Final answer:
The predicted value for the regression equation, with b = 10 and b1 = 2, when the observed value of x is 9, is calculated to be 28. This prediction is within the observed range of data, so it is considered reliable, unlike predictions far outside the observed x values.
Step-by-step explanation:
To find the predicted value for a regression equation where b is the constant term and b1 is the coefficient of the independent variable (slope of the line), one needs to use the general linear equation formula:
y = b + b1x
In this case, we have b = 10, b1 = 2, and the observed value of x = 9. Plugging these values into the equation, we get:
y = 10 + (2 × 9)
y = 10 + 18
y = 28
The predicted value when the observed value of x is 9, is therefore 28.
It's important to note that predictions using regression equations are best made within the range of observed data values. If we were to use an x value that is significantly outside this range, like x = 90, there could be a large amount of prediction error. In such cases, the predicted y value may not be reliable, as is demonstrated by the example in the reference where an x value of 90 yields a y value that should not be trusted when considering the range of the observed x values in the data.