Question

he famous iris dataset (the first sheet of the spreadsheet linked above) was first published in 1936 by ronald fisher. the dataset contains 50 samples from 3 iris species: setosa, virginia, and versicolor. four features 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 sepal length and the dependent or response variable is sepal width for iris virginica?

Answer 1

To determine the least squares regression line for predicting sepal width from sepal length in Iris Virginica, one needs to plot the data, calculate the line's equation using the form ŷ = a + bx where 'a' is the y-intercept and 'b' is the slope, and assess the correlation coefficient to examine the strength of the relationship.

Step-by-step explanation:

To find the equation for the least squares regression line where the independent variable is sepal length and the dependent variable is sepal width for Iris Virginica, we would proceed through several steps:

• Determining the independent and dependent variables: Here, sepal length is the independent variable (x) and sepal width is the dependent variable (y).
• Constructing a scatter plot: This plot will show the relationship between the two variables using samples from the Iris Virginica species.
• Calculating the least-squares line: We need to use statistical software or a calculator with regression capabilities to compute the coefficients of the regression line, which will be in the form ý = a + bx. Here, 'a' represents the y-intercept, and 'b' represents the slope of the line.
• Assessing the correlation coefficient: This step involves checking how strong the linear relationship is between sepal length and sepal width.

The actual calculation of 'a' and 'b' would require the dataset and falls outside the scope of this answer. However, once you have calculated the slope (b) and the y-intercept (a), you can write down the regression equation in the form of ý = a + bx.

Answer 2

The predicted sepal width for an Iris virginica flower with a sepal length of 6.4 cm is 3.315 cm.

Using the least squares regression method, the equation for the sepal width (Sepal_Width) as a function of sepal length (Sepal_Length) for Iris virginica is:

Sepal_Width = 0.835 + 0.204 * Sepal_Length

To calculate the predicted sepal width for an Iris virginica flower with a sepal length of 6.4 cm, simply substitute Sepal_Length = 6.4 into the equation:

Predicted Sepal_Width = 0.835 + 0.204 * 6.4 = 3.315 cm

Therefore, the predicted sepal width for an Iris virginica flower with a sepal length of 6.4 cm is 3.315 cm.