A lecturer was interested in the relationship between a student’s exam score (marks), the number of classes they attended in a trimester and the average number of hours of paid work, per week, the student did in the trimester.  A random sample of students were selected, and data collected. EXCEL was used to create a multiple linear regression, with a portion of the output provided here:
Multiple R  = 0.76
R square = 0.5776
Observations =36
Intercept Coefficients=10.11

Intercept Standard Error=1.06
Attendance Coefficients=4.24
Attendance Standard Error = 	0.98
Hours of paid work Coefficients = -0.02
Hours of paid work Standard Error =  5.19


 What is the estimated exam mark for a student who attended 7 classes in the trimester and did an average of 8 hours of paid work per week?  Please give your answer correct to two decimal places and do NOT include units in your answer.






The estimated exam mark can be found using the formula for a multiple linear regression model:

\[
\text{Estimated Exam Mark} = \text{Intercept} + (\text{Attendance Coefficient} \times \text{Number of Classes}) + (\text{Hours of Paid Work Coefficient} \times \text{Hours of Paid Work})
\]

From the given dataThe estimated exam mark can be found using the formula for a multiple linear regression model:

\[
\text{Estimated Exam Mark} = \text{Intercept} + (\text{Attendance Coefficient} \times \text{Number of Classes}) + (\text{Hours of Paid Work Coefficient} \times \text{Hours of Paid Work})
\]

From the given 

- Intercept = 10.11
- Attendance Coefficient = 4.24
- Hours of Paid Work Coefficient = -0.02
- Number of Classes = 7
- Hours of Paid Work = 8

Substituting these values into the formula:

\[
\text{Estimated Exam Mark} = 10.11 + (4.24 \times 7) + (-0.02 \times 8)
\]

Now let's compute this.

\[
\text{Estimated Exam Mark} = 10.11 + 29.68 - 0.16 = 39.63
\]

The estimated exam mark is **39.63**.

Do you want more details or have any questions?

Here are 5 related questions to expand on this:

1. What does the Multiple R value indicate in this regression output?
2. How does the R square value relate to the accuracy of the model?
3. What role do standard errors play in regression analysis?
4. What does a negative coefficient, such as for hours of paid work, imply in this context?
5. How would the estimated exam score change if the student attended more classes but worked the same number of hours?

**Tip:** In regression analysis, coefficients represent the change in the dependent variable for a one-unit change in the independent variable, holding all else constant.

A lecturer was interested in the relationship between a student’s exam score (marks), the number of classes they attended in a trimester and the average number of hours of paid work, per week, the student did in the trimester. A random sample of students were selected, and data collected. EXCEL was used to create a multiple linear regression, with a portion of the output provided here: Multiple R  = 0.76, R square = 0.5776, Observations =36, Intercept Coefficients=10.11, Intercept Standard Error=1.06, Attendance Coefficients=4.24, Attendance Standard Error = 0.98, Hours of paid work Coefficients = -0.02, Hours of paid work Standard Error = 5.19. What is the estimated exam mark for a student who attended 7 classes in the trimester and did an average of 8 hours of paid work per week? Please give your answer correct to two decimal places and do NOT include units in your answer.

Calculate the estimated exam mark for a student using multiple linear regression. This problem involves the analysis of class attendance, hours of paid work, and their impact on exam scores. Learn how to apply linear regression formulas for precise calculations. Suitable for students in Grades 10-12.

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