Suppose we conduct a study on the time spent studying for an exam and exam scores. We survey students in introductory statistics and find the explanatory variable (time, in hours) ranges from 0 to 16 and exam scores (in points, out of 100 maximum) range from 5 to 100. The correlation between time spent studying and exam scores is 0.80. We fit a simple linear regression model to these data and get the following least squares line: score = 4 + 6*(time). You pick a random student from the course and observe that the number of hours she studied for the exam is 1 standard deviation above the mean time spent studying. How many standard deviations above or below the mean exam score would you expect her to score?
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.
Suppose we conduct a study on the time spent studying for an exam and exam scores. We survey students in introductory statistics and find the explanatory variable (time, in hours) ranges from 0 to 16 and exam scores (in points, out of 100 maximum)
You pick a random student from the course and observe that the number of hours she studied for the exam is 1 standard deviation above the mean time spent studying. How many standard deviations above or below the mean exam score would you expect her to score?
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