Kiley gathered the data in the table. She found the approximate line of best fit to be y = 1.6x – 4. A 2-column table with 5 rows. The fir

Question

Kiley gathered the data in the table. She found the approximate line of best fit to be y = 1.6x – 4. A 2-column table with 5 rows. The first column is labeled x with entries 0, 2, 3, 5, 6. The second column is labeled y with entries negative 3, negative 1, negative 1, 5, 6. What is the residual value when x = 3? –1.8 –0.2 0.2 1.8

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Abigail 1 week 2021-09-08T22:15:22+00:00 2 Answers 0

Answers ( )

    0
    2021-09-08T22:17:04+00:00

    Answer:

    –1.8

    Step-by-step explanation:

    Given the following table:

    x         y

    0       -3

    2       -1

    3       -1

    5        5

    6        6        

    We are also given y = 1.6x – 4

    Therefore, when x = 3, we have

    Predicted y = 1.6(3) – 4 = 0.8

    Since the observed y = – 1 when x = 3 on the table, the residual value can be estimated as follows:

    Residual value = Observed value of y – Predicted value of y = -1 – 0.8 = – 1.8.

    Therefore, the residual value when x = 3 is –1.8.

    0
    2021-09-08T22:17:11+00:00

    Answer:

    The residual value is -1.8 when x = 3

    Step-by-step explanation:

    We are given the following table

    x     |    y

    0    |   -3

    2    |    -1

    3    |    -1

    5    |    5

    6    |    6    

    Residual value:

    A residual value basically shows the position of a data point with respect to the line of best fit.

    The residual value is calculated as,

    Residual value = Observed value – Predicted value

    Where observed values are already given in the question and the predicted values are calculated by using the equation of  line of best fit.

    y = 1.6x - 4

    When we substitute x = 3 in the above equation then we would get the predicted value.

    y = 1.6x - 4 \\\\y = 1.6(3) - 4 \\\\y = 4.8 - 4 \\\\y = 0.8

    So the predicted value is 0.8

    From the given table, the observed value corresponding to x = 3 is -1

    So the residual value is,

    Residual value = Observed value – Predicted value

    Residual value = -1 – 0.8

    Residual value = -1.8

    Therefore, the residual value is -1.8 when x = 3

    Note: A residual value closer to 0 is desired which means that the regression line best fits the data.

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