Suppose you are given the following x,y data pairs: x- 1,3,4 y-2,1,6 Show that the least squares equatuon is y=1.143+1.071x Now suppose you are given these data pairs x-2,1,6 y-1,3,4 Show that the least squares equation for these is y=1.595+0.357x In the data for parts a and b did we simply exchange the x and y values for each data pair? Solve 0.143+1.071x for x. Do you get the least squares equation of part b with symbols x and y exchanged? If we solve this equation for x, will we necessarily get the least squares equation for the set of data pairs y,x with x and y exchanged? 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.
Suppose you are given the following x,y data pairs: x- 1,3,4 y-2,1,6
Show that the least squares equatuon is y=1.143+1.071x
Now suppose you are given these data pairs
x-2,1,6
y-1,3,4
Show that the least squares equation for these is y=1.595+0.357x
In the data for parts a and b did we simply exchange the x and y values for each data pair?
Solve 0.143+1.071x for x. Do you get the least squares equation of part b with symbols x and y exchanged?
If we solve this equation for x, will we necessarily get the least squares equation for the set of data pairs y,x with x and y exchanged? Explain
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