A professor wants to investigate the relationship between the grades students obtain in their midterm exam (X) and the grades they obtain (Y) in the final exam The professor collects data from 60 randomly chosen students. The estimated OLS regression is: Ý = 45 + 0 85X,, where Y, denotes the predicted value of the grades obtained in the final exam by the " individual and X, denotes the grades obtained in the midterm exam From the sample data he makes the following calculations: 60 E (X-X) = 230.48, 60 = 410.25, ^2 where u, is the square of the residual for the " observation. He wants to test whether the grades obtained in the midterm exam have any effect on the grades obtained in the final exam or not. Which of the following are the null and the alternative hypotheses of the test the professor wishes to conduct? O A. Ho B1=0 vs. H: B1#0. O B. Ho B1 = 0.85 vs. H,: B, #0.85. O C. Ho: B, #0 vs. H.: B, =0. Click to select your answer(s).
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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