Chapter 1. Tutorial: Correlation
1.1 Problem Statement
A dataset consists of the composition of 77 breakfast cereals – a portion of the dataset is shown below.
Calories – calories / serving;
Protein, Fat, Fiber, Total Carbohyrates, Sugars – grams/serving.
Here is plot of the relationship between the calories/serving and the number of grams of fat.
1.2 Step 1
questions
Question 1.1
Correlation measures the strength of the cxdcov708lKLv+MHHy35DGPCUFQ2sdAahCO5hsHTFM4= relationship between two 9m9KbbhePVXsSWJWmhlJ2i3R7JpzLCgMy4D0xw== variables.
Question 1.2
The correlation coefficient must lie between SpHyo46ScHQsqFsA/eT2wQ== and bxnxOtrgJcHZ04ZM5Mf50g==.
Question 1.3
The correlation between X and Y is xpZuQiMdRxfpLv9Hi8MAAKtQWLgFHVRkx7OtaP/h9hLHCHc0816K4f3nFW71s9OpSnQJ2g== the correlation between Y and X.
1.3 Step 2
questions
Question 1.4
In the plot of breakfast cereals above, there appears to be 0gIn6fP68oKoU1mRJNfqev8Dl7xIDMRBdcEx2A== correlation between the calories/serving and the grams of fat/serving.
Question 1.5
The correlation between the calories/serving and the number of grams of fat/serving is about om5IH1qBUZO0+yzT3myW+PlpuoB5DZVH
Question 1.6
The amount of fat is converted to ounces/serving rather than grams/serving. (There are about 30 grams/ounce). The correlation will MsUDEhPs+9gejGmNRA2On3o8JCwzk2Q670DrV0AiUfA=.
Question 1.7
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.4 Step 3
Consider the following plots of the correlation between two variables:
questions
Question 1.8
The correlation in (a) is about 63OG6Q03ryQiZbnIKGazQLr6bSE=.
Question 1.9
The correlation in (b) is about AqzxYdjtr7oedi/LILL1YB5L2GY=.
Question 1.10
The correlation in (c) is about 1Ml6qIF7B15XD8BLciylwpWuYqk=.
Question 1.11
The correlation in (d) is about DT5IJ7qii+OnhdaXvhp7xmqDico=.
1.5 Step 4
The following is a plot of the mileage of a vehicle (miles/gallon) vs. the average speed (miles/hour).
questions
Question 1.12
There is ZiehhYxJByuXZ6ZhV9LiyBXAGDRlM7N1E39fkfkbGQQA8MtU6V7F3gGSYmOnVD741Vr65Hn2ZSs/jZJUgjHlVnQBLlA= between the average speed and mileage obtained.
Question 1.13
There is WTQM9qPcB2GJsSnPNY7plI697TQ5+ZSsM4qH5VVFbq9Pb7VKNOtf3jZ1XJMQ+OglAOGmDwaCNhQQjJkoSk6/mUnapKw= between the two variables.
Question 1.14
D2tgDJ8yHZ6bsFFkvH3W23rjrO7qgn5RXAPg0Ya1I44AwUvsYnHmtTkQTo5qpFzm9f+NM/GpNHqdY4NGoKEaAiayzcnbyGJji3fn2qB5WppE7vTY1.6 Step 5
Sometimes it is hard to measure the actual values of variables, but it quite easy to give a qualitative assessment of the size. For example, consider the following table of the number of species classified by the risk of predation and typical body mass.
