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?.

Answer 1

The residual column is given by the difference between the given values

and the values from the fitted line.

• The values of a and b are; a = -0.4 and b = 0.18

Reasons:

The line of best fit equation is; y = 2.55·x - 3.15

The 4-column table is presented s follows;

$\begin{tabular}{|c|c|c|c|}\underline{x}&\underline{Given}&\underline{Predicted}&\underline{Residual}\\1&-0.7&-0.6&-0.1\\2&2.3&1.95&0.35\\3&4.1&4.5&a\\4&7.2&7.02&b\end{array}\right]$

Required:

The values of a and b

Solution;

The residual is given by the difference between actually observed value and the predicted value

RESID = $\mathbf{y_i}$ - $\mathbf{x_i}$·b

Where;

$y_i$ = The given value at point i

$x_i$·b = The predicted value at point i

Therefore;

At x = 1, the residual = -0.7 - (-0.6) = -0.1

At x = 2, the residual = 2.3 - 1.95 = 0.35

At x = 3, the residual = a = 4.1 - 4.5 = -0.4

Therefore;

• a = -0.4

At x = 4, the residual = b = 7.2 - 7.02 = 0.18

Therefore;

• b = 0.18

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