Suppose that you run a correlation and find the correlation coefficient is -0.412 and the regression equation is

Question

ˆ
y
=
−
2.3
x
+
37.74
. The centroid of your data was (5.8,24.6).

If the critical value is .708, use the appropriate method to predict the
y
value when
x
is 7.3

Answer 1

To predict the \( y \) value when \( x = 7.3 \) using the given regression equation, you can simply substitute \( x = 7.3 \) into the regression equation:

\[ \hat{y} = -2.3x + 37.74 \]

Substituting \( x = 7.3 \):

\[ \hat{y} = -2.3(7.3) + 37.74 \]

Calculating the terms:

1. \( -2.3 \times 7.3 = -16.79 \)
2. Then, adding 37.74: \[ \hat{y} = -16.79 + 37.74 \] \[ \hat{y} = 20.95 \]

Therefore, the predicted value of \( y \) when \( x = 7.3 \) is 20.95.

If you need to compare the predicted value to a critical value for significance testing or correlation interpretation, you could mention that the correlation coefficient of -0.412 indicates a moderate negative correlation. However, for the prediction computation itself, the critical value is not needed.

Thus, the final prediction is:

Predicted \( y \) when \( x = 7.3 \) is 20.95.