I'll do problem 1 to get you started. The completed filled out table is shown below in the attached image.
We have x as the input and y as the output. The observed value is the second column, and this is the actual y value we're aiming for. The predicted value is an estimation based on what the linear regression line says. The residual is the error or gap between the observed and predicted.
With that in mind, let's fill out the table. In the first row, we have x = 5 pair up with y = 3. The predicted y value is y = 0.5x = 0.5*5 = 2.5, meaning we'll write "2.5" without quotes in the first blank space of that first row. The residual is
e = error or residual
e = (observed y value) - (predicted y value)
e = (3) - (2.5)
e = 0.5
A positive residual means that the observed y value is larger than the predicted one. The predicted y value is an under-estimate. We'll write "0.5" without quotes underneath "residual" in the first row.
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We'll repeat the same steps for row 2
This time we have x = 10 lead to a predicted y value of y = 0.5*x = 0.5*10 = 5
The residual is
e = (observed) - (predicted) = (4) - (5) = -1
The negative residual tells us the observed value is smaller than the predicted one. The predicted value is an over-estimate.
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For row 3, we have the input x = 15 lead to a predicted y value of y = 7.5 since y = 0.5*x = 0.5*15 = 7.5
The residual is therefore: e = (observed y) - (predicted y) = (9) - (7.5) = 1.5
The nice thing about how this table is set up, is that the observed y values are listed first, then the predicted y values next. This may help you remember how the order of subtraction will go.
The steps for rows 4 through 6 are the same as mentioned earlier, so there's nothing new here.
The completed table for problem 1 is shown below in the attached image.
