Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 9 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ = + x(b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ = + x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? YesNo (d) Solve your answer from part (a) for x (rounded to three digits after the decimal).x = + y Do you get the least-squares equation of part (b) with the symbols x and yexchanged? YesNo (e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). 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 using parts (a) through (d). In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different. In general, switching x and y values produces a different least-squares equation.
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 | 2 | 6 |
| y | 4 | 3 | 9 |
Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data pairs.
| x | 4 | 3 | 9 |
| y | 1 | 2 | 6 |
Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?
(d) Solve your answer from part (a) for x (rounded to three digits after the decimal).
x = + y
Do you get the least-squares equation of part (b) with the symbols x and yexchanged?
(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). 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 using parts (a) through (d).
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