Consider the following data. x 3 4 6 7 y 1 2 4 5 We want to predict y based on observations of x. Answer the following questions. P= Sum Px = 20; Py = 12; Pxy = 70; Px P 2 = 110; and y 2 = 46. n=4 (a) Calculate the sample correlation coefficient r. (b) Calculate the estimates for the y-intercept, βˆ 0, and the slope, βˆ1, for the regression line. (c) Using what you get in part (b), write down the equation of the regression line correctly. (d) Find the coefficient of determination
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.
Consider the following data.
x 3 4 6 7
y 1 2 4 5
We want to predict y based on observations of x.
Answer the following questions. P= Sum
Px = 20; Py = 12; Pxy = 70; Px P 2 = 110; and y 2 = 46. n=4
(a) Calculate the sample
(b) Calculate the estimates for the y-intercept, βˆ 0, and the slope, βˆ1, for the regression line.
(c) Using what you get in part (b), write down the equation of the regression line correctly.
(d) Find the coefficient of determination R2. Based on R2 is the regression line useful for us to do prediction?
(e) Estimate y for x=5.5
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