The following table contains the ACT scores and the GPA (grade point average) for eight college stu- dents. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 2.8 21 3.4 24 3 3.0 26 4 3.5 27 3.6 29 3.0 25 2.7 25 3.7 30 (i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPÅ = Bo + BIACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? (ii) Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. (iii) What is the predicted value of GPA when ACT = 20? (iv) How much of the variation in GPA for these eight students is explained by ACT? Explain.
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.
The following table contains the ACT scores and the GPA (grade point average) for eight college stu- dents. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 2.8 21 3.4 24 3 3.0 26 4 3.5 27 3.6 29 3.0 25 2.7 25 3.7 30 (i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPÅ = Bo + BIACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? (ii) Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. (iii) What is the predicted value of GPA when ACT = 20? (iv) How much of the variation in GPA for these eight students is explained by ACT? Explain.
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