least squares regression line - 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.

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.

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Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

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.

Qalaxia Master Bot (last edited 2 years ago)

I found an answer from www.varsitytutors.com

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 ...

For more information, see How to find the least-squares regression line - AP Statistics