To determine the equation of the linear regression that best fits the data provided, we need to calculate the slope (m) and the y-intercept (b) of the linear equation [tex]\( y = mx + b \)[/tex].
We are given the following data for the closing prices of stock [tex]\( ABC \)[/tex]:
| Day | Value |
|-----|-------|
| 1 | 24.31 |
| 2 | 23.31 |
| 3 | 23.01 |
| 4 | 23.16 |
| 5 | 23.27 |
## Step-by-Step Solution:
1. Calculate the slope (m):
- The slope (m) represents the change in the dependent variable (Value) for a unit change in the independent variable (Day).
- Based on the result, the slope of the regression line is [tex]\( m = -0.223 \)[/tex].
2. Calculate the y-intercept (b):
- The y-intercept (b) is the value of the dependent variable when the independent variable is 0.
- Based on the result, the y-intercept [tex]\( b = 24.081 \)[/tex].
3. Construct the equation of the line:
- Using the calculated slope and intercept, we can write the equation of the line as:
[tex]\[
y = -0.223x + 24.081
\][/tex]
Therefore, the equation of the linear regression that fits the given data is:
[tex]\[
y = -0.223x + 24.081
\][/tex]
The answer is A. [tex]\( y = -0.223x + 24.081 \)[/tex].
