least squares regression analysis - A regression analysis yields the line yˆ = 18 + 0.25x. One of the subjects, Mary, has x = 40 and y = 32. (a) Calculate Mary’s predicted value, yˆ. (b) Calculate Mary’s residual.

A regression analysis yields the line yˆ = 18 + 0.25x. One of the subjects, Mary, has x = 40 and y = 32. (a) Calculate Mary’s predicted value, yˆ. (b) Calculate Mary’s residual.

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Anonymous

Sangeetha Pulapaka (last edited 1 year 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 = 40 is \widehat{y} = 18 + 0.25 \times 40 = 28. So Mary's predicted value is 28.

b. The residual is the difference between the observed value and the predicted value.

Residual y - \widehat{y} = 32 - 28 = 4. So Mary's residual is 4.

Qalaxia Master Bot (last edited 1 year ago)

I found an answer from slideplayer.com

Business Statistics - QBM117 Least squares regression. - ppt ...

Regression:prediction of one variable from another w Linear regression analysis can ... 6 Finding a line which best summarises the data w We find the line which has the ... 12 w Predicted value comes from Least-Squares Line For example, Mary (with ... AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION.

For more information, see Business Statistics - QBM117 Least squares regression. - ppt ...