Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 5 10 14 (a) Develop a scatter diagram for these data. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 3 to 14 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 14 on the vertical axis. The next 3 points are between 3 to 8 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 14 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 2 to 13 on the vertical axis. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y.There appears to be no noticeable relationship between x and y. There appears to be a positive linear relationship between x and y. (c) Try to approximate the relationship between x and y by drawing a straight line through the data. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 14 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 3 to 14 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 14 on the vertical axis. The next 3 points are between 3 to 8 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 2 to 13 on the vertical axis. (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2and b0 = y − b1x. ŷ = 2. 60x+4.20 (e) Use the estimated regression equation to predict the value of y when x = 2.
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
|
1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
yi
|
3 | 8 | 5 | 10 | 14 |
Σ(xi − x)(yi − y) |
Σ(xi − x)2 |
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images