Yes.
There is quite a high degree of linear agreement between the two variables with one showing an increase when the other shows a decrease.
1
1 score = 20 years2 millenia = 2,000 years = 100 score
A score is 20 years. A decade is 10 years. So in 10 decades we've had 100 years. Thus there are 5 scores in 10 decades. 10 Years/1 Decade x 10 Decades ÷ 20 years/1 score = 5 scores
The distribution is skewed to the right.
Linear regression looks at the relationship between two variables, X and Y. The regression line is the "best" line though some data you that you or someone else has collected. You want to find the best slope and the best y intercept to be able to plot the line that will allow you to predict Y given a value of X. This is usually done by minimizing the sum of the squares. Regression Equation is y = a + bx Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) Intercept(a) = (ΣY - b(ΣX)) / N In the equation above: X and Y are the variables given as an ordered pair (X,Y) b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores Once you find the slope and the intercept, you plot it the same way you plot any other line!
Linear regression looks at the relationship between two variables, X and Y. The regression line is the "best" line though some data you that you or someone else has collected. You want to find the best slope and the best y intercept to be able to plot the line that will allow you to predict Y given a value of X. This is usually done by minimizing the sum of the squares. Regression Equation is y = a + bx Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) Intercept(a) = (ΣY - b(ΣX)) / N In the equation above: X and Y are the variables given as an ordered pair (X,Y) b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores Once you find the slope and the intercept, you plot it the same way you plot any other line!
Although not everyone follows this naming convention, multiple regression typically refers to regression models with a single dependent variable and two or more predictor variables. In multivariate regression, by contrast, there are multiple dependent variables, and any number of predictors. Using this naming convention, some people further distinguish "multivariate multiple regression," a term which makes explicit that there are two or more dependent variables as well as two or more independent variables.In short, multiple regression is by far the more familiar form, although logically and computationally the two forms are extremely similar.Multivariate regression is most useful for more special problems such as compound tests of coefficients. For example, you might want to know if SAT scores have the same predictive power for a student's grades in the second semester of college as they do in the first. One option would be to run two separate simple regressions and eyeball the results to see if the coefficients look similar. But if you want a formal probability test of whether the relationship differs, you could run it instead as a multivariate regression analysis. The coefficient estimates will be the same, but you will be able to directly test for their equality or other properties of interest.In practical terms, the way you produce a multivariate analysis using statistical software is always at least a little different from multiple regression. In some packages you can use the same commands for both but with different options; but in a number of packages you use completely different commands to obtain a multivariate analysis.A final note is that the term "multivariate regression" is sometimes confused with nonlinear regression; in other words, the regression flavors besides Ordinary Least Squares (OLS) linear regression. Those forms are more accurately called nonlinear or generalized linear models because there is nothing distinctively "multivariate" about them in the sense described above. Some of them have commonly used multivariate forms, too, but these are often called "multinomial" regressions in the case of models for categorical dependent variables.
Quiz and exam scores are discrete variables because they are defined as one exact number.
There is quite a high degree of linear agreement between the two variables with one showing an increase when the other shows a decrease.
In a linear relationship, the pattern of change between two variables is represented by a straight line on a graph, indicating a constant rate of change. For example, if you consider the relationship between hours studied and exam scores, an increase in study hours consistently leads to higher scores, reflecting a positive linear correlation. Contextually, this means that as one variable increases, the other does so at a predictable rate, allowing for straightforward predictions and interpretations. This consistent pattern helps in understanding how one factor influences the other in real-world scenarios.
Data involving two variables is often referred to as bivariate data. This type of data examines the relationship between two distinct variables to identify patterns, correlations, or causations. Examples include analyzing the relationship between height and weight or studying the impact of study hours on exam scores. Bivariate data can be visualized using scatter plots or analyzed using statistical techniques like correlation and regression.
In my research I consider ESG socres predictors (independent variables). The data will be retrieved from Refinitv and I have doubt on whether ESG scores are categorical or quantitative data. I cannot choose the appropriate statistical test without being sure about this info. If predictor is categorical, then I choose MANOVA If predictor is quantitative, then the choice would be MULTIPLE REGRESSION analysis. Please, if you have time to answer, it would be a huge help getting a clear answer. Thank you.
scatter plot
Independent variables are the factors or conditions that are manipulated or changed in an experiment to observe their effect on dependent variables. They are often referred to as predictors or explanatory variables. For example, in a study examining the impact of study time on test scores, the amount of study time would be the independent variable.
Observation variables are characteristics or properties that can be measured or observed in a research study. These variables help researchers collect data and analyze relationships between different factors. Examples include age, gender, test scores, and survey responses.
In a quantitative research design, variables that can be measured include demographic factors such as age, gender, and income; behavioral variables like frequency of exercise or consumption of a product; and psychological constructs such as anxiety levels or satisfaction scores, often assessed through standardized surveys. Additionally, variables can encompass performance metrics, such as test scores or sales figures, and health indicators like blood pressure or cholesterol levels. These variables are typically quantifiable and analyzed using statistical methods to identify patterns or relationships.