Math Problem Statement
A company is using a system of payment by results. The union claims that this seriously discriminates against the workers. there is a fairly steep learning curve which workers follow with the apparent outcome that more experienced workers can perform the task in about half of the time taken by the new employee. You have been asked to find out if there is any basis for this claim. To do this, you have observed ten workers on the shop floor, timing how long it takes them to produce an item. It was then possible for you to match these times with the length of worker’s experience. The results obtained are shown below:- Month’s experience 2 5 3 8 5 9 12 16 1 6 Time taken 27 26 30 20 22 20 16 15 30 19 Required: (a) Find the regression line of time taken on month’s experience (b) Compute the coefficient of correlation and coefficient of determination and interpret
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Correlation
Statistics
Formulas
y = a + bx
b = (Σxy - n * x̄ * ȳ) / (Σx² - n * x̄²)
a = ȳ - b * x̄
r = (Σxy - n * x̄ * ȳ) / √[(Σx² - n * x̄²) * (Σy² - n * ȳ²)]
Theorems
Least Squares Method
Correlation and Regression Theorem
Suitable Grade Level
Grades 11-12
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