Question

Researchers used data on the average reading and math scores on a national test for each state in a nation to develop a regression equation. The rearchers let the explanatory variable x be the average reading score and the response variable y be the average math score. The regression equation is y = 18.7 +0.953x and the r-squared value is 0.924. a. One state had an average reading score of 502. Use the regression equation to predict the average math score for this state. b. This state had an average math score of 503.7. Calculate the residual associated with this state and comment on its value in the context of the problem. c. Does it appear that a state's average reading score is a reliable predictor of its average math score? a. The predicted average math score for this state is (Round to one decimal place as needed.) - b. The residual associated with this state is (Round to one decimal place as needed.) Which of the following statements best interprets this residual? O A. The average math score for this state is greater than the predicted value by the amount of the residual. OB. The average math score for this state is less than the predicted value by the amount of the residual. OC. The residual is the amount the average math score increases for each increase of 1 in the average reading score c. Is average reading score a reliable predictor of average math score? Since the value of is near 1, the average reading score is a predictor of the average math score.

Answer 1

Regression equation :

$\hat{y}$ = 18.7 + 0.953x

a) Given : Average reading score (x) = 502

$\hat{y}$ = 18.7 + ( 0.953*502 )

$\hat{y}$ = 497.1

The predicted average math score is 497.1

b) Residual =  y - $\hat{y}$

y is observed value = 503.7

$\hat{y}$ is predicted value = 497.1

Residual = 503.7 - 497.1

Residual = 6.6

c) Since the value of coefficient of determination ($r^2$) is near 1, the average reading score is a reliable predictor of the average math score.