Question

Shanti wrote the predicted values for a data set using the line of best fit y = 2. 55x â€" 3. 15. She computed two of the residual values. A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 0. 7, 2. 3, 4. 1, 7. 2. The third column is labeled predicted with entries negative 0. 6, 1. 95, 4. 5, 7. 2. The fourth column is labeled residual with entries negative 1, 0. 35, a, b. What are the values of a and b? a = 0. 4 and b = â€"0. 15 a = â€"0. 4 and b = 0. 15 a = 8. 6 and b = 14. 25 a = â€"8. 6 and b = â€"14. 25.

Answer 1

The residual of a regression is the difference between the actual value and the predicted value

The values of (a) and (b) are -0.4 and 0, respectively.

The entries are given as:

x  Given  Predicted    Residual

1    -0.7         -0.6             -1

2   2.3         1.95            0.35

3   4.1           4.5              a

4   7.2          7.2              b

The residual of a line of best fit is calculated using:

$Residual = Actual - Predicted$

Using the entry headings, the formula would be:

$Residual = Given - Predicted$

To calculate the value of (a), we make use of entry (3).

So, we have:

$a = 4.1- 4.5$

$a = -0.4$

To calculate the value of (b), we make use of entry (4).

So, we have:

$b = 7.2- 7.2$

$b = 0$

Hence, the values of (a) and (b) are -0.4 and 0, respectively.

Read more about residuals at:

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