Linear Regression: calculate the residual for an observation

[bluewater]

Equation: Y = 25 + -1x. If the predicted value of, Y, for an observation is 3, calculate the residual for an observation where the observed value, Y, is equal to 8.

I think I am getting confused because of the predicted value and observed value? I thought it would just be substituting Y=8 and solve for x, but where does the 3 go into or is that extra information? Thank you in advance

 

[Ishuda]

Equation: Y = 25 + -1x. If the predicted value of, Y, for an observation is 3, calculate the residual for an observation where the observed value, Y, is equal to 8.

I think I am getting confused because of the predicted value and observed value? I thought it would just be substituting Y=8 and solve for x, but where does the 3 go into or is that extra information? Thank you in advance

I assume that the
Y = 25 - x
is the 'fit to the data' where you have a set of observed values {y_i} at points (x_i}, i.e. ordered pairs of data (x_i,y_i). After obtaining the fit, you would have a set of predicted values {Y_i | Y_i = 25 - x_i}. So, for some given x_i you have an observed value y_i and a predicted value Y_i. The difference between the observed and predicted value is called the residual (error).

 

[bluewater]

I assume that the
Y = 25 - x
is the 'fit to the data' where you have a set of observed values {y_i} at points (x_i}, i.e. ordered pairs of data (x_i,y_i). After obtaining the fit, you would have a set of predicted values {Y_i | Y_i = 25 - x_i}. So, for some given x_i you have an observed value y_i and a predicted value Y_i. The difference between the observed and predicted value is called the residual (error).

So do the difference of 8-3= 5 and do subsitute for Y and solve for X is the residual?

 

[bluewater]

I assume that the
Y = 25 - x
is the 'fit to the data' where you have a set of observed values {y_i} at points (x_i}, i.e. ordered pairs of data (x_i,y_i). After obtaining the fit, you would have a set of predicted values {Y_i | Y_i = 25 - x_i}. So, for some given x_i you have an observed value y_i and a predicted value Y_i. The difference between the observed and predicted value is called the residual (error).

okay I found the formula as
e=Y-(Y^hat)
e=8-3= 5. Is 5 just the answer or do I just plug it back into the regression line and solve for Y?