Math Problem Statement
a)Construct a scatter diagram for these data.
b)Calculate the correlation of coefficient (r). Interpret the results. Find the regression equation.
c)Plot a regression line on the scatter diagram of part (a).
d)Predict the final grade with 10 number of absences.
Solution
Part (c): Scatter Diagram with Regression Line
The scatter diagram now includes the regression line, which represents the best-fit line for predicting final grades based on the number of absences.
Part (d): Predicted Final Grade for 10 Absences
Using the regression equation, the predicted final grade for a student with 10 absences is approximately 66.27.
Would you like further details on any of these steps or calculations?
Here are some related questions to explore further:
- How does the value of change if a new student with no absences and a perfect grade is added?
- What are the implications of a strong negative correlation in practical scenarios?
- How would the regression line adjust if a student with a very low grade and high absences were removed?
- Can we predict with certainty a student's grade based on their number of absences alone?
- How can outliers affect the calculation of the correlation coefficient?
Tip: When interpreting correlation, remember that correlation does not imply causation; other factors might influence the results.
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Math Problem Analysis
Mathematical Concepts
Statistics
Scatter Plot
Correlation
Regression Analysis
Formulas
Correlation coefficient formula: r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)^2 * Σ(y - ȳ)^2)
Linear regression equation: y = mx + b
Theorems
Least Squares Method for Linear Regression
Suitable Grade Level
High School
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