[DATA] Putting It Together: Exam Scores The data below represe...

Question

[DATA] Putting It Together: Exam Scores The data below represent scores earned by students in Sullivan’s Elementary Algebra course for Chapter 2 (Linear Equations and Inequalities in One Variable) and Chapter 3 (Linear Equations and Inequalities in Two Variables). Completely summarize the relation between Chapter 2 and Chapter 3 exam scores, treating Chapter 2 exam scores as the explanatory variable. Write a report detailing the results of the analysis including the presence of any outliers or influential points. What does the relationship say about the role Chapter 2 plays in a student’s understanding of Chapter 3?

Table displaying two sets of numerical scores across multiple entries, organized in four columns with headers.

Accepted Answer

Hello. In this video, we are given that the table below shows the scores of 8 students on the test A and test B, and we want to summarize the strengths and directions of the linear relationship between A and B. So, in order to approach this problem, the first thing we need to do is we need to go ahead and calculate the correlation coefficient by the following formula. The calculation coefficient are. This is going to be the sum of the product of all the X terms minus their mean, multiplied by all the Y terms minus their mean, and this is going to be divided by the square root. Of the sum Of all the X terms minor means squared. Multiplied by the sum of all the Y terms minus their means squared. Now, because we are looking for summations that require some means, let's go ahead and first calculate the means of both test A and test B. For test A, we are going to label that mean as X. Now, in order to find the mean, we are going to take the sum of all the elements in the row for test aim, and that is going to give us a total sum. Of 620 Then we need to divide this by the sample size, which is going to be 8, and that is going to give us an approximate sum of 77.5. So this is going to be the mean for the X values. Now, we will calculate the mean for test B, which we are going to label as Y bar. Now, the sum of all the elements in row B is going to be 647, and dividing that by the sample size, which is A, gives us an approximate Y mean of 80.875. Now, here, what we need to do is we need to calculate the sum of the products of both X and Y, then we need the sum of X X squad, and the sum of Y minus Y2. So let's go ahead and organize those sums on the table. So what I've done here is I went ahead and I and I organized all of my data into a given table. So, for example, if I wanted to calculate the sum of the numerator, the first thing I would do is I would take each element from the X row, subtract the mean from it, then I would take that element and do the same thing with Ys and multiply those together to give me an element of 160.9375. I will repeat this for all the elements in X and Y, and that's going to give me a total sum of the numerator to be 1,155.5. Then for the denominator. The sum of the X minus X squared is going to be 1,216. And the sum of Y minus Y bar squared is going to be 1,108.8748. Then I'm going to take the square root of this product in the denominator, and by using a calculator, we will get an approximate correlation coefficient of 0.995. Now, because this value is very close to the whole number one, what this tells us is that there is going to be a strong positive linear relationship. And so the solution to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Correlation and Linear Relationship

Outliers and Influential Points

Regression Analysis and Explanatory Variable

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