Math Problem Statement

Find the Pearson's correlation coefficient between yearly profit and yearly expenditure, and the regression coefficient of yearly profit on yearly expenditure.

Solution

The images you provided show a table of data and a set of questions:

  • Table: Contains the yearly profit and yearly expenditure of a company in crores of rupees. The profit and expenditure values are listed as:

    • Yearly Profit (crore rupees): 50, 60, 100, 150, 200, 240
    • Yearly Expenditure (crore rupees): 10, 11, 14, 15, 18, 22

  • Questions:

    1. Find the Pearson's correlation coefficient between yearly profit and yearly expenditure.
    2. Find the regression coefficient of yearly profit on yearly expenditure.

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Correlation

Formulas

Pearson's correlation coefficient formula: r = Σ(xy) - nx̄ȳ / sqrt([Σ(x^2) - nx̄^2][Σ(y^2) - nȳ^2])
Regression coefficient formula: b = Σ(xy) - nx̄ȳ / Σ(x^2) - nx̄^2

Theorems

Pearson's correlation theorem
Least squares regression theorem

Suitable Grade Level

Undergraduate (Statistics/Mathematics)

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