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.

a) Construct a scatter diagram for these data. b) Calculate the correlation 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:

  1. How does the value of rr change if a new student with no absences and a perfect grade is added?
  2. What are the implications of a strong negative correlation in practical scenarios?
  3. How would the regression line adjust if a student with a very low grade and high absences were removed?
  4. Can we predict with certainty a student's grade based on their number of absences alone?
  5. 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