Question

The IQ scores and English test scores of fifth grade students is given by the regression line 9 = -26.7 +0.9346s, where y is the predicted English score and s is the
IQ score. An actual English test score for a student is 65.7 with an IQ of 96.

Find and interpret the residual. (2 points)


-2.68; The regression line underpredicts the student's English test score.

2.68; The regression line overpredicts the student's English test score.

-2.68; The regression line overpredicts the student's English test score.

30.3; The regression line overpredicts the student's English test score.

2.68; The regression line underpredicts the student's English test score.

Answer 1

Answer:

Option E) 2.68; The regression line under predicts the student's English test score.

Step-by-step explanation:

We are given the following information:

The IQ scores and English test scores of fifth grade students is given by the regression line

$y = -26.7 +0.9346s$

where y is the predicted English score and s is the IQ score.

Here English score is the predicted variable that is the dependent variable and the IQ score is the independent variable and plays the role of predictor.

An actual English test score for a student is 65.7 with an IQ of 96. We have to predict the English score with the help of regression equation.

Predicted or interpreted English score =

$y = -26.7 +0.9346(96)= 63.0216$

Thus, predicted English score is 63.0216.

Observed value of English score at IQ 96 is 65.7

Residual = Observed value - Predicted value

= $65.7 - 63.0216 = 2.6784 \approx 2.68$

Since the predicted value is less than the original or observed value we can say that the regression line under predict the English score.

Option E) 2.68; The regression line under predicts the student's English test score.