 |
37 | 75 | 2775 | 1369 |
51 | 88 | 4488 | 2601 |
49 | 85 | 4165 | 2401 |
45 | 85 | 3825 | 2025 |
Total = 353 | 679 | 30261 | 16069 |
b0 = 58.006
b1 = 0.609
the predicted linear regression equation.
y = 58.006 + 0.609 x
(2)
For x =40:
y = 58.006 + ( 0.609 X 40)
= 82.366
So,
Answer is:
82.366
(3)
Another explanatory variable that you could use to predict final grade : Student's attentiveness and punctuality in the class.
But, we prefer to consider Hours studying because Hours studying being quantitative is easy to collect data and input in the model directly.
Student's attentiveness and punctuality in the class.being qualitative is difficult to collect data. The same is to be converted to numerical figures and then only the model is applicable.
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