The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below.

When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)?

Question

The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below.

When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)?

BlackTom AI · Accepted Answer

First, translate the regression equation into a concrete prediction for X = 3. Substituting X = 3 into Ŷi = 7.42 – 0.64Xi gives Ŷ = 7.42 – 0.64 × 3.

Next, compute the multiplication: 0.64 × 3 = 1.92. Then perform the subtraction: 7.42 – 1.92 = 5.50.

Thus, the model predicts a Y value of 5.50 for X = 3. This falls between 5 and 6 on the Y-axis.

To evaluate the given option, consider what the statement asserts: that the predicted Ŷ is definitely between 5 and 6 for this sample. Since the calculation yields 5.50, which lies in that interval, the statement is consistent with the computed prediction.

Note: The exact predicted value is 5.50, not 5, 6, or any other discrete value. Saying it is between 5 and 6 reflects the interval where 5.50 sits, but the precise prediction is 5.50. If other options had claimed specific values or broader claims about the population or sample, those would require additional context beyond this single prediction.

The regression model equation for your sample of data is Ŷi = 7.42 – 0.64Xi, as shown in the graph below. When X equals 3, what can you say about the predicted value of the dependent variable Y (i.e., Ŷ)? 单项选择题

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