Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 19 7 27 21 (a) Develop a scatter diagram for these data. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right starting in the upper left corner of the diagram. Moving from left to right, the first 3 points appear to be plotted in an upward diagonal, direction while the next 2 points are much lower on the diagram. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 7 to 27 on the vertical axis and are fairly spread out. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 7 to 27 on the vertical axis and are fairly spread out. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 24 on the vertical axis and are fairly spread out. (b) Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 6.
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.
xi
|
2 | 6 | 9 | 13 | 20 |
---|---|---|---|---|---|
yi
|
7 | 19 | 7 | 27 | 21 |
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