Question
The least absolute deviation line equation for the data in the table is m = 0.15x + 3 (estimated with technology).x y1 36 2.50.5 84 17.5 1.512 910 1311 4What is the sum of the absolute deviations?(1 point)Responses10.8510.8525.0525.0538
Answers
GPT-4o mini
To find the sum of the absolute deviations for the least absolute deviation line given by the equation \( m = 0.15x + 3 \), we first need to evaluate the predicted \( y \) values for each \( x \) in the provided data table, then calculate the absolute deviations, and finally sum them up.
Given:
- The equation of the line is \( m = 0.15x + 3 \)
### Data Points:
| \( x \) | \( y \) |
|---------|---------|
| 36 | 2.5 |
| 0.5 | 84 |
| 17.5 | 1.5 |
| 12 | 9 |
| 10 | 13 |
| 11 | 4 |
### Step 1: Calculate the predicted \( y \) values using the line equation
1. For \( x = 36 \):
\[
m(36) = 0.15 \times 36 + 3 = 5.4 + 3 = 8.4
\]
2. For \( x = 0.5 \):
\[
m(0.5) = 0.15 \times 0.5 + 3 = 0.075 + 3 = 3.075
\]
3. For \( x = 17.5 \):
\[
m(17.5) = 0.15 \times 17.5 + 3 = 2.625 + 3 = 5.625
\]
4. For \( x = 12 \):
\[
m(12) = 0.15 \times 12 + 3 = 1.8 + 3 = 4.8
\]
5. For \( x = 10 \):
\[
m(10) = 0.15 \times 10 + 3 = 1.5 + 3 = 4.5
\]
6. For \( x = 11 \):
\[
m(11) = 0.15 \times 11 + 3 = 1.65 + 3 = 4.65
\]
### Step 2: Calculate the absolute deviations
| \( x \) | \( y \) | Predicted \( m \) | Absolute Deviation |
|---------|---------|-------------------|--------------------|
| 36 | 2.5 | 8.4 | \( |2.5 - 8.4| = 5.9 \) |
| 0.5 | 84 | 3.075 | \( |84 - 3.075| = 80.925 \) |
| 17.5 | 1.5 | 5.625 | \( |1.5 - 5.625| = 4.125 \) |
| 12 | 9 | 4.8 | \( |9 - 4.8| = 4.2 \) |
| 10 | 13 | 4.5 | \( |13 - 4.5| = 8.5 \) |
| 11 | 4 | 4.65 | \( |4 - 4.65| = 0.65 \) |
### Step 3: Sum the absolute deviations
Now summing all the absolute deviations:
\[
5.9 + 80.925 + 4.125 + 4.2 + 8.5 + 0.65 = 104.3
\]
It seems that none of the provided responses (10.85, 10.85, 25.05, 25.05, 38) match the calculated sum of absolute deviations.
Please double-check the data or the calculations, as there may be a misunderstanding or issue with the listed values and their interpretation.
Given:
- The equation of the line is \( m = 0.15x + 3 \)
### Data Points:
| \( x \) | \( y \) |
|---------|---------|
| 36 | 2.5 |
| 0.5 | 84 |
| 17.5 | 1.5 |
| 12 | 9 |
| 10 | 13 |
| 11 | 4 |
### Step 1: Calculate the predicted \( y \) values using the line equation
1. For \( x = 36 \):
\[
m(36) = 0.15 \times 36 + 3 = 5.4 + 3 = 8.4
\]
2. For \( x = 0.5 \):
\[
m(0.5) = 0.15 \times 0.5 + 3 = 0.075 + 3 = 3.075
\]
3. For \( x = 17.5 \):
\[
m(17.5) = 0.15 \times 17.5 + 3 = 2.625 + 3 = 5.625
\]
4. For \( x = 12 \):
\[
m(12) = 0.15 \times 12 + 3 = 1.8 + 3 = 4.8
\]
5. For \( x = 10 \):
\[
m(10) = 0.15 \times 10 + 3 = 1.5 + 3 = 4.5
\]
6. For \( x = 11 \):
\[
m(11) = 0.15 \times 11 + 3 = 1.65 + 3 = 4.65
\]
### Step 2: Calculate the absolute deviations
| \( x \) | \( y \) | Predicted \( m \) | Absolute Deviation |
|---------|---------|-------------------|--------------------|
| 36 | 2.5 | 8.4 | \( |2.5 - 8.4| = 5.9 \) |
| 0.5 | 84 | 3.075 | \( |84 - 3.075| = 80.925 \) |
| 17.5 | 1.5 | 5.625 | \( |1.5 - 5.625| = 4.125 \) |
| 12 | 9 | 4.8 | \( |9 - 4.8| = 4.2 \) |
| 10 | 13 | 4.5 | \( |13 - 4.5| = 8.5 \) |
| 11 | 4 | 4.65 | \( |4 - 4.65| = 0.65 \) |
### Step 3: Sum the absolute deviations
Now summing all the absolute deviations:
\[
5.9 + 80.925 + 4.125 + 4.2 + 8.5 + 0.65 = 104.3
\]
It seems that none of the provided responses (10.85, 10.85, 25.05, 25.05, 38) match the calculated sum of absolute deviations.
Please double-check the data or the calculations, as there may be a misunderstanding or issue with the listed values and their interpretation.