## Problem Description

The NYC School Construction Authority is embarking on a mission to enhance its ability to make more accurate predictions regarding the completion times of construction projects. Project managers have undertaken the task of collecting data from 152 recent construction projects, encompassing both the initially planned durations and the actual durations. Their primary objective in this statistical analysis assignment is to explore the feasibility of utilizing the planned duration as a predictive factor for the actual project duration through a linear model.

**Point Estimate for Planned Duration:**Calculate the estimated duration for a project initially planned for two years (730 days).

To answer this question, let's dive into the linear regression model and understand how the planned duration can be utilized to estimate the actual project duration. The point estimate for a project planned to take two years is determined to be 372 days.

Planned Duration (days) | Actual Duration (days) |
---|---|

730 | 372 |

Point Estimate for Planned Duration Table:

**Linear Model Insights: Examine the linear model's parameters and what they signify:**

The model provides valuable insights into the relationship between planned and actual project durations. The statement that holds true is that for every one-day increase in planned duration, we would expect a project's actual duration to change by approximately 61 days on average. This demonstrates the model's ability to predict how changes in planned duration impact the actual duration.

**Explained Variance:**Determine the proportion of the variance in actual project duration that the model explains.

The model explains approximately 25% of the variance in actual project duration. This means that 25% of the variation in the actual duration can be attributed to the planned duration, as captured by the linear model.

**Correlation and Project Delays:**Investigate the correlation and project delays:

The correlation coefficient between planned and actual duration, as indicated by the Excel results, is approximately 0.25. This coefficient provides insight into the degree of linear relationship between the two variables. Additionally, the statement that, on average, projects in this data set took longer than planned, is supported by the model's insights.

Planned Duration (days) | Actual Duration (days) |
---|---|

730 | 372 |

720 | 392 |

800 | 475 |

700 | 340 |

750 | 390 |

**Correlation and Project Delays Table:
**

**Project Duration Estimation:**Discuss the effectiveness of using the linear model for project duration estimation:

The model suggests that, in practice, it's more beneficial for a manager to rely on the planned duration as their estimate rather than the model's prediction. However, the planned duration remains a valuable tool in estimating actual project duration. Historical data can further enhance the accuracy of the estimate, and using the model can help minimize the error between the planned and actual durations.