a data set has the following points (0,2) (4,1) (6,0) the slope of the linear regression line is -0.32
To find the slope of the linear regression line, you will need to perform linear regression analysis on the given dataset. Here's a step-by-step explanation of how to calculate the slope:
1. Start by calculating the mean (average) of the x-values and the mean of the y-values in the dataset.
- x₁ = 0, x₂ = 4, x₃ = 6 (where x₁, x₂, x₃ represent the x-coordinates)
- y₁ = 2, y₂ = 1, y₃ = 0 (where y₁, y₂, y₃ represent the y-coordinates)
Mean of x-values: (0 + 4 + 6) / 3 = 2
Mean of y-values: (2 + 1 + 0) / 3 = 1
2. Calculate the differences between each x-value and the mean of the x-values (x - x̄), and the differences between each y-value and the mean of the y-values (y - ȳ).
For example:
- For the first point (0,2):
- Difference in x-values: 0 - 2 = -2
- Difference in y-values: 2 - 1 = 1
Repeat this process for all the points in the dataset.
3. Calculate the sum of the products of the differences in x-values and y-values.
- (-2 * 1) + (0 * 1) + (2 * -1) = -2
4. Calculate the sum of the squared differences in x-values.
- (-2 * -2) + (0 * 0) + (2 * 2) = 8
5. Now, calculate the slope (b) using the formula:
b = sum of products of (x - x̄) and (y - ȳ) / sum of squared differences of (x - x̄)
b = -2 / 8 = -0.25
Therefore, the slope of the linear regression line is -0.25.
Note: It seems there is a discrepancy between the given slope (-0.32) and the calculated slope (-0.25). Please verify the dataset or the intended slope value.