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:
[tex]\[ \text{Sepal Width} = a + b \times \text{Sepal Length} \][/tex]
where:
- [tex]\(a\)[/tex] is the intercept,
- [tex]\(b\)[/tex] is the slope of the regression line.
Given:
- Sepal length [tex]\( x = 5.1 \)[/tex] cm
- Intercept [tex]\( a = 1.0 \)[/tex]
- Slope [tex]\( b = 0.5 \)[/tex]
We can substitute these values into our linear regression equation:
[tex]\[ \text{Sepal Width} = 1.0 + 0.5 \times 5.1 \][/tex]
First, we multiply the slope by the sepal length:
[tex]\[ 0.5 \times 5.1 = 2.55 \][/tex]
Next, we add the intercept to this product:
[tex]\[ 1.0 + 2.55 = 3.55 \][/tex]
Therefore, the predicted sepal width for an iris virginica with a sepal length of 5.1 cm is:
[tex]\[ \boxed{3.550} \][/tex]
Rounded to three decimal places, the predicted sepal width is 3.550 cm.
