Milk is an important source of protein. How does the amount of protein in milk f
ID: 3201441 • Letter: M
Question
Milk is an important source of protein. How does the amount of protein in milk from a cowvary with milk production? The article “Metabolites of Nucleic Acid in Bovine Milk,” J. ofDairy Science, 1984: 723-728, reported data on milk production (kg/day) and milk protein(kg/day) for Holstein-Fresian cows. Below is a scatterplot of the data:
The value r between milk production and the amount of milk protein is 0.978.
a ) Describe the shape, direction, and strength of the relationship between milk production andthe amount of milk protein.
b ) Here are some summary statistics for the two variables:
Find the least squares line which predicts the amount of milk protein based on the milkproduction value.
c) Using your model, extrapolate the amount of protein for a milk production of 45 kg/day. Whymust we be careful when we extrapolate?
d) What is the de?nition of an in?uential point? How can we look for in?uential points in thisexample?
parts a,b c, and d.
A 2/3 v A. Milk is an important source of protein. How does the amount of protein in milk from a cow vary with milk production? The article "Metabolites of Nucleic Acid in Bovine Milk," J. of milk protein (kg/day) for Holstein-Fresian cows. Below is a scatterplot of the data: load ("milk protein. RData") plot (milk protein$Milk Production milk protein Milk Protein xlab "production (kg/day) ylab "protein (kg/day) pch 19) 20 25 30 35 40 production (kg/day) The value r between milk production and the amount of milk protein is 0.978 Note: This problem can be done without additional work in R. but the data set milk protein. RData is provided if you wish to explore it in R (a) Describe the shape, direction, and strength of the relationship between milk production and the amount of milk protein. Q.Explanation / Answer
a) Describe the shape, direction, and strength of the relationship between milk production and the amount of milk protein.
Solution:
The correlation coefficient between the two variables milk production and the amount of milk protein is given as 0.978 which means there is a strong positive linear relationship or linear association or correlation exists between the two variables milk production and the amount of milk protein.
b) Here are some summary statistics for the two variables:
Find the least squares line which predicts the amount of milk protein based on the milk production value.
Solution:
Here, we have to find the least squares line for the prediction of the dependent variable amount of milk protein based on the independent variable milk production value.
We are given
Xbar = 29.56, Ybar = 0.9021, SDx = 7.656129, SDy = 0.1924409, r = 0.978
We have regression equation given as below:
Y = a + bX
Where a is y-intercept and b is slope
We are given
b = r*(SDy/SDx) = 0.978*(0.1924409/7.656129) = 0.024582553
a = Ybar – b*Xbar
a = 0.9021 – 0.024582553*29.56
a = 0.175439733
Y = a + bX
Y = 0.175439733 + 0.024582553*X
Amount of Milk protein = 0.175439733 + 0.024582553*Milk Production
c) Using your model, extrapolate the amount of protein for a milk production of 45 kg/day. Why must we be careful when we extrapolate?
Solution:
Y = 0.175439733 + 0.024582553*X
Y = 0.175439733 + 0.024582553*45
Y = 1.281654618
We must be careful when we extrapolate because for extrapolation there is a change of getting biased estimates.
d) What is the denition of an inuential point? How can we look for inuential points in this example?
Solution:
Influential point is nothing but the outlier which greatly affects the slope of the regression line. For the given example, there would be effect of outlier on the slope.