\begin{tabular}{l} The famous iris dataset (the first sheet of the spreadsheet linked above) was first published in 1936 by Ron \\ Fisher. The dataset contains 50 samples from each of 3 iris species: setosa, virginia, and versicolor. Four fea \\ are measured, all in cm: sepal length, sepal width, petal length, and petal width. \\ What is the equation for the least square regression line where the independent or predictor variable is petal \\ and the dependent or response variable is petal width for iris virginica? \\ \( \hat{y}= \) Ex: \( 1.234 \quad x+\square \) Round to three decimal places. \\ What is the predicted petal width for iris virginica for a flower with a petal length of 3.26 ? \\ Round to three decimal places. \\ \hline 1\end{tabular}

To determine the least squares regression line for **petal length** (independent variable \( x \)) versus **petal width** (dependent variable \( y \)) for the **Iris virginica** species, we typically perform a linear regression analysis using the available data. However, without access to the specific dataset you're referencing, I can provide an example based on typical values observed in the classic Iris dataset. ### Example Regression Equation Assuming a linear relationship based on standard Iris virginica data, the regression equation might look like: \[ \hat{y} = 0.458x - 0.712 \] - **Slope (\( b \))**: 0.458 - **Intercept (\( a \))**: -0.712 *Note: These values are illustrative. For precise results, perform a linear regression on your specific dataset.* ### Predicting Petal Width Using the example regression equation, let's predict the petal width (\( \hat{y} \)) for an Iris virginica flower with a petal length (\( x \)) of **3.26 cm**: \[ \hat{y} = 0.458 \times 3.26 - 0.712 = 1.492 - 0.712 = 0.780 \, \text{cm} \] ### Summary 1. **Regression Equation:** \[ \hat{y} = 0.458x - 0.712 \] 2. **Predicted Petal Width for \( x = 3.26 \) cm:** \[ \hat{y} = 0.780 \, \text{cm} \] *Remember to perform the regression analysis on your actual dataset to obtain precise coefficients.*