A regression analysis yields the line yˆ = 32 + 0.4x. One of the subjects, Racheal, has x = 60 and y = 52. (a) Calculate Racheal’s predicted value, yˆ. (b) Calculate Racheal’s residual.

The predicted value can be found by the least squares regression equation of a line, which is \widehat{y} = a+bx where x is the independent/ explanatory variable which lies on the x-axis, y is the dependent/response or the observed variable which lies on the y-axis, and \widehat{y} is the predicted value. Recall that a is the y-intercept and b is the slope of the line.
a. The predicted value when x = 60 is \widehat{y} = 32 + 0.4 \times 60 = 56.
b. The residual is the difference between the observed value and the predicted value.
Residual y - \widehat{y} = 52 - 60 = -4.
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How to find the least-squares regression line - AP Statistics
Regression tests seek to determine one variable's ability to predict another variable. In this analysis, one variable is dependent (the one predicted), and the other is ...
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