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00:00:00 – 00:09:47
The video focuses on implementing logistic regression using Excel, specifically to predict admission status based on a common entrance test (CET) score. The presenter guides viewers on how to prepare and analyze data by ensuring the Data Analysis Toolpak is installed, selecting the appropriate regression tools, and extracting regression coefficients (β₀ and β₁). Following this, the linear regression equation ( y = beta_0 + beta_1 times x ) is derived and applied across the dataset to compute probabilities using the logistic regression formula ( p = frac{e^y}{1 + e^y} ). The speaker explains the concept of maximum likelihood estimation, converting probabilities to log likelihoods and adjusting the coefficients to maximize the sum of log likelihoods using Excel's 'solver' tool. The final coefficients achieved, (beta_0 = -65.48) and (beta_1 = 0.183), correlate closely with results from a Python tutorial, demonstrating the consistency and effectiveness of the process. The video concludes with the speaker summarizing the key steps and expressing gratitude, ensuring viewers understand logistic regression implementation in Excel.
00:00:00
In this part of the video, the focus is on implementing logistic regression in Excel. The presenter explains the goal of determining the regression coefficients (β₀ and β₁). The data set used includes a common entrance test (CET) score as the predictor variable and an admission status as the response variable. The key task is to predict admission (1 for admitted, 0 for not admitted) based on the CET score.
The steps demonstrated include:
1. Ensuring the Data Analysis Toolpak is added in Excel.
2. Selecting the ‘Regression’ tool under the Data Analysis tab.
3. Specifying the Y range (response variable) and X range (predictor variable) for the regression analysis.
4. Copying the outputted regression coefficients to use as β₀ and β₁ for linear regression.
The segment concludes with the extracted coefficients being prepared for further steps in the logistic regression process.
00:03:00
In this segment of the video, the speaker explains how to derive the equation for linear regression, represented as ( y = beta_0 + beta_1 times x ). They identify specific values for (beta_0) and (beta_1) and use a particular score, ( x ), as input. The speaker demonstrates how to apply this formula across all data points, ensuring to anchor certain cell references in the spreadsheet so they do not change. After computing the linear regression values, the speaker moves on to calculating the probability using the logistic regression formula ( p = frac{e^y}{1 + e^y} ), which they apply to the dataset. Finally, they outline the process of finding the likelihood based on whether there is a 1 in the admitted column, equating the likelihood to the calculated probability.
00:06:00
In this segment of the video, the speaker continues discussing the concept of maximum likelihood by explaining how to derive the likelihood column using probabilities and how to ensure its product is maximized. To simplify, they convert these probabilities into a log likelihood. The goal is to adjust the coefficients, beta naught and beta one, so that the sum of the log likelihoods across the dataset is maximized. They proceed to calculate the sum of log likelihoods for the first 126 values, representing 80% of the dataset used for training. They then employ the ‘solver’ tool in the data tab to adjust the coefficients, ensuring the log likelihood sum is maximized. Initially, the sum is -30.9, but after using the solver, it improves to -6.
00:09:00
In this part of the video, the speaker highlights that the coefficients (beta_0) and (beta_1) obtained for the logistic regression model are (-65.48) and (0.183), respectively. These values were tuned to achieve the maximum value of the sum of the log likelihood. The speaker notes that these coefficients closely match the output obtained from a Python tutorial. The segment concludes with the speaker expressing gratitude and hopes that viewers have understood the process of implementing logistic regression and deriving the coefficients.