To predict the sepal width for an iris virginica flower with a sepal length of 5.1 cm, we will use a linear regression model. In simple linear regression, the relationship between the dependent variable (sepal width in this case) and an independent variable (sepal length) is represented by a linear equation:
\(\[ \text{Sepal Width} = a + b \times \text{Sepal Length} \]\)
where:
- \(\(a\)\) is the intercept,
- \(\(b\)\) is the slope of the regression line.
Given:
- Sepal length \(\( x = 5.1 \)\) cm
- Intercept \(\( a = 1.0 \)\)
- Slope \(\( b = 0.5 \)\)
We can substitute these values into our linear regression equation:
\(\[ \text{Sepal Width} = 1.0 + 0.5 \times 5.1 \]\)
First, we multiply the slope by the sepal length:
\(\[ 0.5 \times 5.1 = 2.55 \]\)
Next, we add the intercept to this product:
\(\[ 1.0 + 2.55 = 3.55 \]\)
Therefore, the predicted sepal width for an iris virginica with a sepal length of 5.1 cm is:
\(\[ \boxed{3.550} \]\)
Rounded to three decimal places, the predicted sepal width is 3.550 cm.
