High School

Since linear regression is fundamental to statistics, it is important to become very comfortable with this concept. Below are four data sets for you to practice and master this subject.

**Data set 1:**

- X1: 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00, 11.00, 12.00, 13.00, 14.00
- Y1: 6.26, 7.68, 9.24, 6.82, 8.95, 10.81, 10.04, 10.33, 12.84, 9.58, 11.96

**Data set 2:**

- X2: 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00, 11.00, 12.00, 13.00, 14.00
- Y2: 5.10, 6.74, 8.13, 9.26, 10.14, 10.77, 11.14, 11.26, 11.13, 10.74, 10.10

**Data set 3:**

- X3: 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00, 11.00, 12.00, 13.00, 14.00
- Y3: 7.39, 7.73, 8.08, 8.42, 8.77, 9.11, 9.46, 9.81, 10.15, 14.74, 10.84

**Data set 4:**

- X4: 8.00, 8.00, 8.00, 8.00, 8.00, 8.00, 10.00, 19.00, 8.00, 8.00, 8.00
- Y4: 8.58, 7.76, 9.71, 10.84, 10.47, 9.04, 7.25, 14.50, 7.56, 9.91, 8.89

**Task:**

1. Draw the best-fit line for each data set, including the scatter plot of all points.
2. Analyze the best-fit lines to determine if there is a pattern.
3. Decide which best-fit line is the most effective and explain why.

Answer :

Final answer:

The best-fitted lines for data sets 1, 2, and 3 represent a positive linear relationship between X and Y, indicating that as X increases, Y also tends to increase.

Explanation:

In linear regression, the best-fitted line represents the relationship between the independent variable (X) and the dependent variable (Y). It is determined by minimizing the sum of the squared differences between the observed Y values and the predicted Y values on the line.

Let's analyze each data set and draw the best-fitted line:

  1. Data set 1: The scatter plot of the data points shows a positive linear relationship between X1 and Y1. The best-fitted line passes through the points and represents the trend in the data.
  2. Data set 2: The scatter plot of the data points shows a positive linear relationship between X2 and Y2. The best-fitted line passes through the points and represents the trend in the data.
  3. Data set 3: The scatter plot of the data points shows a positive linear relationship between X3 and Y3. The best-fitted line passes through the points and represents the trend in the data.
  4. Data set 4: The scatter plot of the data points shows no clear linear relationship between X4 and Y4. The points are scattered and do not form a straight line. Therefore, it is not appropriate to draw a best-fitted line for this data set.

From the analysis, we can conclude that the best-fitted lines for data sets 1, 2, and 3 represent a positive linear relationship between X and Y. This means that as X increases, Y also tends to increase. However, for data set 4, there is no clear linear relationship between X and Y. The points are scattered, indicating no significant pattern or trend.

The best-fitted line for data set 1, 2, and 3 can be considered the best because they represent a clear positive linear relationship between X and Y. These lines can be used to make predictions or analyze the relationship between the variables.

Learn more about best fitted line and patterns in linear regression here:

https://brainly.com/question/34296491

#SPJ14

Other Questions