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The table below represents the closing prices of stock [tex]ABC[/tex] for the last five days. Using your calculator, what is the equation of linear regression that fits these data?

\begin{tabular}{|l|c|}
\hline Day & Value \\
\hline 1 & 24.31 \\
\hline 2 & 23.31 \\
\hline 3 & 23.01 \\
\hline 4 & 23.16 \\
\hline 5 & 23.27 \\
\hline
\end{tabular}

A. [tex]y=-0.223 x+24.081[/tex]
B. [tex]y=0.194 x-24.815[/tex]
C. [tex]y=-0.147 x+19.217[/tex]
D. [tex]y=-0.237 x+25.139[/tex]

Sagot :

GinnyAnswer
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].
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