Final answer:
The regression equation provided is used to estimate values within the observed data range. Substituting an x value into the equation predicts the y value, but predictions outside of the observed range are unreliable.
Step-by-step explanation:
To predict a value using a regression equation, you need to substitute the given x-value into the equation.
If you want to predict when the soap will be y = -5.572x + 123.779, you need to know the value of x that corresponds to y = -5. In mathematics, particularly in statistics, identifying the best-fit line or least-squares regression line is important for making predictions based on historical data.
According to the line of best fit equation provided (ŷ = -173.51 + 4.83x), you can substitute any x value within the range of observed data to estimate the corresponding y value.
For example, using this model, a score of 73 on the third exam would predict a final exam score of 179.08 points.
However, predictions made outside of the observed x values, such as a score of 90, can be unreliable, as demonstrated when ŷ = -173.51 + 4.83(90) = 261.19.