Question

Brenda collected this data from an experiment.
Hours of Sunlight (t) 3 5 7 9 11 13
Height in inches (h) 2.3 3.3 3.9 6.1 7.0 8.4
For the line of fit h = 0.6t + 0.44, what is the residual (difference) of the data point at ???? = 7?

Answer 1

Given:

The data table of an experiment.

Equation of best fit line is

$h=0.6t+0.44$

To find:

The residual (difference) of the data point at t = 7.

Solution:

From the given table, it is clear that the value of h is 3.9 at t =7.

So, observed value is 3.9.

Equation of best fit line is

$h=0.6t+0.44$

Putting t = 7, we get

$h=0.6(7)+0.44$

$h=4.2+0.44$

$h=4.64$

So, the estimated value is 4.64.

Residual formula:

Residual = Observed value - Estimated value

              = $3.9-4.64$

              = $-0.74$

Therefore, the residual value of the data point at t = 7 is -0.74.