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You run a regression analysis on a bivariate set of data \((n = 73)\). With \(\bar{x} = 78.4\) and \(\bar{y} = 46.6\), you obtain the regression equation \(y = 3.923x - 7.076\) with a correlation coefficient of \(r = 0.725\).

You want to predict the value (on average) for the response variable when the explanatory variable is 140.

What is the predicted response value?

\(y =\) (Report the answer accurate to one decimal place.)

A. 85.3
B. 91.7
C. 92.7
D. 98.1

Answer :

Final answer:

By substituting x with 140 in the regression equation (y = 3.923x - 7.076), the predicted response value is calculated to be 542.1 (rounded to one decimal place); none of the provided options match this result.

Explanation:

To predict the response value using the regression equation (y = 3.923x - 7.076) when the explanatory variable is 140, we substitute x with 140:

y = 3.923(140) - 7.076

y = 549.22 - 7.076

y = 542.144

Rounded to one decimal place, the predicted response value is 542.1. Therefore, option (c) 92.7 is not correct. Based on the calculations, there seems to be a misunderstanding or typo in the question since none of the options (a) 85.3, (b) 91.7, (c) 92.7, (d) 98.1 match the calculated result of 542.1.

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