Math Problem Statement

Problem sheet 5 (Business statistics).pdf

134.46 KB

Solution

The document contains multiple exercises focused on statistical analysis and regression. Here’s a breakdown of the problems included:

1. Exercise 1 (12-7):

  • Comparison of language skills between single children, twins, and triplets.
  • Tasks:
    • Perform ANOVA to check for significant differences.
    • Compute effect size (η2\eta^2).

2. Exercise 2 (12-9):

  • Comparing the effectiveness of three therapy techniques for phobias.
  • Tasks:
    • Conduct ANOVA for differences among therapies.

3. Exercise 3 (12-13):

  • Complete missing ANOVA table values for an experiment with four treatment conditions.

4. Exercise 4 (12-21):

  • Sociability scores comparison across three body types.
  • Task:
    • Conduct ANOVA to find significant differences.

5. Exercise 5 (17-1):

  • Graphing two linear equations and analyzing slope coefficients.

6. Exercise 6 (17-3):

  • Correlation and regression for a dataset with n=20n = 20 pairs.
  • Tasks:
    • Compute Pearson correlation.
    • Find regression equation.

7. Exercise 7 (17-4):

  • Regression predictions using y~=2x7ỹ = 2x - 7.

8. Exercise 8 (17-7):

  • Linear regression for a small dataset.
  • Tasks:
    • Find regression equation.
    • Compute predictions and residuals.

9. Exercise 9 (17-8):

  • Multiple regression tasks for a dataset:
    • Find regression equation.
    • Calculate predicted values.
    • Compute SSres and Pearson correlation.

10. Exercise 10 (17-10):

  • Regression equation determination for given data.

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Math Problem Analysis

Mathematical Concepts

Statistical Analysis
ANOVA
Effect Size (η²)
Regression
Correlation
Multiple Regression
Linear Equations

Formulas

ANOVA F-test
Effect Size (η²)
Pearson Correlation
Regression Equation: ŷ = mx + b
Multiple Regression Equation

Theorems

Analysis of Variance (ANOVA)
Regression Theorem
Pearson Correlation Coefficient Theorem

Suitable Grade Level

Grades 11-12 / University Level