In Professor Krugman’s economics course the correlation between the students’ total scores prior to the final examination and their final-examination scores is r 0.5 The pre-exam totals for all students in the course have mean 280 and standard deviation 40. The final-exam scores have mean 75 and standard deviation 8. Professor Krugman has lost Julie’s final exam but knows that her total before the exam was 300. He decides to predict her final-exam score from her pre-exam total. (a) What is the slope of the least-squares regression line of final-exam scores on pre-exam total scores in this course? What is the intercept? (b) Use the regression line to predict Julie’s final-exam score. (c) Julie doesn’t think this method accurately predicts how well she did on the final exam. Use r^2 to argue that her actual score could have been much higher (or much lower) than the predicted value.
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.
In Professor Krugman’s economics course the
students’ total scores prior to the final
examination and their final-examination
scores is r 0.5 The pre-exam totals for
all students in the course have mean 280
and standard deviation 40. The final-exam scores have mean
75 and standard deviation 8. Professor Krugman has lost Julie’s
final exam but knows that her total before the exam was 300. He
decides to predict her final-exam score from her pre-exam total.
(a) What is the slope of the least-squares regression line of
final-exam scores on pre-exam total scores in this course?
What is the intercept?
(b) Use the regression line to predict Julie’s final-exam score.
(c) Julie doesn’t think this method accurately predicts how
well she did on the final exam. Use r^2 to argue that her actual
score could have been much higher (or much lower) than the
predicted value.
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