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 .

1. The correlation coefficient between the number of shipments and delivery time is approximately **0.482**. This indicates a moderate positive correlation.

2. The linear regression model is:
   \[
   \text{Delivery Time} = 0.037 \times \text{Shipments} + 2.93
   \]
   Here, the slope is approximately **0.037** and the intercept is approximately **2.93**.

3. If the number of shipments is 30, the predicted delivery time is approximately **4.04 days**.

Would you like further details or explanations on any part of this analysis?

Here are five related questions for further exploration:
1. How does a correlation coefficient close to 1 or -1 affect predictions?
2. What are the assumptions behind using linear regression in this dataset?
3. How would an outlier impact both the correlation and regression model?
4. Can you explain the concept of residuals in a linear regression model?
5. How would you assess the accuracy of this regression model?

**Tip**: Always plot the regression line along with the data points to visually assess the model's fit.

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.

Learn how to calculate the correlation coefficient and perform linear regression for a dataset containing the number of shipments and delivery times. Understand the key statistical concepts and formulas used, such as the correlation coefficient and the linear regression equation. Suitable for Grades 10-12 students or anyone interested in learning basic statistics.

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