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The average height and weight of a group of students turned out to be 5 ft 6 inches and 65 kilograms respectively. The correlation between heights and weights was found to be 0.6. Using the regression equation for predicting weight from height, the estimated weight of a 6 ft tall student was calculated to be 80 kilograms. Predict the height of a student whose weight is 60 kilograms

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please give me full solution of it. I can't solve it – Argha Jul 16 '12 at 6:08
Think about what the equation of the line of best fit (for weight in terms of height) might be. – user22805 Jul 16 '12 at 7:14
Try the model $h(w) = h_0 + \alpha w$. Figure out what $h_0$ and $\alpha$ must be. – copper.hat Jul 16 '12 at 8:23
up vote 0 down vote accepted

The fitted model can be used to predict height from weight using h= a + bw where a and b are the fitted regression coefficients (intercept and slope respectively).

Now if h=a + bw (h-a)/b = w. Use this equation to solve for w given h.

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the correlation between heights and weights is 0.6. then why we assume the linear function – Argha Jul 17 '12 at 10:06
Linear regression is historically the classical approach first applied by Galton (late 19th cwntury). If you view the correlation between height and weight to be weak enough that a nonlinear relationship between height and weight might increase the correlation you should try it. But first look at a scatterplot and the residuals. It is possible that the scatter plot will show that the linear function best describes how h and w are related and the "low" correlation is strictly due to a large variance for the residuals. – Michael Chernick Jul 17 '12 at 10:47

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