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Shanti wrote the predicted values for a data set using the line of best fit y = 2.55x – 3.15. She computed two of the residual values. What are the values of a and b? a = 0.4 and b = –0.15 a = –0.4 and b = 0.15 a = 8.6 and b = 14.25 a = –8.6 and b = –14.25

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nobillionaireNobley
Residual value is the difference between the observed value of the dependent variable (y) and the predicted value (ŷ) in a data set.

i.e. Residual value = given value - predicted value

From the table, the residual value corresponding to a has 4.1 as the given value and 4.5 as the predicted value.
Therefore, a = 4.1 - 4.5 = -0.4

Similarly, the residual value corresponding to b has 7.2 as the given value and 7.05 as the predicted value.
Therefore, b = 7.2 - 7.05 = 0.15

Therefore, a = -0.4 and b = 0.15

You can use the fact that residual is calculated by measuring the difference between actual value and predicted value.

The residual value and the predicted value for the given set of values is given by

Option B:  a = –0.4 and b = 0.15

How to find the residual value for a given input output pair?

Suppose the given input output pair be (x,y) (actual data point)

Then suppose the prediction be y' from the line of best fit for that input x.

Then the residual value will be calculated for that point as:

Residual value = Actual value - Predicted value

Residual = y - y'

How to find the residuals?

The two outputs missing(not given in question but had to be given) for which the residual values have to be found are

[tex]y_1 = 4.1, y_1' = 4.5\\y_2 = 7.2, y_2' = 7.05[/tex]

Thus, we have the residuals as:

[tex]a = y_1 - y_1' = 4.1 - 4.5 = -0.4\\\\b = y_2 - y_2' = 7.2 - 7.05 = 0.15[/tex]

Thus,

The residual values needed are given by

Option B:  a = –0.4 and b = 0.15

Learn more about residual values here:

https://brainly.com/question/3870996

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