Laboratory work 1 (video, part 1). Pair correlation analysis
Section "Fundamentals of mathematical statistics". Topic "Correlation analysis".
Laboratory work. I offer you a mini-test. Question One: list the main tasks of the correlation analysis.
Answer choice. First: measuring the degree of connection. Second: selection of factors that have the greatest impact on the effective feature on the basis of the connectivity degree between the features. Third: detection of unknown causal relationships. Fourth: all of the above.
Think about it and choose the right answer. Check it at the end of the mini-test. Question Two. If the features of a random variable are independent, then the sample correlation coefficient is equal to… The first answer: -1. Second: 0, 5. Third: 1. Fourth: 0. Choose the correct answer. Check it at the end of the mini-test.
And Question Three. If the features are dependent, then the sample correlation coefficient is equal to… Answer choice. The first is 0, the second is -2, the third is an empty set, and the fourth is two intervals -1, 0, 0, 1. Choose the correct option in your opinion. So, let's check it out. The correct answer for question One is number four. In the second question, the correct answer is 0, which is also the fourth answer. In question Three, the correct answer is also the fourth one. So, let's revise that the formula for the sample correlation coefficient is the following. All the signs were explained to you at the lecture.
Explanatory notes are also provided here. Don’t forget that in Excel macros, correlation can be found using the special correlation function.
Array 1 is the data of the first sample, array 2 is the data of the second sample.
Now try to solve the following task.
10 students were given tests for visual and verbal thinking.
The average time for solving test tasks in seconds was measured.
The researcher wonders whether there is a relationship between the time of solving these tasks?
Here, the variable X (or attribute, or random variable) denotes the average time for solving visual-image test tasks, and the variable Y is the average time for solving verbal test tasks.
The data are presented in a table below. Let’s copy the data to the MS Excel worksheet. Select cell C1 and start searching for the Statistical category function. Find the function КОРРЕЛ.ОК. Array 1. Array 1 – select the range of data corresponding to the first sample set. Array 2 – select the data corresponding to the second sample set.
Click OK. The value that appeared in cell C1 is the value corresponding to the desired correlation coefficient. We got a value of about 0.54.
Thus, the relationship between the time of solving visual and verbal tasks of the test is direct and average.
Now I offer you a task to solve. So, the problem for an independent solution. We know the values of the average daily per capita income in conventional units for some territories of the region's districts.
This will be a feature, a factor, or a random variable X. And a percentage of the total income spent on food purchases (this is a feature, a factor, or a random variable Y). You need to establish a relationship between the variables. The data table is shown on the screen. I wish success in solving the task!
Thank you for your attention.