Math Problem Statement
The provided dataset consists of seven observations, each containing information on the number of shipments and the corresponding delivery time in days. Number of ShipmentsDelivery Time (days) 55 4 60 5 40 5 70 6 55 6 45 4 65 5 1.Calculate the correlation coefficient between the number of shipments and delivery time. 2.Perform a simple linear regression to model the relationship between the independent variable (number of shipments) and the dependent variable (delivery time). 3.Predict delivery time if the number of shipments is 30 .
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Linear Regression
Correlation
Formulas
Correlation coefficient formula: r = (nΣXY - ΣXΣY) / √[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)]
Simple linear regression equation: Ŷ = β₀ + β₁X
Slope formula: β₁ = (nΣXY - ΣXΣY) / (nΣX² - (ΣX)²)
Intercept formula: β₀ = (ΣY - β₁ΣX) / n
Theorems
Least squares method for linear regression
Pearson's correlation coefficient
Suitable Grade Level
College/Advanced High School (Grades 11-12)
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