Question

You plotted a height of a plant every day and found the line of best fit y= 0.23+ 9.9
If the actual data point for day 6 is (6, 7.82) what is the residual of the data point for day 6

Answer 1

To find the residual for the data point on day 6, you first need to calculate the predicted value using the line of best fit equation \( y = 0.23 + 9.9 \).

However, it seems like there may have been a typographical error in the line of best fit you provided since it doesn't seem to depend on \( x \). A more typical equation for a line of best fit would be in the format \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. If you have the actual slope and intercept, please provide those.

For now, if we assume the line of best fit is actually meant to be linear and based on this information, let's say that you wanted to use this constant equation:

Suppose we have the correct format: \( y = mx + b \) where \( x = 6 \), and you have a slope and intercept. If we consider just a general format \( y = 9.9x + 0.23 \):

1. **Calculate the predicted value (\( y_{pred} \)) for day 6**:
\[
y_{pred} = 0.23 + 9.9 \times 6
= 0.23 + 59.4
= 59.63
\]

2. **You also have the actual observed data point for day 6: \( y_{actual} = 7.82 \)**.

3. **Calculate the residual**:
\[
residual = y_{actual} - y_{pred}
= 7.82 - 59.63
= -51.81
\]

The residual for the data point for day 6 is \(-51.81\).

If the given equation was a misunderstanding, please provide the accurate line of best fit, and I can redo the calculation accordingly!