Question

# 1.) You are interested in predicting the final grade of students in a business course. You...

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.

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 X2 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,

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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