For a week prior to their final exam, a group of friends collect data to see whether time spent studying (x) had a strong correlation with their marks on the exam (y). The collected data is summarized in the following table: Time Spent Studying (hours): 10 11 15 14 7 Exam Grade (%): 71 67 81 93 54 66 a) Plot the data (y versus r). Produce a regression of y against r and report an r? value for this fit. Add the b) regression line to the plot in a). Do you think that the regression line captures the most important features of the data set reasonably well? At a 5% significance level, is there a significant linear relationship between the x and y? Does this result agree with the conclusion you made in b)?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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