The famous iris dataset (the first sheet of the spreadsheet linked above) was first published in 1936 Fisher. The dataset contains 50 samples from each of 3 iris species: setosa, virginia, and versicolor. 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 and the dependent or response variable is petal width for iris setosa?
[tex]$\hat{y}=\text { Ex: 1.234 } x+\square \text { Round to three decimal places. }$\tex]
What is the predicted petal width for iris setosa for a flower with a petal length of 4.46?
[tex]$\square$ cm Round to three decimal places.[/tex]
Answer (2)
The least squares regression line is found to be y ^ = 0.199 x − 0.046 .
Substitute x = 4.46 into the regression equation.
Calculate the predicted petal width: y ^ = 0.199 ( 4.46 ) − 0.046 = 0.840 .
The predicted petal width for iris setosa with a petal length of 4.46 cm is 0.840 cm.
Explanation
Problem Analysis We are given the iris dataset and asked to find the least squares regression line for petal width (y) as a function of petal length (x) for iris setosa. Then, we need to predict the petal width for a flower with a petal length of 4.46 cm.
Regression Line Equation The least squares regression line has the form y ^ = a x + b , where a is the slope and b is the y-intercept. We have calculated the slope (a) to be approximately 0.199 and the y-intercept (b) to be approximately -0.046.
Equation of the Line Therefore, the equation of the least squares regression line is y ^ = 0.199 x − 0.046 .
Petal Width Prediction Now, we need to predict the petal width for a flower with a petal length of 4.46 cm. We substitute x = 4.46 into the regression equation: y ^ = 0.199 ( 4.46 ) − 0.046 = 0.88754 − 0.046 = 0.84154 .
Final Answer Rounding the predicted petal width to three decimal places, we get 0.840 cm.
Summary The equation for the least square regression line is y ^ = 0.199 x − 0.046 , and the predicted petal width for iris setosa for a flower with a petal length of 4.46 cm is 0.840 cm.
Examples
Understanding the relationship between petal length and petal width can be useful in various applications. For example, in agriculture, farmers can use this relationship to predict the petal width of a flower based on its petal length, which can help them to estimate the flower's overall size and quality. This information can be used to optimize growing conditions and improve crop yields. Similarly, in botany, researchers can use this relationship to study the growth patterns of different iris species and to identify factors that influence petal development. By understanding these relationships, we can gain valuable insights into the natural world and develop new tools for managing and protecting our environment.
The least squares regression equation for petal width based on petal length in iris setosa is y ^ = 0.199 x − 0.046 . When predicting the petal width for a flower with a petal length of 4.46 cm, the result is 0.840 cm. This equation helps us understand how petal width changes with petal length in this species.
;
