The Relationship Between Study Time and Test Scores: A Correlation and Regression Analysis

Abstract

Institutional Affiliation Course Name and Number Instructor’s Name Part A Correlation refers to the relationship between two variables. It can also be defined as a number that lies between -1 and 1 that shows the strength and direction of the two variables. There are 3 types of correlation, perfect positive, perfect negative and zero correlation. Perfect positive correlation is denoted by 1 where the two variables change in the same direction. Perfective correlation which is denoted by 1 occurs where the two variables in examination change in opposite direction while zero correlation means that the two variables do not have any relationship. One can determine the correlation of a given scatter by examining the pattern of the points plotted. It is also possible to calculate the correlation using Excel by using the CORREL function which provides the strength and the variable of the two variables. If the correlation is closer to +1 and -1, it implies that the variables have a strong positive and negative correlation respectively. For instance, study time and exam grades are known to have a positive relationship. Correlation scores of +0.88 imply that the two variables have a strong positive corelation. Part B A regression line refers to a model that illustrates the relationship between y and x. In a regression model, y is the response variable while x is the explanatory variable. One can find regression using the regression formula or by first plotting a scatter plot in excel, then adding a linear regression line. The regression formula is Y=mX+b, where m is the slop of the data and b, is the y intercept. The main use of the regression line is to predict the value of y, when one is given x values. Part C Correlation and Causation are closely intertwined because the are data analysis concepts. Corelation explains the relationship between two variables while the causation implies that variable A causes the outcome of Variable B. Further, in causation, one event does not cause the occurrence of the second event while in correlation, event A cause the outcome of event B. An example of difference correlation and causation can be illustrated using the educational level and income since they have a positive relationship. People with high education level earn more income compared to the people with low education level. Nevertheless, a high education level does not necessarily mean that it causes high level of income. Part 2: Calculations Dataset 1 Figure 1: A Scatter Plot of Students and The Number of Hours They Studied for the Test The scatter plot of figure 1 illustrates a positive correlation between the test scores and the number of hours the student studied. The correlation coefficient for this dataset is 0.8647 which implies that the test scores and the number...