Correlation & Regression
A fifth grade science teacher wants to know if there is a relationship between final exam scores and overall coursepoints after adjusting for a quiz score.
In order to determine whether there was a significant relationship between overall coursepoints and final exam scores, after controlling for quiz scores, a hierarchical regression was run. All assumptions were assessed using SPSS. There was independences of residuals, as assessed by a Durbin-Watson statistic of 1.08. An examination of various scatterplots indicated a general linear relationship between variables of interest, although perfect linearity was not observed.
Overall Scatterplot
Partial Regression Plot: Final Exam Score & Quiz Score
Figure 3. Partial Regression Plot: Final Exam Score & Course Points
The assumption of homoscedasticity was violated, as the scatterplot in Figure 1 demonstrates (i.e., the values were not evenly spread across the scatterplot). There was no evidence of multicollinearity as evidenced by no correlations between independent variables greater than .7 and no tolerance statistics less than .1. Additionally, no outliers were detected, as evidence by no studentized deleted residuals values greater than +/- 3 standard deviations. An examination of the leverage scores indicated that there were none greater than .5, and as such, no individual cases were exerting high leverage. Furthermore, there were no Cook's distances greater than 1, indicating that there were no unduly influential cases. Although examination of the historgram (Figure 4) indicated less than perfect normality of data,
The results of the model indicated that while quiz scores were not a significant predictor of final exam scores, F (1, 18) = 1.1, p = .308, the addition of course points did significantly improve the model an lead to a significant increase in R2 of .219, F (1,17) = 5.154, p = .036. The full model of quiz scores and course points to predict final exam scores (Model 2) was not statistically significant, R2 = .277, F (2, 17) = 3.254, p = .064; adjusted R2 = .192. Consequently, the null hypothesis that there is no relationship between coursepoints and final exam after controlling for quiz scores cannot be rejected. In other words, there is no statistically significant relationship between coursepoints and final exam scores after controlling for quiz scores.
Case Study 2
Results
The assistant principal wants to know if students' cumulative GPAs on an 8-point scale can predict students' final exam grades in their fifth grade science class. He wants to predict the final exam score of a student who has a GPA of 8.0.
In order to determine whether students' cumulative GPAs can predict final exam scores, a…
Correlation, Regression, and T-Tests Linear regression analyses are conducted after correlation has been established (Cohen, West & Aiken, 2014). Correlation shows how two variables are related, that is how one variable behaves when the other changes. Regression analyses somehow quantify this relationship -- we use it to predict the value of the dependent variable at different values of the independent variable. Since regression analyses yield numerical values, they can only be
Linear, Logistic or Multiple Correlation/Regression Proposal Objective of this paper is to use the statistical test to investigate whether the middle income earners in developing countries are capable of becoming home owners. The paper uses Nigeria as a case study. Unlike the developed countries such as the United States and United Kingdom where middle income earners can become house owners, however, the issues are different in developing countries because various
Regression vs. correlation? Correlation is used to test whether two variables covary, the strength of the relationship, and the direction of the association. A correlation calculation will generate a P-value and a correlation coefficient (r). By comparison, regression will generate the slope and intercept for a best-fit line that can be used to predict unknown values for the dependent variable. What percentage of depression is not associated with Facebook usage? The coefficient of
Regression Analysis: Real Estatee Sales Prices and Distance to City This regression analysis seeks to answer the question of how the sales price of Real Estate listed houses changes with the distance from the city. Does the sales price increase or decrease as the distance from the city increases or is there a relationship between the variables at all? Given the attraction of city living and the general trends of suburban
Correlation, Simple Linear Regression In this paper, we perform a linear regression analysis on previously collected data related to the number of daily e-mails received (R) and sent (S) by a particular user (the author). We have depicted the original daily e-mail data as a time series, incrementing N. By 1 for each day's measurement. The computed regression coefficient r is the slope of the regression line. A time series consists of
Its name tells us the criterion used to select the best fitting line, namely that the sum of the squares of the residuals should be least. In other words, the least squares regression equation is the line for which the sum of squared residuals is a minimum (Dallal, 2008). Multiple regression - the general purpose of multiple is to learn more about the relationship between several independent variables and a
Our semester plans gives you unlimited, unrestricted access to our entire library of resources —writing tools, guides, example essays, tutorials, class notes, and more.
Get Started Now