child height prediction
2007
Please help me wit this math?
Any problem in mathematics have an idea of how to do that? The following table shows data the average height of children in the school of certain ages. It may contain errors. You were asked to predict the level of 13.5 years and 40 years of age, these data. How high can predict? Comment on the validity of their predictions. Age (years )—————— average height (cm) 7.5 ——————- 127 , 91 8 ———- 130.5 8.5 —— ——– —————————— 133.07 9 —————————— —————- 135.75 9.5 —————— — ————- —— 138.41 10 ——————- —– – 141.38 10.5 —————————– 144.38 11———- – —- —————– ———————- 146.82 11.5 149.44 12———– —————- —— ——- 152.37 12.5 155.12 13 ———- —————————— —— —————– 116.97
When Given a set of data for use in some kind of numerical analysis, The first step is to inspect to see if any additional information can be deduced, and for signs of irregularities or errors. From the heights are given to 0.01 cm (less than the thickness of a sheet of writing paper), one might expect that the values have been carefully and accurately compiled. Unfortunately, the latest figure in the set, for the age of 13, is clearly and obviously wrong, and can only be removed from the data to be analyzed. Furthermore, given the heights of between 10 and 10.5 have same decimal values (.38) and although it may occur by chance, is often an indication that an error in the copying of data has occurred. If you look at the regularity of heights, ie the differences between adjacent values, we find that between these two values is higher than any other in the set, while for the next pair (10.5 and 11 years) is less than any other. This can be interpreted as a clear sign that the height of 10.5 years also contains a transcription error. However, I have decided to keep and analyze the resulting uncertainty of final results at the end of the year. It is also apparent from inspection that the data were more or less linear, and the next step would be to install linear least-squares fit to it. For those who do not have it on their calculators (possibly labeled as linear regression), the procedure is simple. We evaluate the best linear fit y = β α.x + The first step is to calculate the mean value xm, ym of data by the sum values X and Y separately and dividing by the number of valid data points in this case 11 when the two last data was deleted. The best estimate slope α is obtained from α = Σ (XI-XIII). (Yi – m) / (xi – xm) ² where xi, Yi are the individual data points. β is then derived from this and m = mean values + β α.xm got The linear fit was y = 86.7 + 5.468.x The average deviation between the calculated and given the height was 0.1 cm, with no apparent deviation high linearity. The effect of possible clerical error at 10.5 years was too small for ages in or near the range considered. I calculated the height to ages of 13.0 and 13.5 years from the above linear fit, obtaining values of 157.8 and 160.3 cm, respectively, with an estimated uncertainty of ± 0.2 cm. To be asked to extrapolate the adjustment to the age of 40 years is, of course, completely absurd. I have no doubt that gives an estimate fun for height, largely human and growth stops at about 20 years, but the danger is that students may believe that such extrapolation range is acceptable in other circumstances. The message should be that extrapolation is extremely dangerous, should only be undertaken by experts and only a very limited range.
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